Document [original]

Contribution to Load Alleviation in Aircraft

Pre-design and Its Influence on Structural Mass

and Fatigue

vorgelegt von

Vega Handojo, M.Sc.

ORCID iD 0000-0001-6030-2383

an der Fakultät V – Verkehrs- und Maschinensysteme

der Technischen Universität Berlin

zur Erlangung des akademischen Grads

Doktor der Ingenieurwissenschaften

- Dr. Ing. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr.-Ing. Henning Jürgen Meyer

Gutachter: Prof. Dr.-Ing. Robert Luckner

Gutachter: Prof. Dr.-Ing. Wolf-Reiner Krüger

Gutachter: Dr.-Ing. Thomas Klimmek

Tag der wissenschaftlichen Aussprache: 04. September 2020

Berlin 2020

Abstract

This thesis develops and demonstrates an aircraft pre-design process for loads analysis, load

alleviation, structural optimization and fatigue analysis. It is shown that the consideration of

maneuver and gust load alleviation in early design stages is a promising concept to reduce

wing bending moments, structural mass and extend the fatigue life. The reference aircraft

considered are two mid-range configurations: one with a backward and another one with a

forward swept wing, respectively.

In the loads analysis, quasi-steady maneuvers and dynamic 1-cos gusts are considered. For the

load alleviation during maneuvers, the ailerons are deflected symmetrically with pre-

calculated amplitudes. For the gust load alleviation, a feed-forward, proportional control

algorithm is set up and the main input for the controller is the gust angle of attack. Analogous

to maneuver load alleviation, the ailerons are deflected symmetrically.

With the post-processed loads from the simulations, the structure of the wing and horizontal

tailplane (HTP) is optimized toward mass minimization. The constraints considered are

material strength, buckling stability and static aeroelastic requirements. The steps loads

analysis and structure optimization of the developed design process are conducted iteratively

until the wing box mass converges. For the reference aircraft, the load alleviation yields a

reduction of wing box mass by 2.8% and 6.1%, respectively.

Beyond that, a qualitative fatigue analysis is carried out to compare the fatigue behaviors of

the active and passive aircraft (with and without load alleviation). In this step, loads due to

continuous turbulence and ground-air-ground cycles are considered. For the reference

missions, the fatigue life of the active aircraft is improved by 28% and 12% respectively, on

top of the mass benefit. However, these numbers of fatigue life improvement are only valid

for the considered loads and selected positions. If more loading conditions or structure

elements are taken into account, the fatigue benefit may vary.

As a conclusion, the proposed process can serve to gain an insight into the benefits of load

alleviation for a given aircraft in the pre-design phase, before it advances to the next design

stage.

Keywords: load alleviation, loads analysis, structural optimization, fatigue analysis,

aircraft pre-design, feed-forward control

Kurzfassung

In dieser Arbeit wird ein Prozess zur Lastanalyse, Lastabminderung, Strukturoptimierung und

Ermüdungsanalyse im Flugzeugvorentwurf entwickelt und demonstriert. Dabei wird gezeigt,

dass bei Berücksichtigung von Manöver- und Böenlastabminderung in den frühen Phasen des

Flugzeugentwurfs die Biegemomente am Flügel und die Strukturmasse reduziert, und die

Lebensdauer der Struktur verlängert werden kann. Die für die Untersuchung verwendeten

Referenzflugzeuge sind zwei Mittelstreckenkonfigurationen, jeweils eine mit einem rückwärts

und eine mit einem vorwärts gepfeilten Flügel.

In der Lastanalyse werden quasistatische Manöver und dynamische 1-cos-Böen

berücksichtigt. Die Lastabminderung bei Manövern geschieht durch symmetrisch

ausgeschlagene Querruder. Für die Böenlastabminderung wird ein proportionaler Vorsteuer-

algorithmus entwickelt, dabei stellt der Böenanstellwinkel die Eingangsgröße für die

Vorsteuerung dar. Analog zur Manöverlastabminderung werden hierbei die Querruder

symmetrisch ausgeschlagen.

Mit ausgewählten Lasten aus der Lastanalyse wird die Struktur des Flügels und des

Höhenleitwerks hinsichtlich minimaler Strukturmasse optimiert. Die in der Struktur-

optimierung berücksichtigten Randbedingungen sind Zugfestigkeit des Materials,

Beulstabilität und statische aeroelastische Anforderungen. Die Lastanalyse und

Strukturoptimierung im entwickelten Entwurfsprozess wird iterativ durchgeführt, bis die

Flügelmasse konvergiert. Bei den Referenzflugzeugen ergeben sich Masseneinsparungen für

den Flügelkasten von jeweils 2,8% bzw. 6,1%.

Darüber hinaus wird eine Ermüdungsanalyse durchgeführt, um das Ermüdungsverhalten der

aktiven und passiven Flugzeuge (mit und ohne Lastabminderung) zu vergleichen. Dabei

werden Lasten aufgrund von kontinuierlicher Turbulenz und von Boden-Luft-Boden-Zyklen

berücksichtigt. Für die ausgewählten Referenzmissionen erhöht sich die Lebensdauer der

Flugzeuge mit aktiver Lastabminderung jeweils um 28% bzw. 12%, zusätzlich zu der

Masseneinsparung. Die Werte gelten jedoch nur für die berücksichtigten Lastkonditionen und

Positionen. Falls weitere Lastszenarien oder Strukturelemente berücksichtigt werden, kann die

Erhöhung der Lebensdauer variieren.

Insgesamt ermöglicht der entwickelte Vorentwurfsprozess, den Nutzen der Lastabminderung

bei einem gegebenen Flugzeug zu berücksichtigen, bevor dieses in die nächste Entwurfsphase

voranschreitet.

Stichwörter: Lastabminderung, Lastanalyse, Strukturoptimierung, Ermüdungsanalyse,

Flugzeugvorentwurf, Vorsteuerung

iii

Acknowledgments

Since my Bachelor’s studies, I have been interested in the multidisciplinary world of aircraft

design, and I am grateful to have the opportunity to do research on the topic. This thesis

evolved during my employment as research scientist at DLR German Aerospace Center,

Institute of Aeroelasticity in Göttingen, Germany.

My gratitude goes to Prof. Dr. Robert Luckner for supervising, supporting the thesis, for the

time and the fruitful discussions. I would like to thank Prof. Dr. Wolf Krüger for giving me

the freedom and opportunity to write this thesis, for the supervision and support for its entire

duration. Moreover, I would like to thank Dr. Thomas Klimmek for introducing me to

aeroelastic modeling and design, for providing the baseline models of the reference aircraft,

for supervising and supporting this thesis.

Many thanks go to my colleagues (and former colleagues) at the institute who supported my

work in various ways. Dr. Markus Ritter introduced me to DLM and its applications, Matthias

Schulze supported me in learning about gust loads in the beginning of my time at DLR.

Dr.BArne Voß and I worked on our theses in roughly the same period and our topics have

similarities, so that we could motivate each other and have technical discussions. Dr. Gabriel

Pinho Chiozzotto inspired me with his expertise in aircraft conceptual design. I would also

like to thank Dr. David Quero for the helpful discussions, both regarding technical topics or

PhD in general. Furthermore, I would like to thank Yasser Meddaikar for the fruitful

discussions, among others regarding composite materials. Many thanks go to Kjell Bramsiepe

and Kautuk Sinha for their support and help in the projects. My thanks go to the whole

institute as well, I have been enjoying my time at DLR and it is a pleasure to have colleagues

to share after-work evenings, go on holidays and play music with.

I would also like to thank Dr. Roeland De Breuker for supervising and motivating me during

my research stay in Delft. My thanks also go to Paul Lancelot for the pleasant and successful

collaboration, and to all colleagues in Delft for the hospitality.

Moreover, I would like to thank my schoolmates: Philipp, Máté, Martin and Daniel for their

morale support. My gratitude goes to my beloved Citra for her abundant support, patience and

for always being there for me. Last but not least, I would like to express my gratitude to my

parents who have made all this possible, for always supporting, encouraging me and for

teaching me to stay curious and persistent.

Göttingen, November 2020

Table of content
Table of content
Abstract.........................................................................................................................i
Kurzfassung................................................................................................................iii
Acknowledgments.......................................................................................................v
Table of content.........................................................................................................vii
List of figures..............................................................................................................ix
List of tables...............................................................................................................xi
Nomenclature............................................................................................................xiii
Introduction..............................................................................................................1
1  Motivation............................................................................................................................1
2  State of the art......................................................................................................................2
3  Derivation of contribution....................................................................................................5
4  Dissertation layout...............................................................................................................7
Reference aircraft and their aeroservoelastic modeling.....................................9
1  Reference aircraft.................................................................................................................9
2  Structural and mass models................................................................................................13
3  Aerodynamic models..........................................................................................................16
4  Structural and aerodynamic modeling of control surfaces.................................................19
5  Model adaptation – ALLEGRA configuration...................................................................20
Design process of loads analysis and structural optimization........................25
1  Maneuver simulation..........................................................................................................25
2  Dynamic gust simulation...................................................................................................26
3  Loads post-processing for structural optimization.............................................................28
4  Structural optimization.......................................................................................................30
5  Aeroelastic constraints.......................................................................................................31
6  Subsonic flutter check........................................................................................................33
7  Workflow of the design process.........................................................................................34
Modeling of load alleviation systems..................................................................37
1  Objectives and restrictions.................................................................................................37
2  Maneuver load alleviation concept....................................................................................38
3  Gust load alleviation concept.............................................................................................40
Methodology of fatigue analysis.........................................................................47
1  Reference flight parameters...............................................................................................47
2  Reference atmospheric turbulence.....................................................................................48
3  Aircraft responses in turbulence analysis...........................................................................50
4  Rainflow-counting.............................................................................................................52
5  Ground-air-ground cycle....................................................................................................55
6  Fatigue damage accumulation............................................................................................56
vii

Table of content
Loads, optimization and fatigue results of D150 configuration.......................57
1  Parameter space for loads analysis and structural optimization.........................................57
1.1  Mass configurations...................................................................................................57
1.2  Flight conditions within the design envelope.............................................................59
1.3  Gust load conditions...................................................................................................60
1.4  Maneuver load conditions..........................................................................................62
1.5  Overview of the optimization task.............................................................................62
1.6  Constraints in the structural optimization..................................................................63
2  Comparison of design loads, structural masses and aeroelastic parameters......................64
2.1  Design loads...............................................................................................................64
2.2  Structural masses........................................................................................................67
2.3  Aeroelastic parameters...............................................................................................70
3  Turbulence loads and fatigue analysis...............................................................................73
3.1  Reference parameters.................................................................................................73
3.2  Cut load and stress collectives....................................................................................75
3.3  Fatigue damage accumulation....................................................................................78
4  Further results....................................................................................................................80
Loads, optimization and fatigue results of ALLEGRA configuration..............83
1  Parameter space for loads analysis and structural optimization.........................................83
1.1  Mass configurations...................................................................................................83
1.2  Flight conditions within the design envelope.............................................................84
1.3  Gust and maneuver load conditions...........................................................................85
1.4  Overview of the optimization task.............................................................................85
1.5  Constraints in the structural optimization..................................................................86
2  Comparison of design loads, structural masses and aeroelastic parameters......................87
2.1  Design loads...............................................................................................................87
2.2  Structural masses........................................................................................................90
2.3  Aeroelastic parameters...............................................................................................93
3  Turbulence loads and fatigue analysis...............................................................................95
3.1  Reference parameters.................................................................................................96
3.2  Cut load and strain collectives....................................................................................97
3.3  Fatigue damage accumulation..................................................................................100
4  Further results..................................................................................................................103
Investigations of load alleviation variations and practical aspects..............105
1  Fixed MLA deflection......................................................................................................105
2  Variation of GLA delay time............................................................................................106
3  Retrofit of passive aircraft with load alleviation..............................................................108
4  Load factor threshold for MLA activation.......................................................................111
Evaluations, conclusions and outlook..............................................................113
1  Evaluations.......................................................................................................................113
2  Conclusions......................................................................................................................115
3  Discussion of contribution...............................................................................................116
4  Outlook.............................................................................................................................117
Bibliography.............................................................................................................119
Appendix..................................................................................................................127
viii

List of figures

Figure 2.1. Geometry of the D150 configuration.....................................................................10

Figure 2.2. Geometry of the ALLEGRA configuration...........................................................12

Figure 2.3. Jig shape twist distribution of the ALLEGRA configuration................................12

Figure 2.4. Full FE model of the D150 configuration.............................................................13

Figure 2.5. Fuel tank division on the D150 configuration.......................................................14

Figure 2.6. Desirable payload locations on the D150 configuration.......................................14

Figure 2.7. View into the wing box of the ALLEGRA configuration......................................15

Figure 2.8. Condensed stiffness and mass model of the D150 configuration..........................15

Figure 2.9. Lifting surface discretization in DLM...................................................................16

Figure 2.10. Aerodynamic model of the D150 configuration with slender body element.......18

Figure 2.11. Aerodynamic model of the D150 configuration with interference body.............18

Figure 2.12. Structural modeling of an aileron and its hinge...................................................20

Figure 2.13. Principal sketch of a control surface hinge..........................................................20

Figure 2.14. Wing twist due to bending-torsion-coupling.......................................................21

Figure 2.15. Wingtip position relative to MAC.......................................................................21

Figure 2.16. Rotation of skin laminate orientation..................................................................22

Figure 2.17. Rotation of laminate orientation and their effects on the trim.............................23

Figure 3.1. Monitoring stations on the D150 configuration....................................................28

Figure 3.2. Extracted snapshots from a gust encounter...........................................................28

Figure 3.3. Exemplary superposition of load factors during gust encounter...........................29

Figure 3.4. 2D envelope surrounding gust and maneuver loads..............................................29

Figure 3.5. Structural optimization flowchart..........................................................................31

Figure 3.6. Exemplary flight envelope for aeroelastic constraints...........................................31

Figure 3.7. Workflow of loads analysis and optimization chain..............................................35

Figure 4.1. Wing root bending moment response to elevator deflection.................................38

Figure 4.2. Change of spanwise lift distribution with MLA during a pull-up maneuver.........38

Figure 4.3. Block diagram of feed-forward GLA....................................................................41

Figure 4.4. Illustration of angle of attack and aileron deflection.............................................41

Figure 4.5. Visualization of the reference positions xwing on D150 (a) and ALLEGRA (b)..43

Figure 4.6. Comparison between actual ξ and commanded aileron deflections ξc..................44

Figure 4.7. Sub-workflow of the GLA integration in the 1-cos gust simulation.....................45

Figure 5.1. Exemplary von Kármán power spectral density....................................................48

Figure 5.2. Probability of exceedance for various turbulence RMS [96]................................49

Figure 5.3. Sub-workflow of aircraft response calculation in continuous turbulence.............52

Figure 5.4. Exemplary time history reduced to its peaks.........................................................52

Figure 5.5. Raindrops emerging on the left (a) and right (b) side of the pagoda roof.............53

Figure 5.6. Rainflow continuation on the left (a) and right (b) side of the pagoda roof..........54

Figure 5.7. Visualization of load cycle generation in rainflow-counting algorithm................54

Figure 5.8. Stress cycles during an exemplary flight mission.................................................55

List of figures

Figure 6.1. Mass and balance diagram of considered configurations – D150.........................58

Figure 6.2. Flight conditions in the design envelope – D150..................................................60

Figure 6.3. Overview of the 1-cos gust profiles.......................................................................61

Figure 6.4. Considered maneuver cases in an exemplary V-n diagram...................................62

Figure 6.5. Wing bending moment of passive D150................................................................65

Figure 6.6. Wing bending moment of active D150..................................................................65

Figure 6.7. Selected cut load monitoring stations on D150.....................................................66

Figure 6.8. 2D load envelope comparison on D150................................................................66

Figure 6.9. Wing box mass trend in the loads and optimization process of D150...................68

Figure 6.10. RMS of material thickness change of D150 wing box........................................68

Figure 6.11. Wing material thickness distribution of D150.....................................................69

Figure 6.12. HTP material thickness distribution of D150......................................................70

Figure 6.13. Design envelope for aeroelastic stability of D150...............................................70

Figure 6.14. Curves of the flutter point of D150.....................................................................72

Figure 6.15. Dominant Eigenmode involved at the flutter speed of D150..............................72

Figure 6.16. Visualization of the reference flight mission of D150.........................................74

Figure 6.17. Selected structure elements for strain response of D150.....................................75

Figure 6.18. Cut load collectives during the climb phase of D150..........................................76

Figure 6.19. Stress and hinge moment collectives during the climb phase of D150...............77

Figure 6.20. S-N curve for the turbulence analysis of D150...................................................79

Figure 6.21. Illustration of stress amplification near a hole.....................................................81

Figure 7.1. Mass and balance diagram of considered configurations – ALLEGRA................84

Figure 7.2. Flight conditions in the design envelope – ALLEGRA.........................................85

Figure 7.3. Wing bending moment of passive ALLEGRA......................................................88

Figure 7.4. Wing bending moment of active ALLEGRA........................................................88

Figure 7.5. Selected cut load monitoring stations on ALLEGRA...........................................88

Figure 7.6. 2D load envelope comparison on ALLEGRA.......................................................89

Figure 7.7. Wing box mass trend in the loads and optimization process of ALLEGRA.........91

Figure 7.8. RMS of material thickness change of ALLEGRA wing box.................................91

Figure 7.9. Wing material thickness distribution of ALLEGRA.............................................92

Figure 7.10. HTP material thickness distribution of ALLEGRA.............................................92

Figure 7.11. Design envelope for aeroelastic stability of ALLEGRA.....................................93

Figure 7.12. Curves of the flutter point of ALLEGRA............................................................95

Figure 7.13. Dominant Eigenmode involved at the flutter speed of ALLEGRA.....................95

Figure 7.14. Visualization of the reference flight mission of ALLEGRA...............................96

Figure 7.15. Selected structure elements for strain response of ALLEGRA...........................98

Figure 7.16. Cut load collectives during the climb phase of ALLEGRA................................99

Figure 7.17. Strain and hinge moment collectives during the climb phase of ALLEGRA...100

Figure 7.18. S-N curve for the turbulence analysis of ALLEGRA........................................102

Figure 8.1. 2D load envelope on D150 with variable (a) and fixed (b) deflection................106

Figure 8.2. Incremental gust load envelope with variation of GLA buffer – D150...............107

Figure 8.3. Incremental gust load envelope with variation of GLA buffer – ALLEGRA.....107

Figure 8.4. Stress and hinge moment collectives during the climb phase of D150...............109

Figure 8.5. Strain and hinge moment collectives during the climb phase of ALLEGRA......110

List of figures

Figure A-1. 2D gust and maneuver load envelopes of active D150 (a) and active

ALLEGRAB(b)......................................................................................................................127

Figure A-2. Flutter curves of the passive (a) and active (b) D150 configuration..................128

Figure A-3. Symmetric (a) and antisymmetric (b) HTP torsion mode of the D150

configuration........................................................................................................................129

Figure A-4. Flutter curves of the passive(a) and active (b) ALLEGRA configuration..........130

Figure A-5. VTP bending mode of the ALLEGRA configuration.........................................131

List of tables

Table 1.1. Positioning of the contribution of this thesis..............................................................7

Table 2.1. Key parameters of the D150 configuration..............................................................10

Table 2.2. Material properties of D150 wing structure.............................................................10

Table 2.3. Key parameters of the ALLEGRA configuration.....................................................11

Table 2.4. Material properties of carbon-epoxy IM6 composite [44].......................................12

Table 2.5: Ply angle distributions on ALLEGRA wing structure..............................................13

Table 2.6: Overview of the number of elements of the full FE models....................................15

Table 2.7. Reference trim condition for laminate rotation study..............................................22

Table 5.1. Parameters of the climb condition............................................................................56

Table 6.1. Overview of the mass configurations – D150..........................................................58

Table 6.2. Overview of the flight conditions – D150................................................................59

Table 6.3. Overview of the gust gradients.................................................................................61

Table 6.4. Parameters of aileron effectiveness calculation on D150........................................70

Table 6.5. Aileron effectiveness values of D150.......................................................................71

Table 6.6. Parameters of flutter calculation on D150................................................................71

Table 6.7. Reference flight route and masses for D150............................................................73

Table 6.8. Reference parameters for each flight phase – D150................................................74

Table 6.9. Reference parameters for the ground-air-ground cycle – D150...............................74

Table 6.10. Turbulence fatigue damage per flight on D150......................................................79

Table 6.11. Fatigue damage per ground-air-ground cycle on D150..........................................79

Table 6.12. Total fatigue damage per flight on D150................................................................80

Table 6.13. Engine lateral acceleration RMS on D150.............................................................82

Table 7.1. Overview of the mass configurations – ALLEGRA................................................84

Table 7.2. Overview of the flight conditions – ALLEGRA......................................................85

Table 7.3. Parameters of divergence calculation on ALLEGRA..............................................93

Table 7.4. Divergence dynamic pressures of ALLEGRA.........................................................94

Table 7.5. Parameters of flutter calculation on ALLEGRA......................................................94

Table 7.6. Reference flight route for ALLEGRA......................................................................96

Table 7.7. Reference parameters for each flight phase – ALLEGRA.......................................97

Table 7.8. Reference parameters for the ground-air-ground cycle – ALLEGRA.....................97

Table 7.9. Turbulence fatigue damage per flight on ALLEGRA............................................102

Table 7.10. Fatigue damage per ground-air-ground cycle on ALLEGRA..............................102

Table 7.11. Total fatigue damage per flight on ALLEGRA....................................................103

List of tables

Table 8.1. Fatigue damage overview of retrofitted D150.......................................................109

Table 8.2. Fatigue damage overview of retrofitted ALLEGRA..............................................111

Table 8.3. Fatigue damage on active D150 with MLA threshold...........................................112

Table 8.4. Fatigue damage on active ALLEGRA with MLA threshold..................................112

Table A-1. Selected modes of the D150 configuration at operating empty mass...................127

Table A-2. Selected modes of the ALLEGRA configuration at operating empty mass..........127

Table A-3. Turbulence fatigue damage per hour on D150......................................................132

Table A-4. Turbulence fatigue damage per hour on ALLEGRA............................................132

xii

Nomenclature

Abbreviations

AIC : aerodynamic influence coefficient matrix

ALLEGRA : DLR project, AeroeLastic stability and Loads prediction for Enhanced GReen

Aircraft

ATC : air traffic control

CAS : calibrated airspeed

CG : center of gravity

CS : coordinate system

CPACS : Common Parametric Aircraft Configuration Schema

CS25 : Certification Specifications and Acceptable Means of Compliance for Large

Aeroplanes

DLM : doublet lattice method

DLR : German Aerospace Center

EAS : equivalent airspeed

EFCS : electronic flight control system

FCC : flight control computer

FE : finite element

FL : flight level

GLA : gust load alleviation

HTP : horizontal tailplane

iLOADS : DLR project on integrated loads analysis

LamAiR : DLR project, Laminar Aircraft Research

LIDAR : light detection and ranging

LRA : load reference axis

MAC : mean aerodynamic chord

MDO : multidisciplinary optimization

ModGen : Model Generator, an in-house program to generate Nastran simulation models

MLA : maneuver load alleviation

MLM : maximum landing mass

MONA : ModGen-Nastran, a process to generate and optimize FE models

MSC.Nastran : commercial FE program

MTOM : maximum take-off mass

MZFM : maximum zero fuel mass

OEM : operating empty mass

PSD : power spectral density

RAM : random-access memory

RMS : root mean square

SOL101 : static loads analysis in MSC.Nastran

xiii

Nomenclature

SOL144 : quasi-steady aeroelastic analysis in MSC.Nastran

SOL145 : flutter analysis in MSC.Nastran

SOL146 : dynamic aeroelastic analysis in MSC.Nastran

SOL200 : structural optimization in MSC.Nastran

TAS : true airspeed

TF : transfer function

VAMP : DLR project, Virtual Aircraft Multidisciplinary Analysis and Design

Processes

VTP : vertical tailplane

Latin alphabet

: aerodynamic influence coefficient matrix in general

: damping matrix in general

: buckling field width

: constants in general

: mean aerodynamic chord

: lift coefficient

: roll moment coefficient due to aileron deflection

: pressure coefficient

: differentiation matrix in general

: fatigue damage

: artificial damping

: tensile modulus

: aerodynamic force in general

: gust alleviation factor

: shear force

: safety factor

: frequency

: objective function in structural optimization

: coupling matrix in general

: gravitational acceleration

: optimization constraints

: gust gradient

: imaginary number

: structural stiffness matrix in general

: reduced frequency

: GLA amplification factor in the aerodynamic coordinate system

: compressive buckling coefficient

: gain of gust load alleviation

: shear buckling coefficient

: turbulence scale

: mass matrix in general

: bending moment

: torsion moment, hinge moment

: Mach number

xiv

Nomenclature

: maximum take-off mass

: number of cycles to failure in general

: number of elements in general, S-N curve exponent in general

: vertical load factor

: force on structural nodes in general

: roll velocity

: flutter eigenvalue

: aerodynamic matrix in general

: pitch velocity

: dynamic pressure

: mass ratio in general

: yaw velocity

: stress or strain ratio

: distance between aerodynamic sensor and aircraft center of gravity

: root mean square in general

: wing reference area

: transfer function in general

: material thickness

: delay time

: gust speed in general

: displacement in general

: design maneuvering speed

: design cruise speed – not necessarily equal with the economic cruise speed

: design dive speed

: maximum operating speed

: stall speed

: true airspeed

: downwash in general

: vertical wind speed

: aircraft response quantity in general, longitudinal coordinate

: distance penetrated into gust

: design variable

: longitudinal position of the wing

: lateral displacement, lateral coordinate

: analysis variable

: altitude

: vertical displacement

Greek alphabet

: angle of attack

: slip angle

: twist angle

: strain in general

: elevator or control surface deflection in general

: aircraft pitch angle

: potential doublet strength

Nomenclature

: Poisson ratio

: aileron deflection

: circle constant

: air density

: stress in general

: shear stress

: turbulence power spectral density

: phase angle, sweep angle

: circular frequency

Notation conventions

: matrix

: vector

: first derivative

: second derivative

xvi

1 Introduction

1.1 Motivation

The design of new aircraft is a long, complex multidisciplinary process. It has to comply with

a variety of requirements, among others regarding safety and performance. At the same time,

manufacturers strive to minimize the aircraft’s development risk and optimize the production

as well as operational cost, where each of those factors is already a challenge itself.

To minimize the aircraft’s development risk and time, it is advisable to shift as many analyses

and calculations as possible to earlier stages of the design. This is due to the fact that the

aircraft becomes more complex with every the design stage, so that a late consideration and

implementation of functions/technologies is more expensive and time consuming.

One solution to lower the aircraft’s operational cost is by minimizing the fuel consumption.

This can be achieved e.g. by reducing the structural mass. At the same time, the structural

mass directly depends on the design loads. Hence, structural mass can be reduced by

alleviating the design loads. One possible method is by using active control to redistribute lift

during maneuvers or reduce lift increments induced by gusts or turbulence. Nowadays, active

load alleviation is implemented on commercial transport aircraft as a part of the electronic

flight control system (EFCS). However, before the load alleviation is well adjusted to the

aircraft, it has to be modeled in the design process first – the earlier the better.

Depending on the stage of the aircraft design process, the suitable modeling depth of the load

alleviation also varies. In the conceptual stage, empirical regression formulae – including

technology factors for load alleviation – are often used since information about the aircraft is

insufficient. In the preliminary design stage, the aircraft configuration is frozen and more

details about the aircraft are known. In this case, a physics-based modeling of load alleviation

systems is seen as appropriate since it can be efficiently integrated into the physics-based

loads analysis as shown by this thesis. With a physics-based method, there are more degrees

of freedom in setting the load alleviation parameters to maximize the load reduction.

However, the algorithm should be computer-time efficient so that the load calculations, which

can comprise hundreds or more load cases, are considerably fast. These large number of load

cases argue against the use of high-fidelity methods such as computational fluid dynamics

(CFD). Besides, CFD grids are not always available for any aircraft in the early design stages.

With differences in the design loads between the aircraft with and without alleviation,

differences in the structural masses are expected. These changes in the structural masses will

also likely influence the fatigue behavior of the aircraft. Therefore, to gain an understanding

of the interdependency between load alleviation, structural mass and fatigue, all three aspects

should be investigated simultaneously. Even if a quantitative statement concerning the fatigue

behavior e.g. “the aircraft can survive x flight cycles” cannot be made in the pre-design yet, a

qualitative trend can be obtained using relatively simple analysis methods.

1 Introduction

1.2 State of the art

Based on the motivation in Section 1.1, an overview of literature references from the fields

related to this thesis is provided. The first references comprise methods of gust and maneuver

loads analysis that are essential for designing and optimizing aircraft structures. These are

followed by references on active control technology on aircraft, the functions that are

available and the applications that exist. Development of load alleviation technology in

research is also elaborated, followed by a brief overview of fatigue analysis.

Gust and turbulence loads analysis

Gust loads have been investigated since the beginning of aviation, and the theory of an

airplane encountering gusts has been described in the first NACA report from 1915 by

Hunsaker et al. [43]. Over the years, methods of gust loads analysis with various levels of

fidelity have been developed for aircraft design and certification [30]. Those can be classified

into quasi-steady and dynamic methods.

Examples of the quasi-steady approach are the method from Rhode and Lundquist [81], where

the gust is assumed to have a sharp edge, and the method of Pratt with the assumption of a

1-cos gust shape [74]. Until 2017, the Pratt method was used for the certification

specifications for smaller aircraft with up to 19 passengers or a maximum take-off mass up to

8168Bkg (19000Blbs) as described in EASA CS23 (until Amendment 4) [19]. In the earlier

version of European and US American certification specifications for large aircraft JAR25

[45] and FAR25 [24], the Pratt method was also utilized to calculate gust loads until dynamic

simulations became obligatory in change 14 of JAR25 since 1994 [46] (today CS25) and in

FAR25 since 1996 [23].

To model the aerodynamics in dynamic simulations, there have been a large range of methods

such as the doublet lattice method (DLM) in the frequency domain, developed by Albano et

al. [3] and implemented in MSC.Nastran [64], or the computational fluid dynamics (CFD) in

the time domain, as described by Harlow et al. [38] and Raveh [78]. For certification, gust

loads have to be calculated in the entire flight envelope of the aircraft in combination with

various mass configurations and gust parameters. In CS25 [20], there are two approaches to

be considered, the first one assumes discrete 1-cos gusts. Methods of calculation of 1-cos gust

loads in the frequency domain for whole aircraft configurations have been described by

Stauffer et al. [89], Crimaldi et al. [13] and Handojo et al. [35]. To identify the gust evoking

the highest loads, Khodaparast et al. [52] developed an interpolation method employing a

Gaussian process (kriging).

The second approach in CS25 incorporates continuous atmospheric turbulence where von

Kármán turbulence spectra with a turbulence scale of 2500Bfeet are assumed [20]. A

turbulence loads analysis method using power spectral techniques has been introduced by

Houbolt [42]. While 1D turbulence analysis is necessary for certification, Teufel [92] and

Crimaldi et al. [13] researched the modeling of 2D turbulence. With 2D turbulence, smaller

fluctuations of the wing root bending moment compared to 1D turbulence have been

observed. However, other load quantities show higher values, such as shear stress in the rear

1.2 State of the art

section of an airliner as stated by Teufel [92], the torsion on Northrop Grumman B-2 as

mentioned by Crimaldi et al. [13] and the wing torsion of Lockheed L-1011 as written by

Hoblit [40]. According to Crimaldi et al. [13], the stress increase is to be considered in

correlation with structure fatigue.

Beyond that, approaches such as the statistical discrete gust, matched filter theory, random

process theory and solution of the Lyapunov equation have been developed [27,73]. Jones

[48] describes the statistical discrete gust method where gust profiles are generated using step

functions based on defined probability distributions. The method enables an assembly of a

sizing relevant gust profile in the time domain, e.g. for the wing root bending moment. The

sizing relevant gust profile can also be identified with the matched filter theory and random

process theory as proposed by Pototzky et al. [73]. A recent development in gust loads

analysis is Loads Kernel, a DLR in-house simulation platform developed by Voß [97]. Loads

Kernel incorporates the flight mechanics according to Waszak et al. [98] and enables

simulations in the time domain.

Maneuver loads analysis

Analogous to gust loads analysis, maneuver load analysis can be performed with various

modeling depths. Example of a maneuver simulation method with potential theoretical

aerodynamics is the vortex-lattice method (VLM) implemented in MSC.Nastran [65] or by

Voß [97], where the latter combines the maneuver and gust analysis in one single simulation

run. Maneuver simulations with consideration of nonlinear effects such as shock waves in

transonic flow conditions can be carried out with CFD as shown by Dean et al. [15] as well as

by Ritter et al. [82].

For certification according to CS25.331 [20], maneuvers in balanced (zero pitch acceleration)

and pitching conditions (with pitch acceleration) must be investigated. For the sizing loads on

the wing however, maneuvers with zero pitch acceleration are expected to be more relevant.

Active control technology and load alleviation on aircraft

Research activities concerning active control technology (ACT) [17,41] began in the 1960’s.

With the introduction of fly-by-wire and electronic flight control system, the implementation

of additional active control functions became simpler, so that the degrees of freedom of using

the available control surfaces became more diverse. Active control can be utilized to fulfill

flight control functions, such as ride comfort improvement, and also structural functions, such

as load alleviation, mode control and flutter suppression, as described by Brockhaus et al. [7]

and Regan et al. [80].

An early example of active control from the 1960’s is the Load Alleviation and Mode

Stabilization (LAMS) on the Boeing B-52 described by Burris et al. [9]. The function has

been incorporated to reduce fatigue loads due to turbulence by increasing the damping of the

rigid body motion and selected elastic modes. On the Lockheed C-5A, Disney [17] describes

an Active Lift Distribution Control System (ALDCS) that has been implemented to decrease

wing bending loads due to both gusts and maneuvers. Brockhaus et al. [7] state that the Airbus

A320 had a load alleviation function based on acceleration feedback and involves the

1 Introduction

deflection of ailerons and spoilers during extreme gust and turbulence encounter. On the

Northrop Grumman B-2, the wing bending moment due to continuous turbulence has been

significantly reduced by using a gust load alleviation (GLA) system, according to Britt et al.

[6]. On the Lockheed L-1011, a maneuver load alleviation (MLA) system is implemented to

increase the wingspan without having to extensively reinforce the structure, as described by

Ramsey et al. [77]. Another example of active control is the Load Alleviation and Ride

Smoothing (LARS) system by König et al. [55] that has been tested on the modified

VFW-614 aircraft ATTAS (Advanced Technologies Testing Aircraft System). Its aim is to

reduce vertical accelerations of the aircraft in gusty weather. The system uses the angle of

attack data as input to control the rigid body motion with direct lift control (DLC) flaps. Since

the controller is a feed-forward system, it has the advantage that the stability and dynamic

characteristics of the aircraft remain unchanged [56]. For lateral gusts, Hoblit [39] states that

the presence of a yaw damper on the Lockheed L-1011 leads to a shear force reduction by up

to 27% by increasing the damping of the Dutch roll mode. Furthermore, control systems to

improve ride comfort by increasing the damping of fuselage modes are found on the

BoeingB747, BoeingB777 and AirbusBA340, according to Hönlinger et al. [41] and Teufel [92].

Moreover, Reckzeh [79] describes a multifunctional flap system to optimize the lift

distribution on the AirbusBA350 XWB during cruise flight.

Simulations and experiments with load alleviation

A typical aim of load alleviation using active control is to reduce the wing bending moment

since it influences the wing structural mass significantly [41,105]. Depending on the aircraft,

the maximum bending moment in flight is reached either due to design maneuvers or design

gusts [62]. Nevertheless, Xu [105] states that both maneuver and gust load alleviation system

should be implemented simultaneously to maximize the benefit of load alleviation.

Load alleviation in quasi-steady longitudinal, book-case maneuvers according to CS25 can be

achieved by a symmetric deflection of the wing control surfaces [105]. However, in transient

maneuver and dynamic gust simulations, a control system is required. Examples of control

systems for transient maneuvers have been developed by Burlion et al. [8], Paletta [69] and

Woods-Vedeler et al. [103].

Concerning gust load alleviation (GLA) in simulations and experiments, various control

systems have been developed and the modeling depth also varies. The GLA system proposed

by Xu [105] incorporates a rather simple proportional derivative (PD) controller, while the

GLA proposed by Capello et al. [10] utilizes a comprehensive robust adaptive controller.

Furthermore, Fonte [28] proposes a GLA algorithm with static output feedback. GLA systems

that incorporates light detection and ranging (LIDAR) and disturbance model to predict the

upcoming turbulence have been introduced by Giesseler et al. [32] and Fezans et al. [26].

Alam [2] shows a comparison of several feedback controllers to alleviate gust loads on a

blended-wing-body configuration. An adaptive feed-forward GLA with the angle of attack as

input has been introduced by Zhao et al. [106]. For wind tunnel experiments, Cheung et al.

[11] developed folding wingtip devices to alleviate gust loads. Concerning the structural

1.2 State of the art

resizing, the research elaborated by Wildschek et al. [100] shows for a blended-wing-body

airliner that a reduction of the structural weight by approx. 2000Bkg or 0.5% of the maximum

take-off weight can be achieved with a feed-forward GLA.

Beside the control laws, Moulin et al. [63] and Pusch et al. [75] performed studies concerning

the control surface concepts and layouts to alleviate gust loads. Furthermore, Kaiser [50]

investigated alternative concepts of aileron architectures. Beside using classical control

surfaces, load alleviation concepts with active winglets [101] or hinged wingtips [11,102]

have been proposed with promising potentials of weight saving.

Fatigue analysis

Fatigue problems on airframes became a significant aspect during the 1950’s and 1960’s as

the cruise altitude of passenger aircraft increased and with it also the pressure difference

between the cabin and atmosphere. As stated by Payne [70], considerable loading conditions,

that are relevant for fatigue, are ground-air-ground cycles, maneuver and turbulence loads.

For fatigue calculations, standardized load spectra such as the TWIST spectrum [49] are

commonly used.

On the experimental side, tests ranging from specimen fatigue experiments, e.g. described by

Mayer et al. [60], to full-scale tests, as described by Grover [33], have been carried out. While

specimen tests can provide an overview of the scatter in the fatigue life, full-scale tests

provide findings of fatigue behavior of particular structures. For composites, among others

Tan et al. [90] carried out fatigue tests and elaborates the effect of joints on the fatigue

behavior.

For damage accumulation, Miner developed a method known as the Palmgren-Miner’s rule

[61]. Further fatigue prediction methods based on Palmgren-Miner’s rule have been

developed, e.g. in the method proposed by Schön et al. [86] with focus on spectral loading of

composites. The Federal Aviation Administration (FAA) described a fatigue prediction

method for composites using life- and load-enhancement factors as guidelines [22]. These

factors are intended to take the scatter in the fatigue behavior of composites into account.

In connection with loads, Paletta [69] shows the contribution of load alleviation systems in

extending the fatigue life on an aircraft. For that aim, ground-air-ground cycles, in-flight

maneuvers and discrete gusts are considered.

1.3 Derivation of contribution

According to the state of the art, the majority of the referred publications investigates the

influence of load alleviation on loads only. In the industry, dynamic gust and turbulence loads

are typically investigated in the detail design phase. This thesis addresses those aspects for the

preliminary design to gain insight into the influence of load alleviation in an earlier stage,

where potential design changes are more cost-efficient. Beyond that, the following

dissertations investigate the impact of load alleviation on the structural mass, fatigue or

analysis of both gust and turbulence loads:

1 Introduction

•Xu [105] proposes an aircraft conceptual design process with load alleviation and

aircraft optimization. The latter also comprises variations of aircraft geometry along

with structural optimization. As a result, differences in structural masses and load case

hierarchy emerge, where the aircraft with load alleviation (active aircraft) is lighter

than the passive counterpart. Furthermore, the operating costs between the respective

aircraft are compared.

•Paletta [69] shows the influence of load alleviation on the loads and fatigue life of a

business jet aircraft. In doing so, a reference ground-air-ground cycle, maneuvers, as

well as discrete gusts based on the Pratt formula [74] during several flight phases are

considered in the fatigue calculation. The conclusion is that load alleviation can extend

the fatigue life of the reference aircraft.

•Teufel [92] elaborates the effect of load alleviation on gust and turbulence loads.

Analogous to Paletta [69], the gust loads of the active aircraft tend to be lower

compared to the passive aircraft. Furthermore, Teufel considers the effects of 2D

turbulence on the loads.

From the dissertations mentioned above, however, the chain of impact of load alleviation

ranging from design loads, structural mass to fatigue has not been addressed. Hence, the

contribution of this thesis is to develop a method/process that considers:

Load alleviation in aircraft pre-design and its influence on design loads, structural mass

and fatigue.

The term “load alleviation in aircraft pre-design” implies that the aircraft geometry is frozen,

only the available control surfaces should be used for load alleviation, but the properties of

the primary structure still have to be determined. For the design loads, quasi-steady

maneuvers and dynamic 1-cos gusts are considered. The influence on structural mass means

that the structure is optimized iteratively according to the previously calculated design loads

until the structural masses converge. By doing so, the active and passive aircraft (with and

without load alleviation) are expected to have different structural properties and hence also

different fatigue behaviors. To investigate this, a qualitative fatigue analysis is conducted. The

analysis focuses on a reference ground-air-ground cycle and turbulence loads in selected

flight phases. Furthermore, the entire method should be robust and computationally efficient.

Table 1.1 visualizes the positioning of the contribution of this thesis. The investigated

influence of load alleviation on the various aspects listed in the columns are illustrated using

block diagram symbols. The three mentioned dissertations by Xu, Paletta and Teufel – which

have high correlations with this thesis – are featured as comparison. Furthermore, the general

trends of aspects addressed in the publications mentioned in Section 1.2 are included in the

illustration. As apparent, no publication considers the influence of load alleviation on all

aspects listed in the columns simultaneously.

1.3 Derivation of contribution

Beside the major aspect, this thesis addresses several minor points comprising:

•The analysis of a forward swept wing configuration as one of the reference aircraft.

This includes the problem of unstable bending-torsion-coupling and a decrease of

flight mechanic stability due its aeroelastic behavior.

•The consideration of elastic aircraft, unsteady aerodynamics, active control and

continuous turbulence in the analyses.

•The investigation of a retrofit (see Section 8.3) of the passive aircraft with load

alleviation instead of including it already in the design process.

Table 1.1. Positioning of the contribution of this thesis

1.4 Dissertation layout

Chapter 2 introduces the two reference aircraft and elaborates their simulation models. The

latter includes the structural, aerodynamic models of the aircraft, their coupling and the

control surface models. For one reference aircraft, a model adaptation to enhance its flight

mechanic stability is described. Chapter 3 addresses the design process featuring the

methodology of the loads analysis and structural optimization applied in this thesis. The

methodology part comprises the equations of motion used in the maneuver, gust and flutter

simulations as well as a description of the structural optimization problem along with the

constraints. Furthermore, the considered aeroelastic constraints are explained. An overview of

the design process workflow is subsequently shown. Chapter 4 elaborates the load alleviation

1 Introduction

applied in this thesis. At first, the considerations and restrictions for the load alleviation

algorithm are listed. Then, the control algorithm for the maneuver and feed-forward gust load

alleviation is derived. For the gust load alleviation, constraints are considered such as a

maximum control surface deflection rate and the delay time representing the computing time

of the flight control system. Moreover, the integration of the load alleviation into the design

process is addressed. Chapter 5 deals with the methodology for turbulence and fatigue loads.

It begins with a selection of the reference flight missions for the reference aircraft. This is

followed by an approach to simulate turbulence loads emerging in the reference flight

missions. Loads due to ground-air-ground cycles are also taken into account since these are

seen to be relevant for the fatigue life of the aircraft. To estimate the fatigue life, methods to

calculate the fatigue damage based on the obtained loads are elaborated. Chapter 6 and 7

contain an overview of the simulation parameters, the calculation results of each reference

aircraft – with and without load alleviation – and their discussions. The first part of the results

comprises the design loads, structural masses and aeroelastic parameters of the reference

aircraft. The second part of the results deals with the reference flight missions, the emerging

loads collectives as well as the resulting fatigue damage. Further practical aspects are

investigated in Chapter 8. The investigations cover several variations of the load alleviation

algorithm and their effects on the design loads or fatigue life. As the final part, Chapter 9

elaborates the evaluations, conclusions and outlook of this work.

2 Reference aircraft and their aeroservoelastic modeling

For the investigations concerning the load alleviation, structural masses and fatigue

mentioned in Section 1.3, reference aircraft have to be selected and their models have to be

generated first. This chapter starts with a brief explanation about why the two mid-range

commercial aircraft are taken as reference for the investigations. A description of each

reference aircraft with an overview of selected parameters follows. Subsequently, the

structural and mass modeling as well as the respective model generation aspects are

explained. Furthermore, the aerodynamic theories behind the aeroelastic analyses are

described. The last section in this chapter describes the structural and aerodynamic modeling

of control surfaces. Since the number of load cases considered in the analyses – including

dynamic simulations – is expected to be high (>100), the priority in the aircraft modeling lies

in minimizing the computing time.

2.1 Reference aircraft

Two reference aircraft are investigated: the backward swept D150 configuration and the

forward swept ALLEGRA configuration. The D150 configuration is similar to the

AirbusBA320, a typical mid-range commercial aircraft with a conventional configuration. The

term conventional configuration represents a backward swept wing, engines mounted under

the wing and fuselage mounted empennage. Among Airbus aircraft, the A320 family has the

highest number of aircraft in operation [1], which underlines its significance for commercial

aviation.

The ALLEGRA configuration is selected as the second reference aircraft. The configuration

was studied for future mid-range aircraft. Its parameters such as payload, operating Mach

number and design masses are similar to the D150 configuration. ALLEGRA has an

unconventional forward swept wing and T-tail configuration. These aspects are expected to

evoke aeroelastic effects that are not observable on the D150 configuration. One of such

effects is the increase of the lift slope at high dynamic pressures caused by the bending-

torsion coupling of the forward swept wing. This effect is elaborated further in Section 2.5.

D150 configuration

D150 is a mid-range transport aircraft configuration with an aluminum structure. It is

designed for 150 passengers and originates from the DLR project VAMP (Virtual Aircraft

Multi-disciplinary Analysis and Design Processes, 2010-2012) [107]. The aircraft geometry

and data are based on the CPACS data set from the DLR project iLOADS (2013-2016)

[57,58]. Figure 2.1 shows the geometry of the D150 configuration in cyan. The FE model of

the engine cowling generated using the DLR in-house program ModGen [53] is visualized in

yellow. Table 2.1 lists the aircraft’s key parameters. Since the design of the D150

configuration originates from a process on a conceptual level, the wing twist distribution

along the span is constant at 2° (leading edge up).

2 Reference aircraft and their aeroservoelastic modeling

Table 2.1. Key parameters of the D150 configuration

Parameter Value

Wing surface 122.3 m²

Wingspan 33.91 m

Mean aerodynamic chord 4.19 m

Wing aspect ratio 9.4

Wing taper ratio 0.246

Sweep angle of 25% chord line 24.94°

Operating empty mass (OEM) 40638 kg

Maximum zero fuel mass (MZFM) 60562 kg

Maximum landing mass (MLM) 62959 kg

Maximum take-off mass (MTOM) 72545 kg

Design cruise speed, Mach number 180 m/s CAS, Mach 0.82

Design dive speed, Mach number 205 m/s CAS, Mach 0.89

Service ceiling 13000 m

Figure 2.1. Geometry of the D150 configuration

The wing of the D150 configuration is made of aluminum alloy Al2024. Table 2.2 lists the

material properties.

Table 2.2. Material properties of D150 wing structure

Material parameter Value

Tensile modulus 73.8 GPa

Ultimate strength 441 MPa

Poisson number 0.33

Mass density 2800 kg/m³

2.1 Reference aircraft

ALLEGRA configuration

ALLEGRA is a mid-range transport aircraft configuration for 150 passengers which was

investigated in the DLR project ALLEGRA (AeroeLastic stability and Loads prediction for

Enhanced GReen Aircraft, 2012-2016) [59]. Its distinguishing features are the forward swept

wing that enables natural laminar flow at a cruise Mach number of 0.78 [88] and the T-tail.

The design originates from the DLR project LamAiR (Laminar Aircraft Research, 2009-

2012). Its structure is made of composite materials [88]. Figure 2.2 shows the geometry of the

ALLEGRA configuration. Table 2.3 lists key aircraft parameters. Moreover, Figure 2.3

visualizes the twist distribution of the jig shape. The flight shape twist distribution is a

result of an optimization for natural laminar flow (NLF) using CFD. Its jig-shape is derived

from the flight shape using the structural stiffness and the design lift distribution [104].

Table 2.3. Key parameters of the ALLEGRA configuration

Parameter Value

Wing surface 132.0 m²

Wingspan 35.81 m

Mean aerodynamic chord 4.01 m

Wing aspect ratio 9.7

Wing taper ratio 0.3

Sweep angle of 25% chord line -19.6°

Operating empty mass (OEM) 43712 kg

Maximum zero fuel mass (MZFM) 62962 kg

Maximum landing mass (MLM) 65949 kg

Maximum take-off mass (MTOM) 73365 kg

Design cruise speed, Mach number 180 m/s CAS, Mach 0.80

Design dive speed, Mach number 203 m/s CAS, Mach 0.87

Service ceiling 12500 m

For the structure of the lifting surfaces of the ALLEGRA configuration, Carbon-Epoxy (IM6)

[44] is used. The ply angle distributions are set to predefined values, each for the skins, spars

and ribs. With this approach, the structure is optimized by varying the material thicknesses

only, analogous to the aluminum D150 configuration. Aeroelastic tailoring can indeed be

considered in the structural optimization of the composite wing [44]. However, since it is not

the main focus in this work and requires significantly longer computing times, it is not taken

into account.

2 Reference aircraft and their aeroservoelastic modeling

Figure 2.2. Geometry of the ALLEGRA configuration

Figure 2.3. Jig shape twist distribution of the ALLEGRA configuration

Table 2.4 shows the material properties of the ALLEGRA wing structure.

Table 2.4. Material properties of carbon-epoxy IM6 composite [44]

Material parameter Value

Longitudinal modulus 177 GPa

Transverse modulus 10.8 GPa

Shear modulus 7.6 GPa

Poisson number 0.27

Mass density 1578 kg/m³

Table 2.5 lists the ply angle distributions for the different parts of the wing structure. With

these ply angle distributions, the skins have a relatively large stiffness in spanwise direction.

Hence, they can absorb the majority of bending moments, particularly because they have a

large second moment of area in the bending axis. The spars have a relatively high shear

stiffness to absorb the majority of vertical shear forces and torsion moments. Furthermore, the

shear stiffness on the ribs is supposed to provide wing box stability.

2.1 Reference aircraft

Table 2.5: Ply angle distributions on ALLEGRA wing structure

Component 0° plies ±45° plies 90° plies

Skins 50% 40% 10%

Spars 10% 80% 10%

Ribs 10% 40% 50%

2.2 Structural and mass models

For the loads analysis and structural optimization, MSC.Nastran models of the reference

aircraft generated with the DLR in-house MONA process [53] are used. The primary structure

on the lifting surfaces is modeled with shell elements for the spars, skins and ribs, as well as

with bar elements for the stiffeners. The fuselage is modeled with beam elements.

Furthermore, the engine pylons are modeled using bar elements, and the engine masses are

attached to the respective center of gravity positions. In the MONA process, the finite element

(FE) models undergo a preliminary structural sizing using analytic-empirical methods [54].

Figure 2.4 shows the FE model of the D150 configuration, while the shell elements of the

fuselage and engines are represented for illustration purpose only. In addition, nodes at the

leading and trailing edge of the lifting surfaces are visualized.

Figure 2.4. Full FE model of the D150 configuration

The total mass of both aircraft models consists of structural masses, secondary masses,

systems, fuel modeled according to Klimmek [54] and payload. To resemble realistic load

distributions due to fuel masses, the defueling sequence is set to: center tank – inner tank –

outer tank, and the fueling sequence is set to: outer tank – inner tank – center tank. The latter

is considered when distributing a defined fuel total mass into the fuel tanks. Moreover, this

sequence reduces the wing bending moment since fuel mass placed far from the symmetry

2 Reference aircraft and their aeroservoelastic modeling

plane creates a larger relieving bending moment compared to fuel mass near the symmetry

plane. Figure 2.5 illustrates the division of the wing fuel tanks with exemplary, arbitrary fuel

levels.

Figure 2.5. Fuel tank division on the D150 configuration

For the payload, masses are distributed over the fuselage to meet the target total masses and

center of gravity (CG) positions. To evoke the highest loads resulting from high moment of

inertia, the masses are placed as near as possible to the first seat row or the last seat row, see

Figure 2.6. At the same time, each fuselage node should carry no more than 1200Bkg of

payload to avoid having excessively high concentrated masses. This would correspond with a

seat row with six passengers weighing 100Bkg each (including luggage), combined with a

cargo mass of 600Bkg.

Figure 2.6. Desirable payload locations on the D150 configuration

Table 2.6 gives an overview of the number of elements of the full FE models. It is apparent

that the ALLEGRA configuration has significantly more bar elements than the D150

configuration. This is because the D150 only has five stringers along the wing box chord with

a variable stringer pitch. In the D150 model generation, the total stringer area is distributed

into the five stringers of the FE model. In contrast, the ALLEGRA configuration has a fixed

stringer pitch with a variable number of stringers along the wing box chord. This results in

larger numbers of stringers – up to 15 around the root. Figure 2.7 shows a cut FE model of the

starboard wing box where the bar elements of the stringers on the skins as well as stiffeners

on the spars and ribs are visible.

2.2 Structural and mass models

Table 2.6: Overview of the number of elements of the full FE models

Aircraft Grids Shell elements Bar elements

D150 10800 11000 5400

ALLEGRA 13000 13700 14100

Figure 2.7. View into the wing box of the ALLEGRA configuration

To reduce computing time in the loads analysis, the stiffness and mass properties of the

reference aircraft are condensed onto the load reference axis (LRA) nodes. Figure 2.8 shows

those nodes using the orange triangle markers. Besides, the condensed models have dependent

nodes at the leading and trailing edge of the lifting surfaces which are used for the spline of

the aerodynamic forces. Those nodes are connected to the LRA nodes with rigid body

elements. In total, the FE model of the D150 configuration has 261 LRA nodes and the

ALLEGRA configuration has 214 LRA nodes.

Figure 2.8. Condensed stiffness and mass model of the D150 configuration

2 Reference aircraft and their aeroservoelastic modeling

2.3 Aerodynamic models

The aerodynamic forces are modeled using the doublet lattice method (DLM) which is based

on the potential theory. DLM is introduced by Albano et al. [3], implemented in MSC.Nastran

[64] and a fast method to calculate motion-induced aerodynamic forces in the subsonic

regime. In DLM, the lifting surfaces are assumed as thin plates and divided into trapezoidal

lifting elements (boxes), while the lateral edges are parallel to the free stream, see Figure 2.9.

Figure 2.9. Lifting surface discretization in DLM

The pressure difference between the upper and lower side is modeled with a potential

doublet at the 25% chord line on each box. In a steady flow condition, this corresponds to a

horseshoe vortex where the bound segment coincides with the 25% chord line of the box. The

evaluation of the downwash induced by the doublets is done at the collocation point that is

located at mid-span and 75% chord of each box [3].

Since the downwash velocity is also influenced by vortices of neighboring boxes, the

influence coefficients of the vortices are written in an aerodynamic influence coefficient

(AIC) matrix as defined by:

,(2.1)

with:

,(2.2)

and:

: Mach number [-],

: reduced frequency [-],

: frequency [Hz],

: mean aerodynamic chord [m],

: true airspeed [m/s].

The downwash velocity is bound to the condition that the flow at the collocation points must

be tangential to the oscillating lifting surface as:

,(2.3)

2.3 Aerodynamic models

with:

: imaginary number [-],

: reduced frequency [-],

: differentiation matrix [1/s],

: displacements of aerodynamic grid points [m],

: static aerodynamic downwash velocity from angle of attack, camber or twist

[m/s].

Since the aerodynamic forces can only be calculated for harmonic motions, they are known in

the frequency domain. For investigations in the time domain, an inverse Fourier transform is

necessary [3]. The upper frequency limit , at which the calculation results are considered

as reliable, correlates with the discretization of the DLM boxes and the airspeed [66].

According to the MSC.Nastran documentations [64,66], the aspect ratio of the DLM boxes

should be less than three and the chord length should satisfy:

,(2.4)

with:

, (2.5)

and:

: typical chord length of aerodynamic box [m],

: lowest true airspeed in the analysis [m/s],

: highest frequency to be analyzed [Hz],

: number of boxes in chordwise direction [-].

On the D150 configuration, the upper frequency limit is 41BHz, and on the ALLEGRA

configuration it is 37BHz. With 12Bboxes in the chordwise direction, Equation (2.2), (2.4) and

(2.5) yield a maximum observable reduced frequency of 3.0.

To consider the aerodynamic effect of the fuselage, the subsonic wing-body interference

theory is used [31,65]. For that purpose, a slender body element (see Figure 2.10) and a set of

interfering lifting surfaces (see Figure 2.11) are defined. The interfering lifting surfaces

circumscribe the slender body and consists of DLM boxes. The wing-body interference is

approximated by the doublets on the interfering lifting surfaces . The slender body element

itself implements a line of doublets along its longitudinal axis . With the boundary

condition of no flow through the body, the doublet strength distribution can be determined.

The downwash Equation (2.1) is then extended to:

,(2.6)

with:

: aerodynamic box downwash at 75% chord,

: downwash on slender body element,

: aerodynamic influence coefficient,

2 Reference aircraft and their aeroservoelastic modeling

: pressure coefficient on aerodynamic box,

: acceleration potential interference doublet,

: acceleration potential slender element doublet.

To consider the aerodynamic effects due to the twist and camber of the wing, a downwash

correction with W2GJ matrix [54,64] created using ModGen is implemented. The W2GJ

matrix practically describes the incidence angle of each aerodynamic element. The entries

correspond to the slope of the respective camber line at the box position. Hence, the entries

for a symmetric profile are zero. Furthermore, for transonic flow conditions, a correction of

the AIC matrices can be taken into account, for example using data from CFD [36]. For this

purpose, prior CFD calculations are necessary. However, CFD grids are not always available

in the early stages of the aircraft design process, so that CFD based corrections are not always

possible.

Figure 2.10. Aerodynamic model of the D150 configuration with slender body element

Figure 2.11. Aerodynamic model of the D150 configuration with interference body

2.3 Aerodynamic models

For the next step, a coupling between the aerodynamics and the structure is necessary. This is

done by introducing a dimensionless coupling matrix :

,(2.7)

with:

: deflection of aerodynamic grid points,

: displacement of structural nodes.

For the structural forces, the coupling is done with the transposed matrix:

,(2.8)

with:

: forces on structural nodes,

: coupling matrix,

: aerodynamic forces.

For the lifting surfaces, the surface spline method is used. In this case, the aerodynamic forces

are splined onto the LRA nodes and their dependent nodes at the leading and trailing edges.

On the fuselage, the aerodynamic forces are mapped onto the LRA nodes using a beam spline

method. The spline for each lifting surface and slender body is carried out separately to avoid

having aerodynamic forces on one component being mapped onto an adjacent one.

In total, the aerodynamic model of the D150 configuration has 939 aerodynamic elements and

the ALLEGRA configuration has 1176 elements.

2.4 Structural and aerodynamic modeling of control surfaces

To implement the load alleviation functions, the control surface structures – in this case the

ailerons, elevators and rudder – are modeled. For the aerodynamic part, the corresponding

DLM boxes are assigned to the control surface and a local coordinate system for the

orientation of the deflection is defined. Besides, an aerodynamic effectiveness of 0.7 is

assumed to take disturbances due to the sudden contour change at the control surface hinge

[84] and the vortices at the lateral edges into account. The aerodynamic effectiveness modifies

the theoretical forces of an ideal control surface by the set value.

To model the dynamics of the control surface as well, a structural and a mass model are

necessary. Hence, an FE model of each control surface is created with ModGen which is one

of the main programs used in the MONA process [53]. Analogous to the wing structure, the

control surface model consists of a front and rear spar, upper and lower skin, ribs and

stiffeners. The skin thickness is adjusted so that the control surface mass matches the

estimation by Torenbeek [94] which refers to the mass per control surface area.

The control surface hinge connection is modeled using massless, stiff connector bars. For that

aim, several hinge nodes along the hinge line are defined. At the hinge points where an

actuator is located nearby, the hinge nodes are connected to the wing, horizontal tailplane

(HTP) or vertical tailplane (VTP) box with four bars each. Every other hinge node is

2 Reference aircraft and their aeroservoelastic modeling

connected to the primary structure with two bars. On the control surface side, the aileron,

elevator and rudder structure is connected to each hinge node using two bars. Figure 2.12

shows an FE model of an aileron. The thick blue lines represent the massless bars for the

hinge modeling, and the dashed/dotted green line visualizes the hinge line. Moreover, a hinge

spring is also visible. The spring is defined to avoid a stiffness singularity of the control

surface, and its stiffness is set to 1BNm/rad. In simulations where the control surface should

remain at the neutral position, the spring stiffness is increased to 107BNm/rad. Figure 2.13

shows a principal sketch of the hinge.

Figure 2.12. Structural modeling of an aileron and its hinge

Figure 2.13. Principal sketch of a control surface hinge

2.5 Model adaptation – ALLEGRA configuration

Background

According to Wunderlich [104], the aeroelastic effects of the LamAiR configuration – the

base of the ALLEGRA configuration – are not considered in its conceptual design. However,

the aeroelasticity of aircraft wings can change the wing lift slope and even shift the

aerodynamic center of the whole aircraft. The latter is a crucial aspect since the longitudinal

stability of the aircraft may be affected in a negative way.

On the forward swept ALLEGRA configuration, the lift slope of the elastic aircraft becomes

larger with increasing dynamic pressure. This is caused by the following points:

2.5 Model adaptation – ALLEGRA configuration

•An increase in angle of attack causes more lift and the wing tip bends up.

•Due to the forward sweep and its bending-torsion-coupling, the wing tip’s upward

bending causes a nose-up twist.

•This nose-up twist amplifies the local angle of attack and with it the local lift,

especially at the wingtip.

•Due to the local lift amplification, the lift slope is larger compared to the rigid aircraft.

Figure 2.14 illustrates the wing twist caused by the bending-torsion-coupling.

Figure 2.14. Wing twist due to bending-torsion-coupling

The wingtip is the most affected area by the bending-torsion-coupling. It lies further forward

compared to the 25% chord line of MAC, see Figure 2.15. Since the 25% chord line of MAC

represents the aerodynamic center of the rigid aircraft, the wingtip twist and the amplified

local lift on the elastic aircraft result in a forward shift of the aerodynamic center.

Figure 2.15. Wingtip position relative to MAC

Challenge

On the initial model with IM6 composite, the shift of the aerodynamic center in flight was so

large that the the aircraft became unstable in the pitch axis. To solve this problem, the rear CG

limit was moved forward from 40% to 35% MAC, and the wing skin laminate orientation was

rotated to reduce the wingtip twist and also the shift of the aerodynamic center. Figure 2.16

visualizes the laminate rotation and Figure 2.17 shows its effects, among others on the

location of the aerodynamic center.

2 Reference aircraft and their aeroservoelastic modeling

Figure 2.16. Rotation of skin laminate orientation

Reference load case

The trim condition at the design dive speed / as described in Table 2.7 is taken as

reference. This trim condition is chosen because it provides the combination of the highest

design dynamic pressure and the highest design Mach number, and this maximizes the

magnitude of the aeroelastic effects. The trim calculation is conducted using MSC.Nastran as

described in Section 3.1.

Table 2.7. Reference trim condition for laminate rotation study

Parameter Value

Altitude 7010 m

Airspeed 271.6 m/s TAS (Mach 0.87)

Load factor 2.5

Results and discussion

In this investigation, only the laminate rotation and the subsequent reference trim calculation

is carried out; no further structural optimization is conducted for the various laminate rotation

angles. The reference wing stiffness distribution is taken from the optimized passive aircraft

according to Chapter 7 with 30° laminate rotation.

In principle, the laminate rotation – about the positive z-axis of the aircraft – couples the tip-

up wing bending with a nose-down twist. On one hand, this can compensate the nose-up twist

due to the bending-torsion-coupling by up to 75%, as can be seen in Figure 2.17(a). On the

other hand, the wing bending stiffness decreases since a fraction of it is transformed into the

coupling stiffness between bending and torsion. This is reflected by the increasing wingtip

deflections in z-direction with larger laminate rotation angles in Figure 2.17(b). Hence, with a

decreasing bending stiffness, the coupled nose-up twist becomes larger, and the compensation

effect by rotating the laminate becomes less effective at a certain point, as can be seen in

Figure 2.17(a) between the laminate rotation angles of 30° and 40°. A way to restore the

bending stiffness and minimize the wingtip twist at high laminate rotation angles (>30°) is to

increase the material thickness, and with it also the wing box mass.

2.5 Model adaptation – ALLEGRA configuration

(a) (b)

Figure 2.17. Rotation of laminate orientation and their effects on the trim

Trends similar to the wingtip twist in Figure 2.17(a) also appear in the graphs for the

aerodynamic center and lift slope Figure 2.17(c) and (d) where a laminate rotation of 30°

yields the smallest differences compared to the rigid aircraft. In Figure 2.17(d), the lift slope

of the rigid aircraft is larger than 2 due to compressibility effects. To fulfill the stability

requirement that the rear CG limit has to be in front of the aerodynamic center, a laminate

rotation between 20° and 40° can be considered, as visible in Figure 2.17(c). Since a laminate

rotation of 30° provides the largest stability margin, it is taken for the investigations in this

thesis.

As a remark: with parameters in Table 2.7, the dynamic pressure is 21717BPa. Since the shift

of the aerodynamic center becomes larger with increasing dynamic pressure, the aircraft’s

stability margin is expected to become negative if the dynamic pressure is further increased.

As a comparison: On the elastic D150 configuration, the aerodynamic center at / is at

49.8% MAC, and the rear CG limit is at 45% MAC. Hence, the elastic aircraft stays stable at

/ .

2 Reference aircraft and their aeroservoelastic modeling

3 Design process of loads analysis and structural optimization

3 Design process of loads analysis and structural

optimization

The interdependency between loads and structural properties has to be considered during the

optimization of elastic aircraft. However, the load calculation and the optimization of the

structure cannot always be conducted simultaneously, especially when dynamic simulations

are included. For this reason, an iterative design process – as it is commonly applied in the

industry – is set up for the reference aircraft. Each iteration cycle consists of a loads analysis

based on the DLR loads process as described by Krüger et al. [58] and a subsequent structural

optimization with gradient-based algorithms.

To prepare for the loads and optimization process, load cases according to CS25 [20] are

defined for the simulations. The load cases comprise symmetric maneuvers (+2.5g pull-ups

and -1g push-downs) and vertical 1-cos gusts with gust gradients ranging from 9Bm to 107Bm.

The maneuver and gust simulations to obtain the loads are described in the Sections 3.1 and

3.2. The resulting loads are then post-processed to select load cases – among the thousands –

that are relevant for the structural optimization. This post-processing is elaborated in Section

3.3 and the gradient-based structural optimization is described in Section 3.4. Beside the

structural strength and stability criteria, aeroelastic constraints explained in Section 3.5 are

also considered in the optimization. For the optimized models, a flutter calculation as

elaborated in Section 3.6 is conducted to identify the flutter speed of the reference aircraft.

Section 3.7 gives an overview of the whole loads analysis and structural optimization

workflow including the interconnection between the modules.

3.1 Maneuver simulation

The maneuvers are simulated with SOL144 of MSC.Nastran [64] which is designed to

perform quasi-steady aeroelastic analyses. The equations of motion solved in SOL144 are:

,(3.1)

with:

: structural stiffness matrix,

: dynamic pressure,

, : aerodynamic stiffness matrices,

: nodal displacements,

: structural mass matrix,

: control and rigid body motion variables,

: applied loads, including downwash from twist and camber corrections.

3 Design process of loads analysis and structural optimization

The equations of motion are solved in physical coordinates (thus the index a) and valid for a

free flying aircraft. The control and rigid body motion variables in the equation can comprise:

•angle of attack ,

•slip angle ,

•angular velocities , , ,

•translational accelerations , ,

•angular accelerations , , ,

•control surface deflections .

To obtain an explicit solution, the equation system has to be determined. This means, the

number of equations has to be equal to the number of unknown variables.

In this thesis, only symmetric maneuvers (pull-ups and push-downs) are considered; no roll

and yaw maneuvers are taken into account. For the simulations, the prescribed vertical load

factors are +2.5 and -1.0 and the pitch rate of the aircraft are considered [20]. In the

simulation, all maneuvers are assumed as quasi-steady pull-ups and push-downs, and the pitch

rate is calculated by:

,(3.2)

with:

: gravitational acceleration [m/s²],

: aircraft true airspeed [m/s].

3.2 Dynamic gust simulation

The gust simulations are performed with SOL146 of MSC.Nastran [64], that is designed for

dynamic aeroelastic analyses in the frequency domain. The DLM elaborated in Section 2.3 is

applied to compute the aerodynamic loads. The equations of motion in SOL146 are:

,(3.3)

where:

: modal mass matrix,

: circular frequency,

: modal damping matrix,

: modal stiffness matrix,

: dynamic pressure,

: aerodynamic matrix,

: Mach number,

: reduced frequency,

: modal displacements,

: generalized applied loads.

3.2 Dynamic gust simulation

The differential equation system is solved in modal coordinates (thus the index h) to reduce

the computing time. This is done for every frequency step. Since the aerodynamic matrix

can only be created for a small number of reduced frequencies due to its size, it is interpolated

over the range of the observed circular frequency . For the damping matrix , a structural

damping of 3% is set, as it can be assumed according to CS25 [20].

In the simulations, frequencies up to 50BHz and AIC matrices with reduced frequencies up to

1.0 are considered. With the flight parameters of the reference aircraft, a reduced frequency of

1.0, as stated in Equation (2.2), is equivalent to a frequency of up to 20BHz. This is seen as

sufficient since more than 99% of the energy of 1-cos gusts is contained in frequencies up to

twice of the gust base frequency defined by:

,(3.4)

with:

: gust base frequency [Hz],

: aircraft true airspeed [m/s],

: gust gradient [m].

Gust base frequencies, that are potentially relevant for the structural optimization, are

expected to be close to the first wing bending frequency. For commercial transport aircraft,

the first wing bending mode typically occurs between 1BHz and 5BHz, depending on the

aircraft geometry and mass configuration. As a conclusion, AIC matrices that cover at least

frequencies up to 10BHz are seen as sufficient for the gust loads analysis.

To obtain the aircraft response to a particular 1-cos gust, the time history of the gust is

introduced as the generalized applied loads . Within MSC.Nastran, the time history is

transformed into the frequency domain for further processing. In the output, the aircraft

responses are given in the time domain again. For the active aircraft, control surface

deflections during a gust encounter are inputted as enforced motions. In the equations of

motion, the enforced motions are handled as generalized applied loads . This procedure is

applied for the design gust load calculations in this thesis.

To obtain the transfer functions, e.g. of the aircraft response to gusts or control surface

deflections in general, the loads are introduced as white noise or spectral gust excitation

with a predefined amplitude in the frequency domain. The transfer function results are given

in the frequency domain as well. This case is relevant for the turbulence analysis described in

Section 5.3.

3 Design process of loads analysis and structural optimization

3.3 Loads post-processing for structural optimization

As gust simulations consist of several hundred time steps for every gust encounter, the

number of load cases for the structural optimization – comprising all maneuvers and all time

steps of every gust encounter – would be too high. In literature references, the typical number

of load cases considered in the optimization is below 20, as listed by Bramsiepe et al. [4]. On

a composite wing, Dillinger [16] included 13 load cases in the optimization and Klimmek [54]

took 16 load cases on an aluminum wing into account. Hence, an algorithm to filter the

relevant load cases is necessary. This algorithm is divided into two steps: the first one is to

reduce the number of time steps extracted from each gust encounter, and the second one is to

identify the load cases with the largest cut loads among all the maneuver and gust cases.

For that aim, monitoring stations for cut loads are defined on the wing and HTP, see Figure

3.1. At the positions of the green circles, the loads are monitored in the local coordinate

system. In the gust simulations, those monitoring stations are used for the first step of

filtering: when at least one of the monitoring stations reaches its maximum or minimum in

shear force , bending moment or torsion moment , all nodal loads at that time step

are extracted [12]. Figure 3.2 illustrates this extraction using an exemplary load quantity.

Figure 3.1. Monitoring stations on the D150 configuration

Figure 3.2. Extracted snapshots from a gust encounter

3.3 Loads post-processing for structural optimization

The gust simulations with SOL146 only yield the incremental gust loads acting on the

aircraft. To obtain the total loads, the gust loads have to be superposed with the corresponding

trim loads:

.(3.5)

The trim loads are calculated with SOL144 with a load factor of 1.0 and a pitching velocity of

0Brad/s. Figure 3.3 visualizes an exemplary superposition – in this case of the load factor –

during a gust encounter in a V-n diagram.

Figure 3.3. Exemplary superposition of load factors during gust encounter

The second step of filtering is carried out after the superposition. 2D envelopes are generated

for the maneuver cut loads and the superposed cut loads from the gust simulations. The

combination of the load component is / (see Figure 3.4) as well as / . The 2D

envelopes are created at every monitoring station. The load cases appearing on the edges of

the 2D envelopes comprise the loads considered in the structural optimization.

Figure 3.4. 2D envelope surrounding gust and maneuver loads

3 Design process of loads analysis and structural optimization

3.4 Structural optimization

Based on the resulting loads from the maneuver and 1-cos gust simulations, the primary

structure of the wing and HTP is optimized using SOL200 of MSC.Nastran [65] that

implements gradient-based algorithms. The considered constraints are material strength,

buckling stability and minimum thickness that are described in more detail in Subsection 6.1.6

and 7.1.5, as well as aeroelastic constraints elaborated in Section 3.5. The mathematical

formulation of the optimization task is:

,(3.6)

with:

: objective function to be minimized, e.g. structural mass,

: design variables,

: optimization constraints,

, : lower and upper limits of the design variables.

An example of the constraint formulation for the stress is:

,(3.7)

with:

: stress constraint,

: limit stress,

: von-Mises stress.

Figure 3.5 visualizes the structural optimization algorithm in MSC.Nastran. At the beginning

of the optimization process, an initial design – either from the preliminary cross-section sizing

in ModGen as described by Klimmek [53] or the previous cycle of loads and optimization – is

put in. Along with the included applied loads, a structural analysis is run. The output of the

structural analysis such as stresses and strains is declared as analysis variables .

Subsequently, a constraint screening and a sensitivity analysis is conducted. Together with the

structural analysis results, the design sensitivities are used to create an approximate model

based on Taylor series expansions of objectives and constraints according to the optimization

algorithm [65]. With this approximate model, the number of analyses of the full structural

model is kept to a minimum and the approximated variables are defined as , and . The

optimizer then communicates with the approximate model. The optimization algorithm used

in this thesis is IPOPT (interior point method) that is very robust [65]. After the optimizer has

finished the task, the structural model is updated. With the new structural model that is

denoted as the improved design, a new structural analysis can be conducted. This iterative

design optimization continues until a predefined convergence criterion is met. For the D150

configuration, the defined convergence criterion is a relative mass change of 5.0·10-4 between

two design iterations, while a relative mass change of 1.0·10-3 is set for the ALLEGRA

configuration due to its non-isotropic material properties and thus longer computing time

within the structural optimization. The objective of the structural optimization lies in

minimizing the structural mass while complying with the constraints under the applied loads.

3.4 Structural optimization

Figure 3.5. Structural optimization flowchart

3.5 Aeroelastic constraints

Beside constraints concerning the structural strength, buckling stability and minimum

thickness, static aeroelastic requirements are considered in the structural optimization as well.

According to CS25.629, there must be no instability at any speed up to / +15% [20]

where is the design dive speed and is the design dive Mach number. Figure 3.6 shows

an exemplary flight envelope for the aeroelastic constraints with the stall speed and design

dive speed . In this thesis, the focus lies on aileron reversal and divergence.

Figure 3.6. Exemplary flight envelope for aeroelastic constraints

3 Design process of loads analysis and structural optimization

Aileron reversal

On an elastic aircraft, an aileron deflection during flight causes the wing to twist due to the

torsion moment generated. The twist itself changes the local angle of attack of the wing and

counteracts the aileron deflection. As a result, the effectiveness of the aileron is reduced. This

effect becomes more pronounced with increasing dynamic pressure. An aileron reversal

occurs at the dynamic pressure where the aileron effectiveness becomes negative.

In this case, the aileron effectiveness is defined as the ratio between the roll derivative due to

aileron deflection of the elastic aircraft and that of the rigid aircraft . To

meet the requirement defined in CS25, the aileron effectiveness at the aforementioned flight

envelope has to be positive:

.(3.8)

Backward swept wing configurations are more prone to aileron reversal since the bending-

torsion-coupling of the wing reduces the aileron effectiveness further. Therefore, this

phenomenon is investigated on the D150 configuration [54].

The constraint is implemented in SOL200 of MSC.Nastran by setting the minimum allowable

aileron effectiveness to 1% at / +15%. If a reversal occurs, the wing is re-optimized,

where the objective function is minimum mass and only an increase of the material

thicknesses is allowed [54].

Divergence

On forward swept wing configurations, the static aeroelastic instability that is more likely to

occur is divergence. In a two-dimensional case where the center of pressure is in front of the

wing’s elastic axis, the lift force induces a torsional moment which causes the wing to twist

nose up. This in turn increases the lift and torsion until an equilibrium between the

aerodynamic and elastic forces of the wing is reached. With increasing dynamic pressure, the

wing twist at the equilibrium state increases, and a divergence occurs when the theoretical

wing twist is infinite. In a 1 DoF system with the elastic wing twist angle , the

mathematical formulation of the divergence is:

,(3.9)

with:

: stiffness matrix,

: divergence dynamic pressure,

: aerodynamic stiffness matrix,

: elastic wing twist angle.

If the wing is swept forward, the bending-torsion-coupling increases the effect of positive

wing twist, and this decreases the divergence dynamic pressure. Therefore, this phenomenon

is investigated on the ALLEGRA configuration.

3.5 Aeroelastic constraints

The constraint is implemented in SOL200 of MSC.Nastran by setting a dynamic pressure

equivalent to / +15%, up to which divergence must not occur. If a divergence occurs,

the wing is re-optimized, and the objective function is mass minimization. In doing so, only

an increase of the material thicknesses is allowed.

Theoretically, all constraints – in this case strength, buckling and aeroelastic stability – can be

considered in one single optimization run. Due to the heterogeneous constraints however,

such an optimization problem would significantly become more complex and the computing

times would significantly increase. Since the aeroelastic constraints are not expected to have a

large impact on the design that is optimized for material strength and buckling stability, the

consideration of aeroelastic constraints in a separate optimization is seen as acceptable.

3.6 Subsonic flutter check

The subsonic flutter checks are intended to ensure that the optimized reference aircraft do not

flutter at the prescribed dynamic pressure. These checks are performed with SOL145 of

MSC.Nastran [64]. The chosen flutter solution method is the fast KE-method that is based on

the K-method. The equation of motion involved in the K-method is similar to Equation (3.3)

that is used for the gust simulation:

,(3.10)

with:

: modal mass matrix,

: circular frequency,

: modal damping matrix,

: modal stiffness matrix,

: dynamic pressure,

: aerodynamic matrix,

: Mach number,

: reduced frequency,

: modal displacements.

Within MSC.Nastran, Equation (3.10) is modified slightly by introducing an artificial

damping :

.(3.11)

Equation (3.10) is only valid at the flutter point, i.e. where is zero. Besides, the airspeed

is written as:

.(3.12)

In the fast KE-method, all viscous dampings such as structural or control system

damping are neglected, so that the physically relevant results are restricted to eigenvalues

around the flutter point. Moreover, complex eigenvectors of the flutter modes are not

available in the KE-method [64]. The equation of motion implemented in MSC.Nastran is:

3 Design process of loads analysis and structural optimization
,(3.13)
with:
  : mean aerodynamic chord [m],
  : mass density of air [kg/m³],
  : true airspeed [m/s],
  : artificial structural damping [-].
Thus, the square of the eigenvalues   is defined by:
.(3.14)
Equation   (3.13)   is   solved   for   each   mode   and   each   step   of   reduced   frequency.   Within 
MSC.Nastran, the eigenvalues are sorted based on their finite differences between the reduced 
frequencies. With the sorting method, V-d (airspeed and damping) and V-f (airspeed and 
frequency) curves can be created and interpreted physically [64].
With the Doublet-Lattice-Method, transonic effects cannot be considered. This can become 
relevant around the transonic dip where the dynamic pressure of the flutter point is reduced 
due to the transonic effects. To cover this case, high-fidelity simulations such as CFD would 
become necessary.
3.7  Workflow of the design process
The steps described in the previous sections are implemented in an automated, iterative 
workflow for the design process with loads analysis and structural optimization. With the 
initial presized design from ModGen, a condensation of the global stiffness and properties 
(see Section 2.2) is conducted. The condensed FE-model, along with the aerodynamic model, 
is used for the gust (see Section 3.2), trim and maneuver (see Section 3.1) calculations. The 
loads extracted from the gust simulations are then superposed with the corresponding trim 
loads. Subsequently, the maneuver and gust load cases – which are relevant for the structural 
optimization – are filtered using the load envelopes (see Section 3.3). With the filtered load 
cases, the structure of the wing and HTP is optimized (see Section 3.4). The resulting design 
is   put   in   for   the   aeroelastic   optimization   (see   Section  3.5).   If   the   defined   aeroelastic 
constraints are violated, the design is adjusted to fulfill the constraints. The design properties 
from the aeroelastic optimization are then extracted for the next cycle of loads analysis and 
structural optimization. The cycle is repeated until the relative change in wing structural mass 
between two cycles is below 0.5%. After the optimized design is reached, a subsonic flutter 
check (see Section  3.6) is run to ensure that the aircraft does not flutter at the prescribed 
dynamic pressure envelope. In case of an emerging flutter problem, an implementation of a 
flutter   optimization   would   become   necessary.  Figure   3.7  visualizes   the   implemented 
workflow.
34

3.7 Workflow of the design process

Figure 3.7. Workflow of loads analysis and optimization chain

3 Design process of loads analysis and structural optimization

4 Modeling of load alleviation systems

This chapter explains the objectives of load alleviation and which restrictions are to be

considered. These restrictions comprise the assignment of control surfaces used in the

maneuver and gust load alleviation respectively. A synthesis of the algorithm for maneuver

load alleviation (MLA) that is based on the potential theory follows.

Subsequently, the derivation of the gust load alleviation (GLA) algorithm is explained. This

begins with a list of restrictions concerning the dynamics of the GLA. Furthermore,

considerations regarding the selection of input parameters for the GLA are elaborated. While

taking the mentioned aspects into account, a transfer function of the GLA is synthesized in the

frequency domain. Using the transfer function and the respective input during a gust

encounter, the GLA command is calculated. This is then transformed into the time domain. To

meet the time domain requirements as well, rate limiters are implemented before the GLA

deflection is fed into the simulation. A flowchart visualizing the inclusion of GLA in the gust

simulation is shown at the end of this chapter.

4.1 Objectives and restrictions

The aim of load alleviation is to reduce the wing loads – especially bending moment –

resulting from the design load cases. In the preliminary aircraft design stage, the wing

planform and the control surface layout are fixed. This means that the load alleviation should

be carried out using the existing control surfaces. High lift systems are not used since the

conventional ones can only be extended at low airspeeds. Spoilers are indeed used for load

alleviation as well [7]. In this thesis however, spoilers are not included in the load alleviation

algorithm since the modeling of spoilers aerodynamics without any DLM correction is

unreliable as DLM does not consider flow separation when spoilers are extended.

With the constraints mentioned above and the assumption of symmetric loads, the options

available to reduce wing loads are to deflect ailerons and/or elevators. For maneuvers, the

load alleviation deflects the ailerons symmetrically to shift the center of lift towards the wing

root and reduce the wing bending moment. The resulting change in pitching moment due to

the aileron deflection is compensated with the elevators.

During gust encounters, the gust load alleviation deflects the ailerons to reduce the lift

increment induced by gusts and – analogous to maneuver load alleviation – to reduce the wing

bending moment. The elevators can also be used e.g. to compensate the pitching moment

resulting from the aileron deflection. However, elevators are only effective at low frequencies

(up to the short period mode), while the highest gust loads typically emerge at higher

frequencies (around the first wing bending mode). A transfer function of the D150 in a climb

phase emphasizes the effect, see Figure 4.1. The input is the elevator deflection and the

output is the bending moment at the wing root. The Bode plot shows that the short

period mode occurs at approx. 0.2BHz, and above that frequency, the influence of the elevator

4 Modeling of load alleviation systems

on the wing root bending moment decreases rapidly. Indeed, elevators can be actuated at

higher frequencies, however, this would likely excite fuselage modes without significantly

changing the wing loads, and this is undesirable for GLA. For this reason, the elevators are

not used for GLA.

Figure 4.1. Wing root bending moment response to elevator deflection

Furthermore, the load alleviation systems are assumed to have a failure probability below 10-5

per flight hour. Taking this into account, the limit load calculations for the failure condition

only have to consider a safety factor of 1.0 instead of 1.5 according to Appendix K25.2(c)(2)

(ii) of CS25 [20]. Since the load alleviation systems are not expected to reduce loads by more

than 33%, the safety factor of 1.0 is inherently achieved and load calculations for the failure

condition are omitted.

4.2 Maneuver load alleviation concept

The maneuver load alleviation (MLA) is carried out by deflecting the ailerons symmetrically.

To avoid interference with the flight mechanic controller, the MLA should only react to the

commanded load factor, but not to the actual load factor. At a load factor of 2.5, the ailerons

are deflected upward, and at a load factor of -1.0 downward. This is supposed to shift the

center of lift to the root, so that the bending moment is reduced at approximately the same

level of lift force, see Figure 4.2.

Figure 4.2. Change of spanwise lift distribution with MLA during a pull-up maneuver

The aileron deflection for MLA is set to 8° at the design cruise speed and a load factor of

2.5. Compared to the Lockheed L-1011 (13° at 2.5g) [77], the value taken is indeed relatively

small. However, the MLA deflection in this thesis is defined as a function of the airspeed.

Hence, the MLA deflections at airspeeds below are larger than 8°, as shown at the end of

this section.

4.2 Maneuver load alleviation concept

To calculate the aileron deflection amplitude for other airspeeds, an ideal case of a rigid,

symmetric wing profile with no twist is used as reference. To achieve a constant ratio between

lift due to angle of attack and lift from MLA, the aileron deflection has to be proportional to

the angle of attack: . The constant lift ratio also yields a constant ratio between the shear

force and torsion moment . Furthermore, with constant lift, the angle of attack is

inversely proportional to the dynamic pressure: . With those proportionality

relationships, it can be derived that the aileron deflection should be inversely proportional to

the dynamic pressure :

.(4.1)

Indeed, for an aircraft with an elastic wing, twist, camber and variable mass, an MLA

algorithm as stated in Equation (4.1) will not yield a perfectly constant alleviation effect at

every dynamic pressure. However, this approach is still more advantageous compared to

setting a constant aileron deflection gain for the 2.5g case over the whole range of dynamic

pressure. With a constant aileron deflection gain, at low speeds the alleviation effect would be

relatively small, and at high speeds the ailerons might overcompensate the local lift which

would decrease the aerodynamic performance of the aircraft. Additionally, this

overcompensation would create a large aileron hinge and wing torsion moment.

This range between the small alleviation effect and the overcompensation would also make

the 2D load envelopes mentioned in Section 3.3 less slender: the first case would evoke a

large bending moment and a small torsion, while the latter would cause a small bending

moment and a large torsion. This aspect is further investigated in Section 8.1.

With regard to structural optimization, the less slender load envelope would yield a heavier

structure. The reason is: with a slender load envelope, the ratio between bending moment and

torsion is more constant. Hence, the stress distributions and load paths among the different

load cases are more similar.

Therefore, the maximum MLA amplitude for the +2.5g and -1g is set to 8° with

following algorithm:

(4.2)

with:

: aileron deflection [deg],

: commanded load factor [-],

: dynamic pressure at design cruise speed [Pa],

: actual dynamic pressure [Pa].

An example of the MLA deflection: at the maneuvering speed of the D150 where the

dynamic pressure is low with B≈B0.52B , the MLA deflection at 2.5g is -15°. This

value is comparable to the MLA of the Lockheed L-1011 (-13° at 2.5g) [77].

4 Modeling of load alleviation systems

4.3 Gust load alleviation concept

Requirements

Beside for MLA, symmetric aileron deflections are also used to reduce the lift increment

during gust encounters – which also evokes a reduction of wing bending moment. Following

constraints are taken into account for the gust load alleviation (GLA) implemented here:

•Only basic control system elements are used. Those elements comprise proportional,

integral, derivative terms as well as low-pass and high-pass filters.

•A delay time between the signal detection at the sensor and the control surface

actuation is considered. Wildschek [99] applied a delay of 60 ms, while a maximum

value of 100Bms should not be exceeded. In the simulations for this work, a minimum

delay time of 60Bms is assumed.

•A maximum aileron deflection of 10° and a deflection rate of 40°/s – as applied by Xu

[105] – are not exceeded.

Input parameters for GLA

Existing aircraft with GLA function use inertial or aerodynamic sensors or a combination of

both to reduce loads or improve ride comfort [80]. On both reference aircraft, GLA only using

inertial sensors hardly contributes to load reduction during 1-cos gust encounters, and this is

caused by the following:

•The maximum wing loads predominantly emerge when the gust base frequency

defined in Equation (3.4) is approximately equal to the first wing bending frequency.

•The frequency of the first wing bending mode of both reference aircraft lies between

2.0BHz and 3.5BHz.

•With an assumed delay of 60Bms during a gust encounter, the first wing bending

oscillation would almost reach the maximum displacement – with it the maximum

bending moment – before the ailerons start to deflect.

Therefore, aerodynamic sensors are considered in the control algorithm. The sensors are

assumed to be placed at the aircraft nose and the input parameter is the angle of attack

increment due to gust as defined by König et al. [55]:

,(4.3)

with:

: angle of attack increment due to gust [rad],

: measured angle of attack [rad],

: aircraft pitch angle [rad],

: aircraft vertical speed [m/s],

: aircraft true airspeed [m/s],

4.3 Gust load alleviation concept

: aircraft pitch rate [rad/s],

: distance between aerodynamic sensor and aircraft center of gravity [m],

: vertical wind speed [m/s].

Using the aerodynamic sensors at the aircraft nose also has the advantage that there is a time

buffer between the gust detection at the nose and the gust hitting the wing. Hence, the

effective delay of the aileron deflection is significantly smaller. As an example: at a design

cruise speed of 256.0Bm/s TAS and with the 25% of the mean aerodynamic chord (MAC)

placed 16Bm behind the aircraft nose, it takes 62.5Bms for the gust to reach the 25%BMAC after

being detected. In this case, the effective delay of the aileron deflection is 0Bms, and the flight

control computer still has a buffer of 2.5Bms – if the aileron should start to deflect when the

gust reaches the 25%BMAC.

Synthesis of GLA transfer function

Figure 4.3 shows the block diagram of the GLA control loop, with the gust angle of attack as

input and the aileron deflection as output. Since the dynamic behavior of the aircraft is not

affected by the GLA, it is a feed-forward controller. This aspect contributes to the simplicity

in the simulations significantly, as opposed to a feedback controller. Moreover, the delay time

between the gust detection at the nose and the aircraft response is assumed to be included in

the aircraft block in Figure 4.3.

Figure 4.3. Block diagram of feed-forward GLA

For the first step, a proportional term is considered for the GLA, and the amplification factor

is set to -2.0. The term refers to the aileron deflection in the aerodynamic

coordinate system. The value of -2.0 for is derived by applying the potential theory

elaborated in Schlichting-Truckenbrodt [84]: for a trailing edge control surface with a relative

rudder chord of 0.25 and an aerodynamic effectiveness of 0.75, the derivative is 0.5. In

other words, a control surface deflection of 1° generates lift equivalent to a change in angle

of attack by 0.5°. Figure 4.4 shows the orientations of and on a thin wing profile.

Figure 4.4. Illustration of angle of attack and aileron deflection

4 Modeling of load alleviation systems

As reference: the aileron relative chord of the D150 configuration is 0.30, and the aileron on

the ALLEGRA configuration has a relative chord of 0.26. Thus, with an amplification factor

of -2.0, in a steady state and with rigid structure, the aileron deflection roughly

compensates the lift increment at the wingtip area due to a change in the angle of attack. For

the aileron deflection in the hinge coordinate system, the gain is calculated by:

,(4.4)

with:

: sweep angle of the hinge line [deg].

Since gust encounters are transient phenomena and the maximum loads occur within one

second after the gust detection at the aircraft nose, an inclusion of an integral term in the

controller is seen as unnecessary. A derivative term has the advantage that it can reduce the

phase lag caused by the delay, however the control amplitude increases at higher frequencies.

This combination will lead to an accordingly high commanded aileron travel rate and also

high hinge moment values. For this reason, no derivative term is included in the controller.

Beside the proportional term, a second-order low-pass filter is set at 10BHz to further avoid

having excessive commanded aileron travel rates and hinge moments at small deflection

amplitudes. The cutoff frequency of 10BHz also roughly represents the bandwidth of control

surfaces with hydraulic actuation according to Brockhaus et al. [7]. Furthermore, a second-

order high-pass is set at 0.1BHz to eliminate offsets in the measurement of parameters

involved in Equation (4.3).

The delay time is adjusted to the airspeed, so that the ailerons are deflected after a constant

distance of gust penetration to prevent deflecting the ailerons too early or too late at different

airspeeds. With a defined minimum of 60 ms, the delay time is expressed by:

,(4.5)

with:

: delay time [s],

: x-position of the wing [m],

: true airspeed [m/s].

However, the position is not exactly defined yet; this can range e.g. from the foremost

leading edge to the sternmost trailing edge. According to a study elaborated in Section 8.2, it

turns out that setting to 16Bm on the D150 configuration yields the largest reduction of

the wing root bending moment. On the ALLEGRA configuration, is set to 18Bm to

maximize the load alleviation effect. Figure 4.5 visualizes these two positions, and it is

apparent that the ailerons should start deflecting relatively soon after the gust hits the

foremost leading edge of the wing.

With the selected controller features, the transfer function of the GLA with the commanded

aileron deflection as output and gust angle of attack as input is:

4.3 Gust load alleviation concept

(a)

(b)

Figure 4.5. Visualization of the reference positions xwing on D150 (a) and ALLEGRA (b)

,(4.6)

with:

,(4.7)

,(4.8)

, (4.9)

and:

: GLA transfer function [-],

: commanded aileron deflection [rad],

: angle of attack increment due to gust [rad],

: frequency [Hz],

: GLA gain [-],

: transfer function of the low-pass filter [-],

: transfer function of the high-pass filter [-],

: transfer function of the delay time [-],

4 Modeling of load alleviation systems

: low-pass cutoff frequency [Hz],

: high-pass onset frequency [Hz],

: delay time [s].

The term “commanded aileron deflection” implies that the rate limiter has not been applied

yet. With the GLA transfer function in Equation (4.6) and a given vertical wind speed in the

frequency domain, the commanded aileron deflection is calculated by:

,(4.10)

with:

: commanded aileron deflection [rad],

: GLA transfer function [-],

: angle of attack increment due to gust [rad].

Aileron rate limiter

To meet the requirement of the maximum GLA deflection rate, the deflection command is

transformed into the time domain so that a rate limiter can be applied. In the time domain, any

commanded rate magnitude of larger than 40°/s is limited to 40°/s, and any deviation from the

commanded deflection is compensated with a maximum rate of 40°/s. Figure 4.6 shows

exemplary commanded and actual aileron deflections ( and ) for three different gust

gradients ranging from 9 to 107Bm together with the local angles of attack increment due to

gust at 25% MAC. The true airspeed is 256.0 m/s which is equal to the design cruise speed

of the D150 configuration at an altitude of 7000 m. On the short and medium gusts, it is

apparent that the rate limiter intervenes and the actual aileron deflections have an

intermittent lag compared to the commanded deflection . On the long gust, the commanded

aileron deflection rate is low enough that the actual deflection can follow the command

without any intervention of the limiter. Since the commanded aileron deflection is always

below 10° for the considered gusts, the GLA travel limiter at 10° does not intervene. As a

remark: the influence of the low-pass filter is visible for the shortest gust: the gust angle of

attack reaches its maximum earlier compared to the commanded aileron deflection . On

the longest gust, their maximums emerge simultaneously.

Figure 4.6. Comparison between actual ξ and commanded aileron deflections ξc

4.3 Gust load alleviation concept

Integration of GLA in the 1-cos gust simulation

To integrate the derived GLA in the 1-cos gust simulations, a sub-workflow for step 3 of the

workflow shown in Section 3.7 is setup. At first, 1-cos gust time histories encountered by the

aircraft are created in the time domain and transformed into the frequency domain. In the

frequency domain, gust angles of attack are calculated and multiplied with the GLA

transfer function to obtain the commanded aileron deflections . These are transformed back

into the time domain, and the rate limiting algorithm is applied. Subsequently, the actual

aileron deflections are input as time histories into MSC.Nastran, and the aircraft responses

are calculated. Figure 4.7 visualizes this sub-workflow.

Figure 4.7. Sub-workflow of the GLA integration in the 1-cos gust simulation

4 Modeling of load alleviation systems

5 Methodology of fatigue analysis

This chapter describes the calculation of fatigue damage induced by continuous turbulence

and ground-air-ground cycles. For the first step, reference mass configurations, flight phases

and turbulence parameters are defined for the each aircraft. Simulations using those

parameters are run, and aircraft responses caused by the turbulence are extracted. From the

responses, load collectives of the active and passive aircraft are calculated, compared and

analyzed. In addition, strain/stress collectives of each aircraft are investigated to calculate the

fatigue damage due to continuous turbulence. For the active aircraft, the same GLA algorithm

as described in Section 4.3 is used.

5.1 Reference flight parameters

The first parameters to be defined are the mass configurations of the reference aircraft. The

objective lies in defining the worst-case conditions for the loads evoked by turbulence. In

doing so, the mass aspect is divided into two categories:

•Payload masses. During cruise flight, the wing loads – especially at the root – become

larger with increasing fuselage mass. The same applies to incremental turbulence

loads. Therefore, to induce the maximum wing loads in the turbulence analysis, the

aircraft shall carry the maximum payload. The term maximum payload implies that the

payload masses bring an empty aircraft (OEM configuration) to its maximum zero fuel

mass (MZFM).

•Fuel masses. In gust encounters, the highest wing loads typically occur when the gust

base frequency (Equation (3.4)) is near the first wing bending frequency, as

mentioned in Section 3.2. This means, the first wing bending mode has a large

contribution to the wing loads. On the other hand, in continuous turbulence, most of

the energy is stored in the lower frequency range as shown in Section 5.2. Hence, if

the first wing bending mode occurs at a lower frequency, it will receive more energy

from the turbulence. For this reason, the fuel masses for the reference aircraft should

be maximized so that the frequency of the first wing bending is as low as possible. In

this case, the fuel masses should bring the reference aircraft from the MZFM to their

respective maximum take-off mass (MTOM) with the fueling sequence described in

Section 2.2.

Based on the fuel masses, flight routes for the reference aircraft are searched to estimate the

duration of each flight phase. The criteria of the flight route search are:

•The fuel mass calculation is carried out with Fuelplanner [29]. The reference aircraft

for the fuel consumption estimation is the Airbus A320.

•JAR international standard [47] is taken into account for the reserve fuel mass.

•The sum of the trip and reserve fuel should roughly equal the defined fuel masses.

5 Methodology of fatigue analysis

Since the D150 and ALLEGRA configuration have slightly different design masses, each of

them has a different flight route for the turbulence analysis. The D150 is assigned for the

route from Berlin-Tegel (EDDT) to Porto (LPPR), while the route Berlin-Tegel (EDDT)-

Athens International (LGAV) is selected for the ALLEGRA configuration. More details can

be found in Section 6.3 and 7.3.

Based on the flight routes, the durations of the climb, cruise and descent as well as the fuel

masses in the respective phases are estimated. The reference flight condition for each phase is

also defined. For the cruise flight phase, it is assumed that the remaining fuel mass is roughly

the take-off fuel subtracted with the half of the trip fuel. Using the estimation, fuel mass

models for the respective aircraft and flight phases are generated with ModGen.

5.2 Reference atmospheric turbulence

The reference turbulence considered is the von Kármán spectrum with a scale of turbulence of

762 m (2500 ft) as prescribed in CS25.341(b)(2) [20]. The power spectral density (PSD) of

the von Kármán spectrum is defined as follows [40]:

,(5.1)

with:

: power spectral density [m²/s²/Hz],

: root mean square of vertical wind speed [m/s],

: scale of turbulence [m],

: aircraft true airspeed [m/s],

: frequency [Hz].

Figure 5.1 shows an exemplary PSD of the von Kármán spectrum for vertical wind with a

root mean square (RMS) of 1.0Bm/s, a scale of turbulence of 762Bm and an aircraft true

airspeed of 256.0Bm/s.

Figure 5.1. Exemplary von Kármán power spectral density

5.2 Reference atmospheric turbulence

For each reference flight phase, a reference root mean square (RMS) of the vertical wind

speed is defined based on the diagram in Figure 5.2 which is taken from MIL-STD-1797A

[96]. For the turbulence analysis, it is assumed that the turbulence intensity is moderate such

that the probability of exceedance of the RMS is approximately 10-3.

Figure 5.2. Probability of exceedance for various turbulence RMS [96]

To derive the vertical wind speed in the frequency domain, the square root of the reference

spectrum is given a random phase angle for each frequency step. Equation (5.2) is used to

calculate one side of the two-sided Fourier transform of the vertical wind speed in MATLAB:

,(5.2)

with:

: vertical wind speed [m/s],

: frequency [Hz],

: number of elements in the frequency vector [-],

: turbulence power spectral density [m²/s²/Hz],

: random phase angle [rad].

Subsequently, is adjoined with its flipped complex conjugate form. For an adequate

comparability, the phase distribution is set equal for the passive and active

aircraft. In other words: the climb, cruise and descent phase might have different phase

distributions. In each flight phase however, the passive and active aircraft encounter the same

turbulence with the same phase distribution.

5 Methodology of fatigue analysis

5.3 Aircraft responses in turbulence analysis

Transfer function generation

For the defined reference flight phases and the respective turbulence spectra, aircraft

responses can be calculated using transfer functions (TF) which are generated using

MSC.Nastran. The physical principles of the TF generation are the same as gust load

calculations, except that the inputs are spectral excitations and the outputs are obtained in the

frequency domain instead of the time domain. Since transfer functions are single input single

output (SISO) systems, one transfer function is necessary for every combination of input and

output quantities.

In this case, the input quantities are unit vertical wind speed and unit aileron deflection, where

the output quantities consist of:

•cut loads at the wing root, outer wing section (at 70% half-span) and HTP root,

•aileron hinge moment,

•major principal strain/stress of selected structure elements on the lower skin.

Aileron deflection

The GLA transfer function used for the turbulence analysis is the same as described by

Equation (4.6). The input is continuous turbulence expressed by instead of 1-cos

gusts.:

,(5.3)

where:

: GLA transfer function [-],

: commanded aileron deflection [rad],

: angle of attack increment due to turbulence [rad],

: frequency [Hz],

: GLA gain [-],

: transfer function of the low-pass filter [-],

: transfer function of the high-pass filter [-],

: transfer function of the delay filter [-].

The main feature of the transfer function remains the gain factor that is set to

. The second-order low-pass at 10BHz is considered to prevent having

excessive deflection rates at higher frequencies. The second-order high-pass at 0.1BHz

is implemented to avoid having static deflections in a constant wind field. The airspeed-

dependent delay is adopted to adjust the timing of the aileron deflection.

With the vertical wind speed derived in Section 5.2, the commanded aileron deflection is

calculated with:

5.3 Aircraft responses in turbulence analysis

,(5.4)

with:

: commanded aileron deflection [rad],

: GLA transfer function [-],

: angle of attack increment due to turbulence [rad],

: vertical wind speed [m/s],

: true airspeed [m/s].

Subsequently, the commanded aileron deflection is transformed into the time domain. An

aileron rate limiter which is set to a maximum of 40°/s is applied to obtain the actual aileron

deflection. The actual aileron deflection is then transformed back into the frequency domain

for further processing.

Aircraft response calculation

Analogous to the dynamic gust simulations, the highest frequency considered in the

turbulence analysis is 50BHz. With the Nyquist-Shannon sampling theorem [67], this yields a

maximum time increment of 10Bms. To generate statistically relevant load collectives, a

sufficient number of time steps in the observed time period is necessary. On the other hand,

the computation time and memory requirement also rise with increasing number of time steps.

In this case, a number of 10⁵ time steps are seen as a reasonable compromise. The number of

time steps multiplied with the time increment yields an observed time period of 1000Bs and a

frequency increment of 10-³BHz. To obtain this discretization, the transfer functions extracted

from MSC.Nastran are interpolated. This is done since a direct output of 5·10⁴ frequency

steps (from 10-³BHz to 50BHz) is not affordable with regards to computation time and memory

requirements.

As a remark: the interpolated transfer functions with 5·10⁴ frequency steps are still one-sided.

To obtain the two-sided form, the transfer functions have to be adjoined with their flipped

complex conjugate form, so that the vector length in the frequency domain is 10⁵ and equal to

the number of samples in the time domain. Furthermore, to maintain a comparability of the

turbulence loads between the passive and active aircraft, the phase angle distribution in

Equation (5.2) is identical in each flight phase for both aircraft.

For the passive aircraft, the responses in the frequency domain are calculated using a

multiplication of the vertical wind speed and the corresponding transfer functions:

.(5.5)

For the active aircraft, the equation has an additional term that is a function of the aileron

deflection angle:

.(5.6)

Subsequently, the responses are transformed into the time domain for further analysis.

5 Methodology of fatigue analysis

Turbulence analysis sub-workflow

Figure 5.3 shows a sub-workflow featuring the aforementioned steps including the derivation

of the vertical wind speed in Equation (5.2). For the passive aircraft, the sub-workflow has

significantly fewer steps since the aileron deflection is zero and the corresponding operations

are skipped.

Figure 5.3. Sub-workflow of aircraft response calculation in continuous turbulence

5.4 Rainflow-counting

To derive the collectives from the aircraft responses in continuous turbulence, a rainflow-

counting algorithm [68] is applied. The operations conducted are as follows:

1. At first, the time history of e.g. an aircraft response quantity is reduced to its local

maxima and minima as shown by a small example in Figure 5.4.

Figure 5.4. Exemplary time history reduced to its peaks

5.4 Rainflow-counting

2. The graph is then rotated 90° clockwise and imagined as a pagoda roof.

3. For the ‘rain’ on the left side, each local maximum is imagined as a source of

raindrops which start to flow. Vice versa, for the ‘rain’ on the right side, raindrops

appear at each local minimum. Figure 5.5 visualizes the emerging raindrops. It is

apparent that a few raindrops stop flowing before reaching the edge of the imagined

roof, because they will merge with raindrops starting at an earlier peak, as explained in

the next step.

(a) (b)

Figure 5.5. Raindrops emerging on the left (a) and right (b) side of the pagoda roof

4. The flow of the raindrops is continued, and it stops if either:

◦it reaches the end of the time history,

◦it merges with a flow which started at an earlier peak, or

◦the next raindrop source has a higher value (for the left side rain) or a lower value

(for the right side rain).

Figure 5.6 shows the flow continuation.

5 Methodology of fatigue analysis

(a) (b)

Figure 5.6. Rainflow continuation on the left (a) and right (b) side of the pagoda roof

5. Subsequently, each rainflow is counted as a half loading cycle, and half-cycles with

the same magnitude are grouped together. In this example, half-cycles with the same

color (from the left and right side each) form a full loading cycle, see Figure 5.7. In

case of time histories with a large number of peaks, the grouping of the loading cycles

can be conducted in amplitude classes to limit the number of terms in the fatigue

damage accumulation as explained in Section 5.6.

Figure 5.7. Visualization of load cycle generation in rainflow-counting algorithm

The algorithm used in this thesis is developed by Nieslony [68]. With those generated cycles,

load collectives – frequencies of occurrence as a function of discrete amplitudes classes – are

derived.

5.5 Ground-air-ground cycle

Since ground-air-ground cyclic loads are also relevant for the structure fatigue [70], a

simplified ground-air-ground cycle is considered – additionally to the turbulence loads. In this

case, the aircraft is assumed to have zero stress on the ground, and the stresses during flight

are taken from a reference +1.3g maneuver calculation. The load factor of 1.3 should

represent the typical maximum load factor reached in a flight mission, particularly during

take-off [25]. This difference between the minimum and maximum load factor during a flight

cycle is also what would emerge in the rainflow-counting as the one cycle with the largest

amplitude, regardless of other smaller cycles in between. This aspect is visualized by the blue

cycle of the stress load factor in an exemplary flight mission in Figure 5.8. As a remark: a

stress load factor of zero implies the condition on ground, while peak 1 indicates the

maximum load factor of 1.3 during a flight cycle. Furthermore, peak 2 represents the cruise

flight, peak 3 and 5 show the load factor during turns, while peak 4 equals the load factor

during descent initiation.

Figure 5.8. Stress cycles during an exemplary flight mission

The focus of the fatigue analysis is the major principal stress on the lower skin of the wing

and the HTP. Therefore, landing cases are not considered since large parts of the lower skin

are loaded with compressive stress during the impact. Moreover, +1.15g turns – which

correspond to 30° bank angle – flown during flight are seen as irrelevant since the load factor

fluctuation is only 0.15g, as visible between peak 2 and 4 in Figure 5.8.

For the mass configuration, the aircraft is assumed to have the take-off configuration for the

reference mission that is the respective MTOM according to Section 5.1. Table 5.1 defines a

trim condition for both reference aircraft that should represent the climb phase. The pitching

velocity for the trim calculation is obtained using Equation (3.2). The climb phase is

considered instead of the take-off condition since the high-lift systems – that are necessary for

take-off at MTOM and change the spanwise lift distribution – are not modeled.

5 Methodology of fatigue analysis

Table 5.1. Parameters of the climb condition

Parameter Value

Altitude 4572 m (FL150)

Airspeed 181.6 m/s TAS (280 KEAS)

Mach number 0.563

Dynamic pressure 12700 Pa

Load factor 1.3

The MLA deflection of the active aircraft is calculated by:

,(5.7)

with:

: aileron deflection [deg],

: dynamic pressure at design cruise speed [Pa],

: dynamic pressure in the climb phase [Pa].

With the dynamic pressure of the climb phase, Equation (5.2) yields -2.5° for both reference

aircraft. For the fatigue damage calculation, the stress amplitudes are half of the stresses

during the +1.3g maneuver.

5.6 Fatigue damage accumulation

For the linear fatigue damage accumulation, the Palmgren-Miner’s rule [18] is applied. With a

given S-N (stress-cycle) curve for the respective material and stress ratio, the fatigue damage

is accumulated as following:

,(5.8)

with:

: fatigue damage per hour,

: index for amplitude classes,

: frequency of occurrence of respective amplitude class per hour,

: fatigue life limit of respective amplitude derived from S-N curve.

As an example to Equation (5.8): one loading cycle at a low amplitude causes a different

amount of fatigue damage compared to one cycle at a high amplitude . If each of both

cycles occur once, the total fatigue damage is the sum of the individual damage values.

This operation can be extrapolated to as many different amplitudes with different numbers of

cycles each. Furthermore, the Palmgren-Miner’s rule states that structural failure is expected

to occur when an accumulated fatigue damage of 1.0 is reached. While this method is

commonly used for metal fatigue, it is also taken as a first approximation for composite

fatigue. The S-N curves used in this thesis are described in Section 6.3 and 7.3.

6 Loads, optimization and fatigue results of D150 configuration

6 Loads, optimization and fatigue results of D150

configuration

This chapter evaluates the loads, optimization and fatigue results for the D150 configuration.

At first, the parameter space considered in the design process is listed. With those parameters,

iterative cycles of loads analysis and structural optimization according to the design process

workflow described in Section 3.7 are run. The resulting design loads, structural masses and

aeroelastic parameters after the final cycle are listed, and a comparison between the active and

passive aircraft is given.

The turbulence loads and fatigue analysis follows. It begins with a description of the reference

flight mission with its parameters and turbulence intensities. Subsequently, the turbulence

loads are calculated for each flight phase and their collectives are derived using the rainflow-

counting algorithm. With the load collectives, a first overview of the differences between the

active and passive aircraft is gained. The calculations with the continuous turbulence are also

conducted for selected structural elements on the lower skin of the wing and HTP, and

collectives of the major principal stress are derived. Furthermore, stresses emerging from a

reference 1.3g maneuver – that represents a ground-air-ground cycle – are calculated. With

those stresses, the collectives for the reference flight cycle are derived, and the fatigue

damage values for the active and passive aircraft are calculated with the methodology

described in Chapter 5. Subsequently, the differences in the fatigue behavior between the

active and passive aircraft are discussed.

6.1 Parameter space for loads analysis and structural optimization

This section begins with an overview of the parameter space for the loads analysis that

comprises the mass configurations, flight conditions as well as gust and maneuver cases

considered in the simulations. Subsequently, the parameters set in the structural optimization

comprising the objective function, design variables and constraints are explained.

6.1.1 Mass configurations

According to CS25.321, load calculations have to be conducted for a representative number of

mass configurations between the design minimum and maximum mass while covering the

whole design envelope [20]. Theoretically, a large number of mass cases has to be taken into

account (>>100) to cover the design mass envelope adequately while taking various mass

distributions into account. For this thesis however, the number of mass configurations

considered in the loads analysis is set to nine to limit the computational effort for the loads

analysis. The mass cases are defined so that they cover the whole range between the empty

and maximum take-off mass with a large range for center of gravity (CG) locations. As a

comparison: Klimmek [54] covered the mass and balance envelope using four mass

6 Loads, optimization and fatigue results of D150 configuration

configurations. However, since dynamic loads are considered in this thesis and they are

expected to be more sensitive to changes in the mass configuration, nine mass cases are

considered as adequate:

•one operating empty mass (OEM) case,

•two lightly loaded cases, each one for the forward and rear CG position,

•three heavy payload cases: forward and rear CG as well as one with middle CG at the

maximum zero fuel mass (MZFM),

•three maximum take-off mass (MTOM) cases resulting from the heavy payload cases

with fuel masses added.

Figure 6.1 and Table 6.1 show an overview of the mass cases. They are labeled according to

Pinho Chiozzotto [72].

Figure 6.1. Mass and balance diagram of considered configurations – D150

Table 6.1. Overview of the mass configurations – D150

Label Mass [kg] CG [% MAC] Notes

MOOee 40638 26.3 Operating empty mass

MCFfe 45000 13.0 Forward CG, light payload

MCAae 45000 39.5 Rear CG, light payload

MHFFe 52988 16.0 Forward CG, heavy payload

MHAAe 52988 42.0 Rear CG, heavy payload

MZmMe 60548 29.0 Middle CG, maximum zero fuel mass

MTFFJ 72507 16.0 MHFFe with 19.5 t fuel

MTAAJ 72507 35.0 MHAAe with 19.5 t fuel

MTmMG 72507 28.0 MZmMe with 12.0 t fuel

6.1 Parameter space for loads analysis and structural optimization

6.1.2 Flight conditions within the design envelope

Beside the mass configurations, the definition of flight conditions for the loads analysis is also

necessary. To limit the number of simulations, the considered flight conditions consist of three

selected altitudes and the respective airspeeds , and . While the design cruise speed

and the design dive speed are defined during the aircraft specification, the

maneuvering speed needs to be derived first. Assuming that the aircraft has the minimum

dynamic pressure to perform a 2.5g pull-up maneuver at MTOM at the reference using a

maximum lift coefficient of 1.4, is calculated by:

,(6.1)

with:

: reference maneuvering speed [m/s],

: maneuver load factor, set to 2.5 [-],

: maximum take off mass [kg],

: gravitational acceleration [m/s²],

: maximum incompressible lift coefficient, set to 1.4 [-],

: wing reference area [m²],

: air density [kg/m³].

Previous studies show that the largest gust loads on the wing are reached at between sea

level and approximately 7000 m [34]. The latter is the altitude where the design cruise speed

equals the design cruise Mach number: and above which the Mach number

is the constraining factor instead of the airspeed . Hence, only flight conditions at

between sea level and are considered for the gust loads analysis. As a remark:

is not necessarily equal to the economic cruise Mach number.

For the maneuver loads analysis, the aim of the flight condition definition is to cover the

envelope of the dynamic pressure and Mach number. This is achieved by taking airspeeds

from to and altitudes from sea level to into account. At , the aircraft

has the minimum dynamic pressure to perform 2.5g pull-up maneuvers, and it reaches the

maximum dynamic pressure at . Flight conditions at sea level correlate with relatively low

Mach numbers, while the highest Mach numbers can be flown at approximately

and above. To further reduce the number of simulations, altitudes above are

neglected. Figure 6.2 and Table 6.2 give an overview of the considered flight conditions in the

simulations. The labels are also based on Pinho Chiozzotto [72].

Table 6.2. Overview of the flight conditions – D150

Altitude [m] VA [m/s TAS] Label VC [m/s TAS] Label VD [m/s TAS] Label

0 129.9 OA000 180.0 OC000 205.6 OD000

3000 150.8 OA100 208.9 OC100 234.5 OD100

7000 187.2 OA230 256.0 OC230 277.9 OD230

6 Loads, optimization and fatigue results of D150 configuration

Figure 6.2. Flight conditions in the design envelope – D150

6.1.3 Gust load conditions

For the 1-cos gust loads analysis according to CS25, the aircraft is assumed to encounter

symmetric, vertical gusts during level flight. The gust shape is defined by:

,(6.2)

with:

: gust shape [m/s],

: design gust speed [m/s],

: distance penetrated into the gust [m],

: gust gradient [m].

For the load calculation, sufficient gust gradients ranging from 9Bm to 107Bm (30Bft to 350Bft)

must be investigated in dynamic simulations. The design gust speed is a function of the

altitude and the gust gradient [20] as defined by:

,(6.3)

with:

: design gust speed [m/s],

: altitude dependent reference gust speed [m/s],

: altitude dependent profile alleviation factor [m/s],

: gust gradient [m].

The gust profile alleviation factor is defined to be 1.0 at the maximum operating altitude,

and it decreases linearly to the value at sea level calculated by:

6.1 Parameter space for loads analysis and structural optimization

,(6.4)

with:

,(6.5)

,(6.6)

and:

,(6.7)

,(6.8)

with:

: altitude [m],

: maximum operating altitude [m],

: maximum landing mass [kg],

: maximum take-off mass [kg],

: maximum zero fuel mass [kg].

In this thesis, a total of seven gust gradients are considered. Figure 6.3 illustrates the gust

profiles with a reference gust speed of 17.07Bm/s and a profile alleviation factor of 1.0, and

Table 6.3 lists the corresponding gust gradients.

Table 6.3. Overview of the gust gradients

Gust number 1234567

Gust gradient [m] 9 15 30 46 61 76 107

Figure 6.3. Overview of the 1-cos gust profiles

With nine mass configurations, three altitudes, seven gust gradients and two gust directions –

vertical upward and downward – each, there are 378 gust cases that are considered in the

loads analysis.

6 Loads, optimization and fatigue results of D150 configuration

6.1.4 Maneuver load conditions

For the maneuver loads analysis at the flight conditions stated in Table 6.2, symmetrical 2.5g

pull-up and -1g push-down maneuvers are taken into account. According to the V-n diagram

defined in CS25.333 [20], the +2.5g pull-up is to be investigated between and , while

the -1g push-down has to be considered between to . is the stall speed when

performing a -1g push-down. However, to simplify the airspeed calculations, is assumed

to have the same value as . Besides, to further reduce the number of load cases, only the

edges of the maneuvering envelope are considered at every altitude; those are +2.5g pull-up at

and as well as -1g push-down at and . Figure 6.4 illustrates the considered

maneuver cases that are investigated for every altitude. With nine mass configurations, three

altitudes and four maneuvers each, there are 108 maneuver cases considered in the loads

analysis.

Figure 6.4. Considered maneuver cases in an exemplary V-n diagram

6.1.5 Overview of the optimization task

After the simulations with the parameters described in the Subsections 6.1.1 to 6.1.4 and the

post-processing according to Section 3.3, the loads are fed into the structural optimization.

The objective of the optimization task lies in minimizing the structural mass while complying

with the constraints described in Subsection 6.1.6.

On the D150 configuration, every skin area between two ribs, spar area between two ribs and

every rib is counted as one design field each. The term design field implies that the design

variable is constant in the respective area. The design variable in every design field is the

material thickness. The optimization process is conducted separately for each component

(wing and HTP). Moreover, only the starboard half of the wing box and HTP box is included

in the optimization, and the resulting properties are then mapped onto the port half on the

respective component. With 30 ribs in a wing box half, there are 146 design fields for the

wing. An HTP half has 14 ribs and a total of 66 design fields.

6.1 Parameter space for loads analysis and structural optimization

6.1.6 Constraints in the structural optimization

The constraints considered in the structural optimization are von-Mises stress, buckling

stability and minimum thickness. With an ultimate strength of 441BMPa for aluminum

and a safety factor of 1.5, a limit von-Mises stress of 294BMPa is taken into account in

the structural optimization. The calculation of von-Mises stress is defined by:

,(6.9)

where:

: von-Mises stress [Pa],

: tensile stress in x-direction [Pa],

: tensile stress in y-direction [Pa],

: shear stress [Pa].

For buckling stability analysis, the skin fields of the wing are assumed to be sized by

compressive buckling, while the spars and ribs are sized by shear buckling [54]. In the

optimization, the buckling phenomenon is simplified into a two-dimensional buckling by

assuming the buckling fields to be infinitely long plates with a certain width. The width of the

buckling field is set to 15Bcm which represents the average distance between two stringers.

With the buckling field material thickness, bending stiffness and width, the allowable

compressive stress is calculated by:

, (6.10)

with:

: compression buckling stress [Pa],

: compression buckling coefficient [-],

: tensile modulus [Pa],

: Poisson ratio [-],

: material thickness [m],

: buckling field width [m].

With the assumption that the buckling field has an infinite aspect ratio and the edges are

simply supported, the compressive buckling coefficient is set to 4.0. This value represents

the lower boundary of the coefficient as shown e.g. by Timoshenko et al. [93] p.B353. To

fulfill the buckling constraint, the present minor principal stress has to be smaller in

magnitude than the buckling stress.

The allowable shear stress is calculated by:

, (6.11)

with:

: shear buckling stress [Pa],

: shear buckling coefficient [-],

6 Loads, optimization and fatigue results of D150 configuration

: tensile modulus [Pa],

: Poisson ratio [-],

: material thickness [m],

: buckling field width [m].

The shear buckling coefficient can be taken from diagrams that are shown e.g. by Timoshenko

et al. [93] p.B383. In the structural optimization, the maximum shear stress in every element

must be smaller than the allowable shear buckling stress.

For the minimum thickness, a value of 2Bmm is selected for every design field. Furthermore, a

constraint concerning the aileron effectiveness is considered. In this case, the aileron

effectiveness has to be positive at / +15% as explained in Section 3.5.

6.2 Comparison of design loads, structural masses and aeroelastic

parameters

With the parameters described in Section 6.1, the process explained in Section 3.7 is run. The

resulting design loads, structural masses and aeroelastic parameters are elaborated in the

following subsections.

6.2.1 Design loads

Figure 6.5 visualizes the resulting wing bending moment envelopes of the passive aircraft

after ten cycles of loads analysis and structural optimization, while Figure 6.6 shows the

respective envelopes of the active aircraft. It is apparent that maneuvers evoke the largest

bending moment on both aircraft, whereas the active aircraft has 6.2% less wing root

bending moment. At the outer section ( =11Bm) the reduction of wing bending moment due to

maneuver is 18.4%. The gust loads generate 10.7% less bending moment at the root of the

active aircraft, whereas a decrease by 21.0% results at the outer section. Judging by the

bending moment of the active aircraft alone, it is plausible to assume that the MLA could be

set more aggressively to match the levels of the gust loads. At this point however, it has to be

checked whether larger MLA deflections are still aerodynamically feasible – especially at

high Mach numbers. If they are feasible, the additional reduction of the bending moment will

come together with a further increase in torsion as shown in the next paragraphs. In the worst

case, the increase in torsion due to a more aggressive MLA would lead to heavier system and

structural masses.

6.2 Comparison of design loads, structural masses and aeroelastic parameters

Figure 6.5. Wing bending moment of passive D150

Figure 6.6. Wing bending moment of active D150

While the 1D envelopes of Figure 6.5 and Figure 6.6 give an insight into the global trend of

the cut loads, 2D envelopes provide an overview of the correlation between the load

components at the respective positions. For this aim – also for the analysis of turbulence loads

– three reference monitoring stations at the wing root, wing outer section and the HTP root

with the respective local coordinate systems are defined, see Figure 6.7.

6 Loads, optimization and fatigue results of D150 configuration

Figure 6.7. Selected cut load monitoring stations on D150

Figure 6.8 visualizes 2D load envelopes of the wing. It is apparent that the envelopes of the

active aircraft are rotated counter-clockwise in general, it means that the maximum bending

moment is reduced compared to the passive aircraft, however an increase in the torsion

is noticeable. At the outer section, the maximum torsion increases by 12.1%. At the root,

the increase in maximum torsion is 15.9%, whereas the magnitude of the minimum torsion

decreases by 5.2%. However, the rotation of the envelope is however not as clearly visible as

at the outer section. This is caused by the engine – that contributes to the loads at the root –

evoking large torsion due to its large lever between its CG and the wing’s LRA.

(a) (b)

Figure 6.8. 2D load envelope comparison on D150

The maximum bending moment and torsion on the wing is reached during maneuvers,

predominantly with the mass configuration MTFFJ (MTOM with forward CG, Table 6.1).

Moreover, the gust loads generally cause the envelopes to become rounder while the

maneuver loads form a narrow band, see Figure A-1(a) in the Appendix. With the load case

selection algorithm described in Section 3.3, the number of load cases for the structural

optimization ranges between 51 and 62.

6.2 Comparison of design loads, structural masses and aeroelastic parameters

Concerning the aileron hinge moments, the passive aircraft shows a maximum magnitude of

3152BNm during design maneuvers, while the active aircraft has to withstand moments up to

3355BNm during design gust encounters which is 6.4% higher. In this case, the actuators of the

active aircraft have to be slightly reinforced with regards to maximum torque.

6.2.2 Structural masses

Figure 6.9 shows the convergence history of the D150 wing box mass. However, the mass

convergence alone does not always guarantee a convergence of the skin thicknesses on each

design field. To quantify the latter in a number, the RMS of the relative change in material

thicknesses between each cycle is calculated. This operation is expressed by:

,(6.12)

with:

: root mean square of the change in material thickness between two cycles,

: counting variable for the cycle of loads analysis and structural optimization,

: number of design fields,

: counting variable for the design fields,

: material thickness.

Figure 6.10 shows the results.

After ten cycles of loads analysis and structural optimization, the wing box of the active

aircraft is 2.8% or 90Bkg lighter compared to the passive aircraft. Concerning the material

thickness convergence, the RMS values of thickness change between the last two cycles are

1.37% for the passive and 1.11% for the active aircraft.

In a loads and optimization process using static loads as demonstrated by Klimmek [54], the

wing box mass does not significantly change after three cycles. In this thesis however, the

convergence of the wing box mass is slower. This is caused by the number of load cases and

their selection algorithm:

•In total there are 108 quasi-steady maneuver and 378 dynamic gust cases considered to

calculate loads for the structural optimization.

•Before the optimization step, a new load case selection is conducted in every cycle.

Thus, the composition of load cases considered in the optimization step varies between

the cycles. In combination with the large number of load cases, an optimization with

the currently selected load cases may cause others to emerge as critical in the next

cycle.

Apart from those aspects, a decrease in wing box mass also reduces the wing stiffness. Due to

the bending-torsion-coupling of backward swept wings, the lower wing stiffness in turn

reduces the loads. This results in a decrease in wing box mass again in the next cycle. This

phenomenon contributes to the slower convergence of backward swept wing configurations

compared to forward swept ones, as shown in Subsection 7.2.2.

6 Loads, optimization and fatigue results of D150 configuration

During an aircraft design process however, a convergence in the structural optimization

cannot be striven to the last kilogram. The reason is: if a minor modification resulted in a

change in e.g. the secondary mass in a late stage, the entire loads analysis and structural

optimization procedure would have to be conducted again – which is not affordable.

Therefore, at a certain point of the design process, the structural layout is frozen and the target

loads are defined [95]. All following loads analyses are then mainly run to verify that the

results stay below those target loads.

The wing box masses shown in Figure 6.9 refer only to ideal load-carrying masses. Additional

masses due to joints, fasteners, access holes and their reinforcements are not considered.

According to Pinho Chiozzotto [71], an empirical mass factor of 1.45, that is multiplied with

the obtained wing box masses, delivers a reliable estimate for the total wing box mass. Hence,

with a mass factor of 1.45, the wing mass difference between the active and passive aircraft

would be 1.45·90Bkg = 130.5Bkg, assuming that the secondary masses comprising the systems

remain unchanged.

Figure 6.9. Wing box mass trend in the loads and optimization process of D150

Figure 6.10. RMS of material thickness change of D150 wing box

6.2 Comparison of design loads, structural masses and aeroelastic parameters

Figure 6.11 visualizes the difference of 2.8% in the wing box mass. Judging by the load

envelopes in Figure 6.8, the mass decrease of the active aircraft is explained by the lower

wing bending moment . On the upper skin of the passive aircraft, the area with a thickness

around 6.5Bmm in the middle wing section is larger compared to the active aircraft. On the

lower skin, a larger patch with thicknesses around 5.0Bmm is visible on the passive aircraft.

Near the wing root, the lower skin of the passive aircraft is approx. 0.2Bmm thicker which is

also explained by the higher wing bending moment compared to the active aircraft. Near the

wing tip, the area with the minimum thickness on the lower skin of the passive aircraft is also

smaller. On the other hand, the spars and ribs have similar thicknesses. On the HTP, there is

hardly any difference between the active and passive aircraft, as Figure 6.12 shows, and the

mass difference between both HTP boxes is below 1Bkg.

Concerning the structural dynamics, Table A-1 in the Appendix lists the frequencies of several

selected modes. The wing mode frequencies of the active aircraft are up to 2% lower

compared to the passive counterpart, otherwise the differences are negligible.

(a)

(b)

Figure 6.11. Wing material thickness distribution of D150

6 Loads, optimization and fatigue results of D150 configuration

(a) (b)

Figure 6.12. HTP material thickness distribution of D150

6.2.3 Aeroelastic parameters

According to CS25.629, aeroelastic stability calculations have to be conducted in the whole

flight envelope and with speeds up to +15%. Figure 6.13 shows the aeroelastic stability

envelope for the D150 configuration. The investigated aeroelastic stability requirements

comprise the aileron effectiveness and the flutter speed.

Figure 6.13. Design envelope for aeroelastic stability of D150

Aileron effectiveness

Since aileron effectiveness problems occur at high dynamic pressures, the speed +15% is

considered. Furthermore, with DLM aerodynamics, an increase in altitude only results in an

increase in the Mach number and thus a magnification of stability and control derivatives

since no transonic effects are considered. Therefore, the altitude is set to sea level. This flight

condition yields parameters listed in Table 6.4.

Table 6.4. Parameters of aileron effectiveness calculation on D150

Parameter Value

Mach number 0.6948

Air density 1.225 kg/m³

Dynamic pressure 34240 Pa

6.2 Comparison of design loads, structural masses and aeroelastic parameters

The flight mechanic derivative monitored in this analysis is the rolling moment coefficient

due to aileron deflection . In this case, the derivative of the elastic aircraft is

compared to that of the rigid aircraft and the ratio is the defined aileron

effectiveness. The mathematical formulation of the aileron effectiveness is shown in Equation

(3.8) and Table 6.5 shows the results of aileron effectiveness analysis of the D150

configuration.

Table 6.5. Aileron effectiveness values of D150

Aircraft model Aileron effectiveness value

Passive aircraft 0.131

Active aircraft 0.101

With both values being positive, no aileron reversal occurs at any speed up to +15%.

However, the active aircraft has a lower aileron effectiveness value since the wing material

thickness is generally lower than for the passive aircraft, hence the wing stiffness is also

lower. Nevertheless, no modification is needed to comply with the static aeroelastic

requirements.

Flutter speed

Another aeroelastic parameter to compare between the active and passive aircraft is the flutter

speed. For this aim, a subsonic flutter calculation is conducted using MSC.Nastran. Table 6.6

lists the parameters for the reference flight condition in the flutter calculation. The reference

Mach number is set to the equivalent of at sea level to achieve a subsonic reference flow

condition, and the air density is set accordingly. The selection of the Mach number is based on

the assumption that transonic flow conditions emerge at Mach 0.7. Moreover, the 50

Eigenmodes included in the calculation are assumed as sufficient since the potential flutter-

critical modes such as the first wing torsion, the second and third wing bending as well as

HTP torsion and bending are included. As derived in Section 2.3, a maximum reduced

frequency of 3.0 is considered.

Table 6.6. Parameters of flutter calculation on D150

Parameter Value

Reference Mach number 0.6042

Air density 1.225 kg/m³

Number of Eigenmodes 50

Considered reduced frequencies 0.01 to 3.0 with 300 sampling points

Figure 6.14 shows the damping curves of the flutter mode, and Figure 6.15 visualizes the

dominant vacuum mode shape involved in the flutter mode which is the symmetric HTP

torsion. This dominant mode shape is identified through a manual mode tracking toward the

low speeds of the frequency curve where no more changes in the mode sequence occur.

6 Loads, optimization and fatigue results of D150 configuration

Complete diagrams of the damping and frequency curves are attached in Figure A-2 in the

Appendix. As mentioned in Section 3.6, no complex flutter modes corresponding to the flutter

curves can be obtained using the KE-method.

In Figure 6.14, a threshold line at -3% structural damping is drawn (a critically damped

system has a structural damping value of 200% [66]). Since the flutter calculation with the

KE-method does not consider structural damping and a value of 3% may be taken into

account, the aircraft is assumed to flutter if a damping curve passes the -3% line. It is apparent

that the flutter speed is significantly higher than +15%. Hence, there is no risk of flutter in

the subsonic regime. Besides, there is almost no difference in the flutter speeds of the active

and passive aircraft. At the flutter points, the flutter frequencies of both aircraft range between

17.6 and 17.8BHz.

Figure 6.14. Curves of the flutter point of D150

Figure 6.15. Dominant Eigenmode involved at the flutter speed of D150

6.3 Turbulence loads and fatigue analysis

This section begins with a listing of the parameters of the reference flight mission considered

in the turbulence loads and fatigue calculations. With these parameters, cut load and stress

collectives caused by the atmospheric turbulence are calculated. Furthermore, stresses due to

a ground-air-ground cycle are also taken into account. Using reference S-N curves, the total

fatigue damage values for one flight cycle are derived. The resulting differences between the

active and passive aircraft are then discussed.

6.3.1 Reference parameters

According to the considerations in Section 5.1, Table 6.7 defines the selected flight mission

for the D150 configuration.

Table 6.7. Reference flight route and masses for D150

Parameter Value

Origin Berlin Tegel (EDDT)

Destination Porto (LPPR)

Great circle distance 2076 km

Zero fuel mass 60548 kg

Take-off fuel 10450 kg

Trip fuel 7736 kg

Take-off mass 70998 kg

Landing mass 63262 kg

The payload considered is taken from the mass configuration MZmMe in Table 6.1 that brings

the empty aircraft to MZFM. Table 6.8 lists the derived reference flight conditions for the

turbulence and fatigue analysis. The altitude for the reference climb phase is set larger than

10000Bft (3048Bm) to be able to have airspeeds higher than 250Bkts EAS (128.6Bm/s EAS)

without air traffic control (ATC) permission. The selection of the high airspeed is intended to

evoke large turbulence loads. For the reference descent, the airspeed is set to 250Bkts EAS and

the altitude to 4000Bft (1219Bm) that is assumed to be the lowest altitude before the

deceleration for the final approach is initiated. The combination of the airspeed and the

altitude during descent is expected to induce large turbulence loads. Figure 6.16 visualizes the

reference flight mission and the altitudes of the reference flight phases are marked. Table 6.9

lists the parameters for the reference ground-air-ground cycle as described in Section 5.5.

6 Loads, optimization and fatigue results of D150 configuration

Figure 6.16. Visualization of the reference flight mission of D150

Table 6.8. Reference parameters for each flight phase – D150

Flight phase Reference parameter Value

Climb

Altitude 4572 m (FL150)

Airspeed 181.6 m/s TAS (280 kts EAS)

Fuel mass 10086 kg

Turbulence RMS 2.743 m/s TAS

Duration per flight 0.4 hours

Cruise

Altitude 10668 m (FL350)

Airspeed 231.3 m/s TAS (Mach 0.78)

Fuel mass 6456 kg

Turbulence RMS 1.372 m/s TAS

Duration per flight 2.0 hours

Descent

Altitude 1219 m (FL 040)

Airspeed 136.5 m/s TAS (250 kts EAS)

Fuel mass 2826 kg

Turbulence RMS 3.048 m/s TAS

Duration per flight 0.5 hours

Table 6.9. Reference parameters for the ground-air-ground cycle – D150

Reference parameter Value

Altitude 4572 m (FL150)

Airspeed 181.6 m/s TAS (280 kts EAS)

Fuel mass 10450 kg

Load factor 1.3

MLA deflection (active aircraft) -2.5°

6.3 Turbulence loads and fatigue analysis

6.3.2 Cut load and stress collectives

Figure 6.7 shows the monitoring stations observed in the turbulence analysis. Figure 6.17

visualizes the selected structural shell elements for the fatigue analysis. A comparison

between the elements at the wing root, outer section and HTP is seen as relevant in gaining

insight into the fatigue behavior at different positions of the aircraft structure.

Figure 6.17. Selected structure elements for strain response of D150

To discuss the differences in the turbulence loads between the active and passive aircraft, the

climb phase is chosen since it provides higher levels of loads compared to the cruise phase

due to the turbulence RMS value and high equivalent airspeed, see Table 6.8. The wing cut

load collectives of Figure 6.18(a) to (d) show that the active aircraft experiences smaller

amplitudes of bending moment , while the torsion amplitudes are larger, analogous to

the differences in the design loads. The largest difference between both aircraft is found in the

bending moment at the outer section, where the maximum amplitude experienced by the

active aircraft is 41% lower compared to the passive aircraft. This occurs due the fact that the

aileron covers a larger percentage of area monitored at the outer section compared to that

monitored at the root – analogous to the effects of load alleviation on design loads. Hence, the

change of lift from the load alleviation using the aileron has a larger relative contribution to

the cut loads at the outer section of the wing. On the HTP however, there are no significant

differences in the loads between the active and passive aircraft, see Figure 6.18(e) and (f).

Furthermore, Schwochow [87] states that the symmetrical deflection of ailerons on ATTAS

(VFW-614) evokes large lateral accelerations on the engines. On that aircraft, the engines are

attached above the wing and the lateral accelerations are mainly caused by the wing bending.

On the D150 configuration, the engines are attached underneath the wing, however they can

still be affected by wing bending movements. Section 6.4 addresses this aspect.

6 Loads, optimization and fatigue results of D150 configuration

(a) (b)

(e) (f)

Figure 6.18. Cut load collectives during the climb phase of D150

6.3 Turbulence loads and fatigue analysis

(a) (b)

Figure 6.19. Stress and hinge moment collectives during the climb phase of D150

To investigate the differences in the fatigue behavior between the active and passive aircraft,

selected shell elements on the wing box and HTP box are observed as well. In this case, the

reference quantity is the major principal stress of the selected elements. As apparent in

Figure 6.19(a) and (b), the active aircraft has lower cumulative frequencies of occurrence in

general, except at the outer section below 7BMPa. On the HTP (Figure 6.19(c)), the active

aircraft generally has larger numbers of cumulative stress-cycles, and the maximum stress

amplitude is at the same level as the passive aircraft.

In the aileron hinge moment (Figure 6.19(d)), the active aircraft generally has higher

cumulative frequencies of occurrence, and its maximum amplitude is 3.6% larger than on the

passive aircraft. Nevertheless, with a maximum hinge moment during the design maneuvers

of 3152BNm on the passive aircraft and 3355BNm on the active aircraft as stated in Subsection

6.2.1, the maximum hinge moment amplitude of approx. 400BNm during turbulence (Figure

6.19(d)) is seen as uncritical, at least for the fatigue aspect. As an example: if the maximum

hinge moment represents the yield strength of the actuation system made of metals, then

loading cycles with amplitudes of less than 20% of the maximum value would inflict

practically negligible fatigue damage.

6 Loads, optimization and fatigue results of D150 configuration

6.3.3 Fatigue damage accumulation

To quantify the structural fatigue damage according to Palmgren-Miner based on the

generated stress collectives, reference S-N curves from a fatigue experiment campaign by

Mayer et al. [60] are taken into account. Before the damage accumulation is calculated, the

following assumptions are made:

•S-N curves with a stress ratio – ratio between the minimum and maximum stress in a

load cycle – of 0.1 are taken as reference. This assumption is based on the following:

during the 1g-flight, the static major principal stress at the observed element at the root

is 88BMPa. According to Figure 6.19(a), the maximum amplitude of the major

principal stress during turbulence is 50BMPa. This yields a stress ratio of

(88BMPa-50BMPa)/(88BMPa+50BMPa)=0.28. Furthermore, the stress ratio for ground-

air-ground cycles elaborated in Section 5.5 is assumed to be 0.0. For these reasons, S-

N curves with a stress ratio of 0.1 are seen as an acceptable compromise.

•Since the stress amplitudes in the derived collectives are below 70BMPa, the respective

S-N curve approximation function derived by Mayer et al. for amplitudes below

70BMPa is selected and extrapolated.

•A fatigue limit is not considered. This means, there is a finite number of cycles to

failure for every stress amplitude.

•Since a scatter of cycle numbers, at which failure occurs, is observed in the fatigue

experiments, a safety factor of 10 is assumed for the stress cycles to failure.

•Stress amplifications due to structural discontinuities are not taken into account since

the FE-models are also optimized without considering those aspects.

With those assumptions, the approximation function for the S-N curve is:

,(6.13)

with:

: cycles to failure [-],

: S-N curve constant (1.31·10 ) [-],⁶⁶

: major principal stress amplitude [MPa],

: safety factor [-],

: S-N curve exponent (30.69) [-].

Figure 6.20 shows the S-N curve used in the analysis, and Table 6.10 lists the accumulated

fatigue damage values of the observed shell elements for one flight according to Table 6.8.

For every observed shell element, the highest fatigue damage value is highlighted. A more

detailed list of fatigue damage per hour of flight in the respective phases can be found in

Table A-3 in the Appendix.

6.3 Turbulence loads and fatigue analysis

Figure 6.20. S-N curve for the turbulence analysis of D150

Table 6.10. Turbulence fatigue damage per flight on D150

Observed shell

element

Damage per flight –

passive aircraft

Damage per flight –

active aircraft

Wing root 2.15·10-12 9.97·10-15

Outer wing section 1.05·10-15 4.19·10-21

HTP root 2.67·10-21 4.58·10-21

In addition to the turbulence loads, a simplified ground-air-ground cycle according to Section

5.5 is considered in the fatigue calculation. For the ground-air-ground cycle, the aircraft is

assumed to have zero stress on the ground, and the stresses during flight are taken from a

reference +1.3g maneuver calculation. During that maneuver, the MLA of the active aircraft is

deflected by -2.5° (trailing edge up) according to Equation (5.7).

To calculate the fatigue damage, the stress amplitudes are half of the stresses during the +1.3g

maneuver. Table 6.11 lists the resulting stresses on the observed elements and the respective

fatigue damage per flight cycle.

Table 6.11. Fatigue damage per ground-air-ground cycle on D150

Observed shell

element

Passive aircraft Active aircraft

Major principal

stress amplitude

Damage per

cycle

Major principal

stress amplitude

Damage per

cycle

Wing root 56.9 MPa 5.48·10-12 57.0 MPa 5.93·10-12

Outer wing section 55.9 MPa 3.25·10-12 56.9 MPa 5.70·10-12

HTP root 16.8 MPa 3.10·10-28 17.9 MPa 2.10·10-27

To acquire the total fatigue damage in one flight, the values from Table 6.10 and Table 6.11

are added, and Table 6.12 shows the results.

6 Loads, optimization and fatigue results of D150 configuration

Table 6.12. Total fatigue damage per flight on D150

Observed shell

element

Damage per flight –

passive aircraft

Damage per flight –

active aircraft

Wing root 7.62·10-12 5.94·10-12

Outer wing section 3.25·10-12 5.70·10-12

HTP root 2.67·10-21 4.58·10-21

With the fatigue damage values in Table 6.12, and with the probability of exceedance of the

turbulence intensity of approx. 0.1% mentioned in Section 5.2, it is concluded that:

•On both aircraft, the wing receives more fatigue damage from the ground-air-ground

cycle compared to turbulence.

•In turbulence, there is a clear trend that the wing of the passive aircraft shows

significantly more fatigue damage compared to the active aircraft. On the other hand,

the HTP of the active aircraft exhibits slightly more damage. This is caused by the

GLA creating a small amount of additional pitching moment due to the aileron

deflections. Hence, the RMS of pitch acceleration of the active aircraft is up to 8.4%

higher. This induces additional vertical movements and also loads on the HTP.

•One ground-air-ground cycle tends to cause more wing fatigue damage to the active

aircraft than to the passive aircraft.

•In general, the wing root gets more fatigue damage compared to the outer wing

section.

•Judging by the highest damage values of each aircraft (the largest numbers in every

column in Table 6.12) with 7.62·10-12 on the passive and 5.94·10-12 on the active

aircraft, the expected fatigue life of the active aircraft is 1.28 times longer than that of

the passive aircraft.

If the fatigue damage values listed in Table 6.12 are extrapolated to e.g. 40000 flight cycles,

those are still significantly below 1.0 – assuming that the turbulence intensity is equal to the

values in Table 6.8 and there is no stress amplification due to structural discontinuities.

6.4 Further results

Uncertainties in the stress amplifications

If fatigue loads are to be included in the design process, the areas prone to fatigue damage

have to be known and modeled – together with the respective stress amplification factors and

the material reinforcements. The stress amplification factor is defined as the ratio between the

maximum near-field stress and the far-field stress, see Figure 6.21.

6.4 Further results

Figure 6.21. Illustration of stress amplification near a hole

In wing box structures that are optimized with strength and buckling stability constraints, the

limit stress is unlikely to be reached since buckling can occur at considerably lower stresses.

In that case, a stress amplification factor can exist to a certain degree without the structure

having to be reinforced.

However, if such stress amplification exists, the fatigue life can be affected in a negative way.

As an example: if the passive aircraft had an exemplary stress amplification factor of 2.0 at

the root section, the fatigue damage would increase by a factor of 2.030.69 based on Equation

(6.13), namely from 7.62·10-12 to 1.32·10-02, assuming that the same S-N curve is still valid.

This means, the active aircraft is expected to be able to retire way before the intended 40000

flight cycles. This huge degradation of the fatigue life is caused by the large exponent in the

formula for the S-N curve. With local material reinforcements, the increase in near-field stress

can be reduced. As a conclusion, stress amplification factors and the local material

reinforcements play a crucial role in the fatigue life prediction of aluminum aircraft.

Engine lateral accelerations on the D150 configuration

On aircraft configurations with engines attached under the wing such as the D150

configuration, the engine modes and the wing bending movement can affect each other. With

additional excitation from the ailerons, the interaction between the engines and wing bending

movements can be influenced in a negative way, as shown by the following phenomenon:

For an experiment of vortex decay investigation, the DLR research aircraft ATTAS should

perform oscillatory, symmetric trailing edge surface and aileron deflections. A technical report

by Schwochow [87] however states that the symmetrical deflection of ailerons on ATTAS

(VFW-614) evokes large lateral accelerations on the engines. On that aircraft, the engines are

attached above the wing and the lateral accelerations are mainly caused by the wing bending.

To investigate the relevance of the described phenomenon on the D150 configuration, the

engine’s lateral accelerations during turbulence are analyzed. For this aim, the reference flight

conditions as well as the parameters listed in Section 6.3 are considered.

6 Loads, optimization and fatigue results of D150 configuration

Table 6.13 shows the RMS values of the engine’s lateral acceleration in the respective flight

phases, for the active and passive aircraft each. It is apparent that the RMS values of the

passive aircraft are larger, except during the descent phase. However, if averaged per flight,

the passive aircraft has a slightly higher RMS value of the engine lateral acceleration. As a

conclusion, the symmetric aileron deflection on the active D150 configuration does not

increase the engine lateral loads.

Table 6.13. Engine lateral acceleration RMS on D150

Flight phase Duration Passive aircraft Active aircraft

Climb 0.4 hours 1.59 m/s² 1.32 m/s² (-17.0%)

Cruise 2.0 hours 0.69 m/s² 0.55 m/s² (-20.2%)

Descent 0.5 hours 1.35 m/s² 1.41 m/s² (+4.4%)

Average per flight 2.9 hours 0.93 m/s² 0.80 m/s² (-14.0%)

7 Loads, optimization and fatigue results of ALLEGRA configuration

7 Loads, optimization and fatigue results of ALLEGRA

configuration

This chapter sums up the analysis parameters and results for the ALLEGRA configuration.

The analysis of the ALLEGRA configuration is of great relevance from the aircraft design

point of view: it has a forward swept wing and is made of composite materials. Not only its

aeroelastic characteristics are expected to be different compared to conventional

configurations, but also its fatigue behavior is different compared to aluminum.

The first section of this chapter defines the parameter space for the loads analysis and

structural optimization. With the parameters, the process explained in Section 3.7 is run

iteratively. The design loads, structural masses and aeroelastic parameters resulting from the

final cycle are shown, and a discussion regarding the differences between the active and

passive aircraft follows.

Subsequently, the turbulence loads and fatigue analysis along with the reference flight mission

are described. For each reference flight phase, the turbulence loads are calculated and their

collectives are acquired using the rainflow-counting algorithm. Collectives of the major

principal strain on selected structural elements on the lower skin of the wing and HTP are

derived. Furthermore, strains caused by a reference ground-air-ground cycle are calculated.

With those results, strain collectives for the reference flight cycle are derived, and the fatigue

damage values are calculated for the active and passive aircraft with the methodology

elaborated in Chapter 5. At the end of this chapter, a discussion regarding the fatigue results

follows.

7.1 Parameter space for loads analysis and structural optimization

This section gives an overview of the parameters for the loads analysis and structural

optimization. These comprise the mass configurations, flight conditions, gust and maneuver

cases considered in the simulations as well as the objective function, design variables and

constraints in the structural optimization.

7.1.1 Mass configurations

For the ALLEGRA configuration, the same nine mass configurations are selected as for the

D150 configuration (see Subsection 6.1.1). As a remark: the nominal mass values and the

respective mass distributions are slightly different due to the different aircraft geometry and

design masses. Figure 7.1 and Table 7.1 give an overview of the mass configurations. The

mass labels are defined according to Pinho Chiozzotto [72].

7 Loads, optimization and fatigue results of ALLEGRA configuration

Figure 7.1. Mass and balance diagram of considered configurations – ALLEGRA

Table 7.1. Overview of the mass configurations – ALLEGRA

Label Mass [kg] CG [% MAC] Notes

MOOee 43712 25.0 Operating empty mass

MCFfe 48000 10.0 Forward CG, light payload

MCAae 48000 35.0 Rear CG, light payload

MHFFe 58250 10.0 Forward CG, heavy payload

MHAAe 58250 30.0 Rear CG, heavy payload

MZmMe 62962 20.0 Middle CG, maximum zero fuel mass

MTFFJ 73365 18.8 MHFFe with 15.1 t fuel

MTAAJ 73365 34.8 MHAAe with 15.1 t fuel

MTmMG 73365 24.2 MZmMe with 10.4 t fuel

7.1.2 Flight conditions within the design envelope

Analogous to the D150 configuration, the three altitudes selected for the loads analysis range

from sea level to 7000Bm. At 7000Bm, the design cruise speed coincides with the design

cruise Mach number . At each altitude, the speeds , and are considered based on

the ALLEGRA report [85], see Table 7.2. The report [85] also documents the discontinuities

of and at the altitude of 3000Bm. The labels for the flight conditions are based on Pinho

Chiozzotto [72]. Figure 7.2 visualizes the flight envelope.

7.1 Parameter space for loads analysis and structural optimization
Figure 7.2. Flight conditions in the design envelope – ALLEGRA
Table 7.2. Overview of the flight conditions – ALLEGRA
Altitude [m] VA [m/s TAS] Label VC [m/s TAS] Label VD [m/s TAS] Label
0 126.1  OA000 153.0  OC000 182.7  OD000
3000 146.7  OA100 206.6  OC100 212.5  OD100
7000 181.8  OA230 248.7  OC230 271.6  OD230
7.1.3  Gust and maneuver load conditions
The  load  conditions  for   the ALLEGRA  configuration  are  based  on  those  for  the  D150 
configuration, except that the gust alleviation factor as described in Equation (6.4) and the 
design speeds at the respective flight conditions are different. The considered gust cases cover 
seven gust gradients as listed in  Table 6.3. For the maneuvers, the edges of the maneuver 
envelope stated in Section 6.1.4 and illustrated in Figure 6.4 are taken into account.
7.1.4  Overview of the optimization task
With the mass configurations and flight conditions listed in Subsection  7.1.1  and  7.1.2, 
maneuver and gust loads are calculated as described in Subsections  6.1.3  and  6.1.4. The 
resulting   loads   are   filtered   according   to   Section  3.3  and   are   input   into   the   structural 
optimization. The objective in the structural optimization is the minimization of the structural 
mass while considering the constraints explained in Subsection 7.1.5.
The design variable in the optimization is the material thickness. On a composite wing box, 
the   lamination   parameters   can   be   varied   in   addition   to   the   thickness.   However,   since 
aeroelastic tailoring is not in the scope this thesis, the ply angle distributions of the wing box 
are kept constant, see Section  2.1. Furthermore, the skin laminates are rotated by 30° as 
elaborated in Section 2.5.
85

7 Loads, optimization and fatigue results of ALLEGRA configuration

On the ALLEGRA configuration, one design field – in which the design variable is constant –

covers either the skin area between two ribs, spar area between two ribs or one rib. Each

component – in this case the wing and HTP – is optimized separately. In the optimization run,

only the starboard half of the wing box or HTP box is included, and the resulting properties

are mirrored onto the corresponding port half. A wing box half has 28 ribs which results in

136 design fields for the wing whereas an HTP half has 12 ribs and a total of 56 design fields.

7.1.5 Constraints in the structural optimization

On composite structures, the strength analysis is based on strains, in contrast to stress-based

strength analysis of aluminum structures. For the composite ALLEGRA configuration, the

constraints considered in the structural optimization are von-Mises strain and buckling

stability. According to [21], von-Mises strain is defined by:

,(7.1)

with:

: von-Mises strain [-],

: tensile strain in x-direction [-],

: tensile strain in y-direction [-],

: shear strain [-].

A von-Mises strain allowable of 5.0·10-3 is assumed based on IJsselmuiden (Appendix A in

his thesis) [44] and with a safety factor of 1.5 according to CS25, strain limits of 3.3·10-3 are

considered in the structural optimization.

For the buckling constraints, the composite elements on the wing are assumed to be a

homogeneous material with an anisotropic stiffness matrix according to Tetlow [91]. With this

approach, the influence of the stacking sequence on the bending stiffness of the composite

plate is neglected, and the compressive buckling stress is calculated with:

,(7.2)

with:

, (7.3)

and:

: compression buckling stress according to Tetlow [Pa],

: longitudinal tensile modulus [Pa],

: lateral tensile modulus [Pa],

, : Poisson ratios [-],

: shear modulus [Pa],

: material thickness [m],

: buckling field width [m].

The shear buckling constraints for the ribs and spars – which are used for the aluminum

aircraft – are replaced with the compressive buckling constraints.

7.1 Parameter space for loads analysis and structural optimization

Furthermore, a minimum thickness of 2Bmm is selected for every design field. For a realistic

design, the material thicknesses should be equal to integer multiples of the single ply

thickness of approx. 0.125Bmm and a stacking sequence to reach the intended ply angle

distributions should be feasible. In this thesis however, the restrictions concerning the discrete

thickness values and the stacking sequence are not applied.

7.2 Comparison of design loads, structural masses and aeroelastic

parameters

With the parameters from Section 7.1, the design process explained in Section 3.7 is run. The

following subsections describe the resulting design loads, structural masses and aeroelastic

parameters.

7.2.1 Design loads

After seven cycles of loads analysis and structural optimization, the resulting wing bending

moment envelopes are shown in Figure 7.3 and Figure 7.4. On the passive aircraft, gusts

evoke the largest positive bending moments , whereas in the negative range both gusts and

maneuvers are generally at the same level. On the active aircraft, maneuver loads are

dominant in the wing bending moment envelope, it also has 10.7% less wing root bending

moment. At the outer section ( =12Bm), the decrease of wing bending moment on the active

aircraft is 17.8%. At this point, a more aggressive setting for the MLA seems to be a plausible

measure to match the maximum bending moments due to maneuvers and gusts. However,

analogous to the D150 configuration, the aerodynamic feasibility of larger MLA deflections at

high Mach numbers and the additional increase in the maximum torsion have to be checked

first.

The 1D envelopes of Figure 7.3 and Figure 7.4 mainly show the global trend of the cut loads.

The 2D envelopes give insight into the correlation between the load components at the

observed positions. For this aim and for the turbulence analysis, reference monitoring stations

at the wing root, wing outer section and HTP root along with the local coordinate systems are

defined, see Figure 7.5.

Figure 7.6 visualizes 2D load envelopes of the wing. The envelopes of the active aircraft are

visibly rotated counter-clockwise which indicates a reduction of maximum bending moment

along with a noticeable increase in torsion . At the outer section, the increase in the

maximum torsion is 26.2%. At the root, the maximum torsion increases by 5.9%, and the

rotation of the envelope is less distinct since the relative effect of the load alleviation is

smaller compared to the wing outer section.

7 Loads, optimization and fatigue results of ALLEGRA configuration

Figure 7.3. Wing bending moment of passive ALLEGRA

Figure 7.4. Wing bending moment of active ALLEGRA

Figure 7.5. Selected cut load monitoring stations on ALLEGRA

7.2 Comparison of design loads, structural masses and aeroelastic parameters

(a) (b)

Figure 7.6. 2D load envelope comparison on ALLEGRA

On the passive aircraft, the maximum bending moment is reached during gusts with the mass

configuration MTmMG (MTOM with mid CG, Table 7.1) that has the heaviest payload. This

implies that a heavy fuselage induces large bending moments during gust encounters. The

maximum torsion is reached during maneuvers with the mass configuration MTFFJ (MTOM

with forward CG, Table 7.1). On the active aircraft, the maximum bending moment and

torsion is reached during maneuvers, predominantly with the mass configuration MTFFJ.

Compared to the D150 configuration, the maneuver loads form comparably round envelopes,

see Figure A-1(b) in the Appendix whereas the maneuver load envelope of the D150

configuration is more slender as visible in Figure A-1(a). This indicates a larger torsion

fluctuation of the ALLEGRA configuration during maneuvers which is explained by the

following aspects:

•During high-speed pull-ups (at ), the angle of attack is moderate, and the center of

pressure is relatively far backward since the camber has a large contribution to the lift.

This backward center of pressure lies relatively near to the LRA. Hence, the torsion is

relatively low.

•During low-speed pull-ups (at ), the angle of attack is relatively large, and the

center of pressure shifts forward – toward the 25% chord line. This causes the wing to

have a larger torsion and a more pronounced nose-up twist.

•The nose-up twist induces a larger local angle of attack that in turn amplifies the lift.

Due to the bending-torsion-coupling of the forward swept wing, the amplified lift

increases the nose-up twist and the torsion further. Hence, the torsion difference

between a high-speed and low-speed pull-up is relatively large. The load case

selection algorithm described in Section 3.3, the number of load cases for the

structural optimization ranges between 46 and 55.

7 Loads, optimization and fatigue results of ALLEGRA configuration

Concerning the aileron hinge moments, the passive aircraft shows a maximum magnitude of

4220BNm during design maneuvers, while the active aircraft has to withstand a maximum of

3520BNm during design gust encounters that is 16.6% lower. In this case, the aileron actuators

of the active aircraft do not have to be reinforced with regards to maximum power or torque.

7.2.2 Structural masses

Figure 7.7 shows the convergence history of the ALLEGRA wing box mass. To gain a more

detailed insight into the convergence, Figure 7.8 visualizes RMS values of the relative change

in material thicknesses between each cycle according to Equation (6.12). After seven cycles of

loads analysis and structural optimization, the wing box of the active aircraft is 6.1% or

283Bkg lighter compared to the passive aircraft. Concerning the material thickness

convergence, the RMS values of thickness change between the last two cycles are 3.58% for

the passive and 2.91% for the active aircraft.

Compared to the D150 configuration, the convergence of the wing box mass is relatively fast.

E.g. between cycle 5 and 7, the wing box mass fluctuation is always under 0.3%. The faster

convergence is possible because of the characteristic bending-torsion-coupling of forward

swept wings. As an example: If the wing becomes lighter and softer in one optimization run,

the subsequent loads analysis would result in higher loads due to its bending-torsion-coupling

and load amplification effect around the wingtip. Hence, the wing would tend to become

heavier and stiffer in the next optimization run. This in turn reduces the loads in the next

analysis. This interdependency increases the convergence gradient and brings the forward

swept wing to a comparable level of mass convergence in fewer cycles compared to backward

swept wings.

Compared to the loads and optimization process of Klimmek [54] however, the mass

convergence of the ALLEGRA configuration is still slower. This is caused by the significantly

higher number of load cases and their selection algorithm as explained in Subsection 6.2.2.

Judging by the bending moment envelopes, the ALLEGRA configuration tends to be sized

rather by dynamic gust loads than by quasi-steady maneuver loads, see Figure 7.3, or at least

they are on similar levels, as visible in Figure 7.4. The RMS values of thickness change

between cycle 3 and 7 as apparent in Figure 7.8 are generally higher compared to the D150

configuration. These phenomena indicate that dominant dynamic gust loads – combined with

the applied load case selection algorithm – correlate with a higher fluctuation in the material

thicknesses between each loads analysis and structural optimization cycle. As an example: in

a particular cycle, a certain set of snapshots from the dynamic simulations is used for the

optimization, and the structure is optimized with those dominant dynamic loads. Following

that, the loads analysis of the next cycle is run. In the post-processing, the resulting set of

snapshots (see Figure 3.2) and the corresponding spanwise load distributions for the

optimization might differ from the previous cycle. These differences are expected to be larger

compared to those resulting from quasi-steady maneuver simulations. In the worst case, the

optimizer might find a significantly different optimum that would lead to a large RMS of the

change in the material thicknesses.

7.2 Comparison of design loads, structural masses and aeroelastic parameters

The wing box masses shown in Figure 7.7 refer only to ideal load-carrying masses. With an

empirical mass factor of 1.45 as mentioned in Subection 6.2.2, the wing mass difference

between the active and passive aircraft would be 1.45·283Bkg = 410.35Bkg, assuming that the

secondary masses comprising systems remain unchanged.

Figure 7.7. Wing box mass trend in the loads and optimization process of ALLEGRA

Figure 7.8. RMS of material thickness change of ALLEGRA wing box

Figure 7.9 visualizes the wing box mass difference of 6.1%. On the upper and lower skin of

the passive aircraft, the areas with 18Bmm thickness around the root are larger compared to the

active aircraft. In the outer part, the skin areas with the minimum thickness are smaller on the

passive aircraft. This indicates that the outer wing section of the passive aircraft is more

heavily loaded due to the absence of load alleviation. On the other hand, the spars and ribs

have similar thicknesses, except at the root where the rib of the passive aircraft is thicker. On

the HTP, there is almost no difference between the active and passive aircraft, and the mass

difference between both HTP boxes is below 1Bkg, see Figure 7.10.

Regarding the structural dynamics, Table A-2 in the Appendix shows an overview of selected

modes. The wing mode frequencies of the active aircraft are up to 5% lower than those of the

passive aircraft. Those differences are larger compared to D150 (<2% between the active and

passive aircraft). Hence, it can be concluded that an implementation of load alleviation on

ALLEGRA has a larger impact on the wing stiffness reduction compared to D150.

7 Loads, optimization and fatigue results of ALLEGRA configuration

(a)

(b)

Figure 7.9. Wing material thickness distribution of ALLEGRA

(a) (b)

Figure 7.10. HTP material thickness distribution of ALLEGRA

7.2 Comparison of design loads, structural masses and aeroelastic parameters

7.2.3 Aeroelastic parameters

According to CS25.629, calculations concerning aeroelastic stability are to be conducted in

the whole flight envelope and speeds up to +15% have to be covered. Figure 7.11 shows

the design envelope for aeroelastic stability of the ALLEGRA configuration. In this case, the

torsional divergence and the flutter speed are considered.

Figure 7.11. Design envelope for aeroelastic stability of ALLEGRA

Torsional divergence

For the divergence calculation, the reference altitude is set to sea level to enable having high

dynamic pressures at relatively low Mach numbers, since the expected divergence dynamic

pressure corresponds to a Mach number that is significantly higher than the design dive Mach

number . Since the DLM is only valid for Mach numbers smaller than 1.0, the reference

Mach number is set to 0.95. With the DLM, local supersonic areas on the wing cannot be

modeled, nevertheless, the Mach number of 0.95 is selected to take the magnification of the

lift slope due to the air compressibility into account.

Table 7.3. Parameters of divergence calculation on ALLEGRA

Parameter Value

Reference Mach number 0.95

Air density 1.225 kg/m³

To meet the requirements defined in CS25.629, the dynamic pressure, at which the divergence

sets on, has to be larger than the dynamic pressure at +15% that is 32254BPa for the

ALLEGRA configuration. Table 7.4 lists the results of the divergence calculations.

7 Loads, optimization and fatigue results of ALLEGRA configuration
Table 7.4. Divergence dynamic pressures of ALLEGRA
Aircraft model Divergence dynamic pressure
Passive aircraft 102038 Pa
Active aircraft 91743 Pa
With both values being approx. three times larger than 32254BPa, no torsional divergence 
occurs   at   any   speed   up   to   +15%.   However,   the   active   aircraft   has   a   10.1%   lower 
divergence dynamic pressure since the wing material thickness is generally lower than for the 
passive aircraft, hence the wing stiffness is also lower, as mentioned in Subsection 7.2.2.
Flutter speed
For dynamic aeroelastic stability, the parameter to compare between the active and passive 
aircraft is the flutter speed. For this aim, a subsonic flutter calculation using MSC.Nastran is 
run. Table 7.5 lists the parameters for the reference flight condition of the flutter calculation. 
The reference Mach number is set to the equivalent of     (203Bm/s CAS) at sea level to 
ensure a subsonic reference flow condition – with the assumption that a transonic flow 
condition emerges at Mach 0.7. The mass density of the air is set accordingly to the condition 
at sea level. The flutter calculation considers 50 Eigenmodes. This number of modes is 
assumed as sufficient since the potential dominant modes such as VTP torsion and bending as 
well as HTP torsion and bending are included. As mentioned in Section  2.3, a maximum 
reduced frequency of 3.0 is selected.
Table 7.5. Parameters of flutter calculation on ALLEGRA
Parameter Value
Reference Mach number 0.5970
Air density 1.225 kg/m³
Number of Eigenmodes 50
Considered reduced frequencies 0.01 to 3.0 with 300 sampling points
Figure 7.12 shows the damping curves of the dominant mode involved at the flutter point and 
Figure 7.13 visualizes its mode shape that is the first VTP bending mode. This mode shape is 
identified through manual mode tracking of the frequency curve toward the low speeds where 
changes in the sequence of the modes are not anymore expected. Complete diagrams with all 
damping and frequency curves are shown in Figure A-4 in the Appendix. As mentioned in 
Section  3.6, with the applied KE-method, no complex modes corresponding to the flutter 
curves can be obtained.
Analogous to Subsection 6.2.3, a threshold line at -3% structural damping is drawn in Figure
7.12. It is apparent that the flutter speed is higher than  +15% and therefore there is no risk 
of flutter according to the subsonic calculations. The flutter speeds of the active and passive 
aircraft as well as the frequencies (2.87BHz) at the flutter points are almost identical.
94

7.2 Comparison of design loads, structural masses and aeroelastic parameters

Figure 7.12. Curves of the flutter point of ALLEGRA

Figure 7.13. Dominant Eigenmode involved at the flutter speed of ALLEGRA

7.3 Turbulence loads and fatigue analysis

This section explains the parameters of the reference flight used in the turbulence loads and

fatigue calculations. From those calculations, cut load and and strain collectives caused by

atmospheric turbulence are extracted. To obtain a more global overview of the cyclic aircraft

loads, strains resulting from a ground-air-ground cycle are considered as well. Using derived

reference S-N curves, the total fatigue damage values for one flight cycle are accumulated.

The differences between the active and passive aircraft are then discussed.

7 Loads, optimization and fatigue results of ALLEGRA configuration

7.3.1 Reference parameters

Table 7.6 lists the reference flight route for the ALLEGRA configuration according to the

considerations in Section 5.1.

Table 7.6. Reference flight route for ALLEGRA

Parameter Value

Origin Berlin Tegel (EDDT)

Destination Athens International (LGAV)

Great circle distance 1823 km

Zero fuel mass 62962 kg

Take-off fuel 9598 kg

Trip fuel 6910 kg

Take-off mass 72560 kg

Landing mass 65650 kg

Analogous to the D150 configuration, the payload from the mass configuration MzmMe in

Table 7.1 is taken. The payload brings the empty aircraft to MZFM. Table 7.7 shows the

reference flight conditions with the same altitudes, airspeeds and turbulence RMS as for the

D150 configuration, see Subsection 6.3.1. Figure 7.14 illustrates the reference flight mission,

along with markers for the reference flight conditions for each phase. Table 7.8 lists the

parameters for the ground-air-ground cycle according to Section 5.5.

Figure 7.14. Visualization of the reference flight mission of ALLEGRA

7.3 Turbulence loads and fatigue analysis

Table 7.7. Reference parameters for each flight phase – ALLEGRA

Flight phase Reference parameter Value

Climb

Altitude 4572 m (FL150)

Airspeed 181.6 m/s TAS (280 kts EAS)

Fuel mass 9010 kg

Turbulence RMS 2.743 m/s TAS

Duration per flight 0.4 hours

Cruise

Altitude 10668 m (FL350)

Airspeed 231.3 m/s TAS (Mach 0.78)

Fuel mass 5892 kg

Turbulence RMS 1.372 m/s TAS

Duration per flight 1.8 hours

Descent

Altitude 1219 m (FL 040)

Airspeed 136.5 m/s TAS (250 kts EAS)

Fuel mass 2810 kg

Turbulence RMS 3.048 m/s TAS

Duration per flight 0.5 hours

Table 7.8. Reference parameters for the ground-air-ground cycle – ALLEGRA

Reference parameter Value

Altitude 4572 m (FL150)

Airspeed 181.6 m/s TAS (280 kts EAS)

Fuel mass 9598 kg

Load factor 1.3

MLA deflection (active aircraft) -2.5°

7.3.2 Cut load and strain collectives

Figure 7.5 visualizes the monitoring stations used in the turbulence analysis. Figure 7.15

shows the selected structural shell elements for the fatigue analysis. An observation of the

wing root, outer section and HTP is relevant for understanding the fatigue behavior at

different positions of the structure.

7 Loads, optimization and fatigue results of ALLEGRA configuration

Figure 7.15. Selected structure elements for strain response of ALLEGRA

Analogous to the D150 configuration, the climb condition is investigated since it evokes

higher levels of loads compared to the cruise phase due to the turbulence RMS value and high

equivalent airspeed, see Table 7.7. The wing cut load collectives are shown in Figure 7.16(a)

to (d). At the wing root, it is apparent that the bending moment on the active aircraft is

lower while the torsion are at the same level. At the outer wing section, the differences in

the amplitudes of bending moment and the torsion of both aircraft are more pronounced.

There, the maximum amplitude of bending moment on the active aircraft is 36% smaller

compared to the passive aircraft. The more pronounced differences occur due the fact that the

aileron covers a larger percentage of area monitored at the outer section compared to that

monitored at the root, analogous to the D150 configuration. On the HTP, there are no

significant differences in the turbulence loads between the active and passive aircraft, see

Figure 7.16(e) and (f).

To investigate the differences of fatigue behavior between the active and passive aircraft,

selected shell elements on the wing box and HTP box are observed as well. In this case, the

reference quantity to assess the fatigue behavior is the major principal strain of the selected

elements. As shown by the strain collectives in Figure 7.17(a) and (b), the active aircraft has

lower cumulative frequencies of occurrence in general. On the HTP (Figure 7.17(c)), both

aircraft practically have the same trend of load collectives. For the aileron hinge moment

(Figure 7.17(d)), the active aircraft generally has higher cumulative frequencies of

occurrence, and its maximum amplitude is 30.2% larger than that of the passive aircraft.

Analogous to the D150 configuration, these hinge moment amplitudes up to 400BNm are – at

least from the fatigue point of view – uncritical since they are significantly smaller compared

to those found in the design load calculations (4220BNm on the passive aircraft and 3520BNm

on the active aircraft, see Subsection 7.2.1).

7.3 Turbulence loads and fatigue analysis

(a) (b)

(e) (f)

Figure 7.16. Cut load collectives during the climb phase of ALLEGRA

7 Loads, optimization and fatigue results of ALLEGRA configuration

(a) (b)

Figure 7.17. Strain and hinge moment collectives during the climb phase of ALLEGRA

7.3.3 Fatigue damage accumulation

To quantify the structural fatigue damage based on the generated strain collectives, reference

S-N curves of IM7 composite approximated by Tan et al. [90] are applied. The approximation

function considered is:

,(7.4)

with:

: ratio between maximum stress and ultimate tensile strength [-],

: number of cycles to failure [-].

Before the damage accumulation is calculated, the following assumptions are made:

•The ratio between actual stress and ultimate stress is replaced by the ratio between

actual strain and allowable strain.

•The allowable strain is set to 5·10-3.

•There is no fatigue limit; the S-N curve is monotonously decreasing.

100

7.3 Turbulence loads and fatigue analysis

•S-N curves with a stress ratio – the ratio between the minimum and maximum stress in

a load cycle – of 0.1 are taken as reference. This assumption is supported by the

following points: the strain ratio during a ground-air-ground cycle is 0.0, analogous to

the stress ratio of the D150 configuration. During the 1g-flight, the major principal

strain of the observed element at the root is 6.2·10-4. With a maximum amplitude of

the major principal strain of 3.5·10-4 during turbulence – as shown in Figure 7.17(a) –

the resulting strain ratio is 0.28. Therefore, a strain ratio of 0.1 is seen as an acceptable

compromise.

•Since a scatter of cycle numbers, at which failures occur, is observed in the fatigue

experiments, a safety factor of 10 is assumed for the strain cycles to failure.

•Strain amplifications due to structural discontinuities are not taken into account, since

the FE-models are also optimized without considering those aspects.

With those assumptions and after converting Equation (7.4) to a function of strain amplitude,

the approximation for the S-N curve is:

,(7.5)

with:

,(7.6)

and:

: cycles to failure [-],

: relative strain [-],

: coefficient (1.037) [-],

: exponent (-30.59 = 1/-0.03269) [-],

: safety factor [-],

: maximum major principal strain [-],

: ultimate strain (5·10-3) [-],

: major principal strain amplitude [-],

: strain ratio [-].

Figure 7.18 shows the S-N curve used in the analysis. According to Rosenfeld et al. [83], the

Palmgren-Miner’s rule is indeed not conservative for compressive stresses in composites. In

that case however, the Palmgren-Miner’s rule is applied with regards to the static failure

stresses of the composite materials. On the ALLEGRA configuration however, the rule is

applied with regards to the allowable strain. Since the failure stress is not reached yet at the

allowable strain, the Palmgren-Miner’s rule is assumed to be acceptable. Furthermore, since

structural elements on the lower skin are observed, tensile strains are expected to be more

dominant.

101

7 Loads, optimization and fatigue results of ALLEGRA configuration

Figure 7.18. S-N curve for the turbulence analysis of ALLEGRA

Table 7.9 lists the accumulated fatigue damage values of the observed shell elements for one

flight cycle according to Table 7.2. For every observed shell element, the aircraft with the

higher fatigue damage is highlighted. A more detailed list of fatigue damage per hour of flight

in the respective phase can be found in Table A-4 in Appendix.

Table 7.9. Turbulence fatigue damage per flight on ALLEGRA

Observed shell

element

Damage per flight –

passive aircraft

Damage per flight –

active aircraft

Wing root 2.74·10-23 4.49·10-26

Outer wing section 2.83·10-26 9.36·10-30

HTP root 6.24·10-34 2.26·10-33

In addition to the turbulence loads, a simplified ground-air-ground cycle as derived in Section

5.5 is included in the fatigue calculation. In this case, the aircraft is assumed to have zero

strain on the ground whereas the strains while airborne are obtained from a reference +1.3g

maneuver simulation. According to Equation (5.7), the MLA of the active aircraft is deflected

by 2.5° trailing edge up during that maneuver.

To derive the fatigue damage, the strain amplitudes are half of the strains during the +1.3g

maneuver. Table 7.10 lists the strains on the observed elements and the corresponding fatigue

damage for one flight cycle.

Table 7.10. Fatigue damage per ground-air-ground cycle on ALLEGRA

Observed shell

element

Passive aircraft Active aircraft

Major principal

strain amplitude

Damage per

cycle

Major principal

strain amplitude

Damage per

cycle

Wing root 3.76·10-4 5.77·10-24 3.97·10-4 2.97·10-23

Outer wing section 3.23·10-4 5.18·10-25 3.58·10-4 1.24·10-24

HTP root 1.29·10-4 3.40·10-38 1.30·10-4 4.31·10-38

102

7.3 Turbulence loads and fatigue analysis

To acquire the total fatigue damage in one flight, the values from Table 7.9 and Table 7.10 are

added, and Table 7.11 lists the results.

Table 7.11. Total fatigue damage per flight on ALLEGRA

Observed shell

element

Damage per flight –

passive aircraft

Damage per flight –

active aircraft

Wing root 3.32·10-23 2.97·10-23

Outer wing section 8.01·10-25 1.24·10-24

HTP root 6.24·10-34 2.26·10-33

With the fatigue damage values in Table 7.11, and with the probability of exceedance of the

turbulence intensity of 0.1%, it is concluded that:

•In turbulence, there is a clear tendency that the wing of the active aircraft shows

significantly less fatigue damage compared to the passive aircraft. However, the HTP

of the active aircraft receives slightly more damage. This is caused by the GLA

evoking a small amount of pitching moments due to the aileron deflections. This

results in the pitch acceleration of the active aircraft being up to 2.2% higher. This in

turn causes additional vertical movements and also loads at the HTP.

•One ground-air-ground cycle causes higher fatigue damage values on the wing of the

active aircraft compared to the passive aircraft.

•In general, the wing root receives more fatigue damage compared to the outer wing

section.

•Judging by the highest damage values of each aircraft (the largest numbers in every

column in Table 7.11) which are 3.32·10-23 on the passive and 2.97·10-23 on the active

aircraft, the expected fatigue life of the active aircraft is 1.12 times longer than the

passive counterpart.

If the fatigue damage values in Table 7.11 are accumulated for e.g. 40000 flight cycles, those

are still significantly below 1.0 – assuming that the turbulence RMS is equal to the values in

Table 7.2 and there is no strain amplification due to structure discontinuities.

7.4 Further results

Uncertainties in the strain amplification and composite fatigue

If fatigue loads are to be considered in the design process, the potentially relevant areas have

to be identified and modeled – together with the respective strain amplification factors. The

definition of strain amplification is analogous to stress amplification illustrated in Figure 6.21.

Since the wing box of the ALLEGRA configuration is also optimized with buckling stability

constraints, a strain amplification factor can exist to a certain degree without exceeding the

strain allowable. However, if the passive aircraft had an exemplary strain amplification factor

of 2.0 at the root, the fatigue damage would increase by a factor of 2.030.59 based on Equation

103

7 Loads, optimization and fatigue results of ALLEGRA configuration

(7.5), namely from from 3.32·10-23 to 5.35·10-14, assuming that the same S-N curve still

applies. This means, the passive aircraft could still complete 40000 flight cycles, however the

fatigue damage increases by an order of magnitude of 9.2. This huge decrease in the fatigue

life is induced by the large exponent in the equation for the S-N curve. Furthermore, on

composite wings, local material reinforcements are not as easily applicable as on aluminum

wings, so that strain amplifications cannot be suppressed easily. As a conclusion, strain

amplification factors play a huge role in the fatigue life prediction of composite aircraft.

For a more detailed composite fatigue analysis, an investigation using the fatigue model by

Kassapoglou [51] and the Tsai Wu first ply failure criterion [14] can be considered, as shown

by Rajpal et al. [76].

104

8 Investigations of load alleviation variations and practical aspects

8 Investigations of load alleviation variations and

practical aspects

This section addresses the parameter selection for the load alleviation functions as well as

practical aspects for the flight operation. For the first aspect, the effect of a fixed MLA

deflection is investigated. A fixed MLA deflection implies that the MLA algorithm is not a

function of the airspeed. Subsequently, the variation of the GLA delay time is analyzed. The

objective of varying the delay time lies in minimizing the wing root bending moment during

gust encounters.

Concerning operational aspects, a fatigue damage of a retrofitted aircraft is calculated. The

term retrofit means that a passive aircraft – that is produced or in operation – is equipped with

load alleviation. A further investigation deals with a load factor threshold for MLA deflection.

For any commanded load factor below that certain threshold, the MLA is assumed to be

passive. This is potentially beneficial e.g. during take-off where a high maximum lift

coefficient is desirable, since an MLA deflection practically reduces that coefficient.

8.1 Fixed MLA deflection

The MLA design in Section 4.2 defines the maximum MLA deflection as a function of the

dynamic pressure, unlike the MLA of the Lockheed L-1011 [77]. As stated in Section 4.2, the

dependency on the dynamic pressure is expected to cause the 2D load envelopes to be more

slender which is seen to be beneficial as explained by the following example.

Figure 8.1 shows 2D load envelopes of the mid wing section (41% half span) of the D150. In

the graphs, all load cases mentioned in Section 6.1 are included and all maneuver loads are

visualized with scatter markers. The maneuver loads shown in Figure 8.1(a) are obtained

using an MLA implemented according to Equation (4.2). The loads in Figure 8.1(b) result

when the MLA is fixed to the maximum value of 15° (trailing edge up during pull-ups,

trailing edge down during push-downs). The maximum bending moment is indeed in both

cases equal. With the variable MLA deflection however, the maneuver load envelope in

Figure 8.1(a) is more slender. Furthermore, the area in the dashed square – around the

maximum bending moment and torsion moment – requires special attention since load

cases with the largest cut loads have a large influence on the structural mass. As apparent,

with the variable MLA deflection, there is only one load case within the dashed square. With

the fixed MLA deflection on the other hand, there are four load cases found in the dashed

square. This means that fewer load cases are considered in the structural optimization for the

MLA with variable maximal deflection. From the optimization point of view, this means that

the wing structure has to be optimized for fewer loading conditions, so that a potentially lower

structural mass would result.

105

8 Investigations of load alleviation variations and practical aspects

(a) (b)

Figure 8.1. 2D load envelope on D150 with variable (a) and fixed (b) deflection

8.2 Variation of GLA delay time

As stated in Section 4.3, the delay time is calculated using the buffer distance shown in

Equation (4.5). With this approach, the relative delay with regards to the gust penetration is

constant at any airspeed. Otherwise, if a constant buffer time instead of a buffer distance is

used, the GLA would likely deflect too early at low speeds and too late at high speeds.

However, by using a buffer distance, its value is still to be defined. In this case, the objective

of the selection of the buffer distance is to minimize the root bending moment . For this

purpose, gust simulations with different buffer distances are carried out for each reference

aircraft, and those evoking the lowest bending moment values are selected for the

investigations in Section 6 and 7.

D150 configuration

The investigation on the D150 configuration is carried out with the maximum take-off mass

configuration MTmMG (Table 6.1), at 256.0Bm/s TAS and 7000 m above sea level. In the gust

loads analysis according to Section 6.1, this combination of parameters yields the highest

wing root bending moment . Gust simulations are run with a variation of the buffer

distance between 12Bm and 24Bm. For this study, the minimum delay time of 60Bms is

neglected that corresponds to the assumption of an ideally fast flight control computer (FCC).

Figure 8.2 visualizes the resulting envelopes of the incremental gust loads at the wing root.

The wing root bending moment is chosen as the reference parameter since it has a larger

impact on the wing box mass compared to e.g. a bending moment at other positions on the

wing.

106

8.2 Variation of GLA delay time

(a) (b)

Figure 8.2. Incremental gust load envelope with variation of GLA buffer – D150

It is apparent that the sooner the aileron deflects, the smaller the wing root bending moment

becomes. However, a buffer distance of 12Bm is not feasible as the effective delay time at

256Bm/s TAS would be 47Bms, and it is below the minimum of 60Bms. Compared to the

current design with a buffer distance of 16Bm, its increase to 24Bm would raise the bending

moment by 3.2%. On the other hand, the torsion occurring together with the maximum

bending moment is decreased by 1.9%. Moreover, with a buffer distance of 24Bm, the load

envelope has a more pronounced corner at the maximum bending moment.

ALLEGRA configuration

Similar to the D150 configuration, the investigation for the ALLEGRA configuration is

conducted with the maximum take-off mass configuration MTmMG (Table 7.1), at 248.7Bm/s

TAS and 7000Bm above sea level. The buffer distance is varied between 14Bm and 26Bm

and the minimum delay time of 60Bms is neglected. Figure 8.3 visualizes the resulting

envelopes of the incremental gust loads at the wing root.

(a) (b)

Figure 8.3. Incremental gust load envelope with variation of GLA buffer – ALLEGRA

107

8 Investigations of load alleviation variations and practical aspects
A similar tendency compared to  the D150 configuration  is visible: the wing root bending 
moment   is in general smaller with decreasing buffer distance. However, a buffer distance 
of 14Bm is not feasible since the effective delay time at 248.7Bm/s TAS would be 56Bms, and it 
is below the minimum of 60Bms. Compared to the current design with a buffer distance of 
18Bm, its increase to 22Bm or 26Bm would cause the bending moment to rise by 1.6% and 1.4% 
respectively. On the other hand, the increase in maximum torsion   is under 0.4% in both 
cases. Toward the wing tip however, the spread in the bending moment due to the buffer 
distance variation is expected to be larger since the relative influence of the aileron deflection 
on the cut loads becomes larger.
8.3  Retrofit of passive aircraft with load alleviation
Another investigation is a so-called retrofit of a passive reference aircraft. The retrofit is 
defined as implementation of MLA and GLA on a passive aircraft without further structure re-
optimization. The benefit of a retrofit is seen in the fatigue life extension of an existing 
aircraft, especially if high turbulence loads are expected due to flights at low altitudes, e.g. 
during coast patrol, research or firefighting missions. It is assumed that the aileron actuators 
do not need to be significantly reinforced, as shown in Subsection 6.2.2 and 7.2.2. The effect 
of the retrofit on fatigue damage is estimated for both reference aircraft. The fatigue loads are 
assumed to emerge due to one reference flight cycle with the turbulence and the ground-air-
ground cycle described in Subsection 6.3.1 and 7.3.1 respectively.
D150 configuration
Figure 8.4  visualizes the stress     and aileron  hinge moment     collectives of the 
retrofitted aircraft during the climb phase. On the wing, the stress collectives of the retrofitted 
aircraft have similar trends to those of the active aircraft, see Figure 8.4(a) and (b). This is 
marked by the lower stress amplitudes in general. Concerning the collectives on the HTP, the 
retrofitted aircraft has slightly higher stress levels than the passive aircraft, and the graph lies 
closer to that of the active aircraft. However, the aileron hinge moment graph of the retrofitted 
aircraft lies closer to that of the passive aircraft.
Table 8.1  lists the accumulated fatigue damage values due to turbulence in one reference 
flight. In turbulence, a retrofit of the passive aircraft would significantly increase the fatigue 
life of the wing, whereas the HTP would have a slightly shorter fatigue life. To obtain the total 
fatigue damage evoked in one reference flight cycle, the fatigue damage from a ground-air-
ground cycle with MLA according to Subection  6.3.1  is added, and  Table 8.1  shows the 
resulting fatigue damage values. With the maximum damage value on the retrofitted aircraft 
of  2.71·10-12, its overall fatigue life is expected to be 2.81 times longer compared to the 
passive aircraft which has the largest damage value of 7.62·10-12. This fatigue life extension to 
281% is significantly larger than the fatigue life benefit on the active aircraft (28%). This 
results from the lower stress levels on the retrofitted aircraft in general compared to the active 
aircraft due to its higher material thicknesses.
108

8.3 Retrofit of passive aircraft with load alleviation

(a) (b)

Figure 8.4. Stress and hinge moment collectives during the climb phase of D150

Table 8.1. Fatigue damage overview of retrofitted D150

Observed shell

element

Turbulence damage Total fatigue damage

Retrofitted

aircraft

Passive

aircraft

Retrofitted

aircraft

Passive

aircraft

Wing root 6.34·10-15 2.15·10-12 2.71·10-12 7.62·10-12

Outer wing section 2.12·10-22 1.05·10-15 3.91·10-13 3.25·10-12

HTP root 1.85·10-20 2.67·10-21 1.85·10-20 2.67·10-21

ALLEGRA configuration

Figure 8.5 shows the strain and aileron hinge moment collectives of the retrofitted

aircraft during the climb phase. As apparent in Figure 8.5(a) and (b), the strain collectives of

the wing of the retrofitted aircraft show similar shapes to those of the active aircraft.

However, the strain levels of the retrofitted aircraft are lower in general. On the HTP, the

collective of the retrofitted aircraft shows slightly higher strain levels than the passive aircraft,

109

8 Investigations of load alleviation variations and practical aspects

and the agreement with the curve of the active aircraft is higher. Analogous to the strain

amplitudes on the wing, the aileron hinge moment collective of the retrofitted aircraft shows a

trend more similar to that of the of the active aircraft.

Table 8.2 lists the accumulated fatigue damage values due to turbulence during one reference

flight. In turbulence, a retrofit of the passive aircraft would extend the fatigue life of the wing

significantly, whereas the fatigue life of the HTP would slightly decrease. To acquire the total

fatigue damage caused in one reference flight cycle, the fatigue damage emerging from a

ground-air-ground cycle with MLA according to Subection 7.3.1 is superposed, and Table 8.2

shows the results. With the maximum damage value on the retrofitted aircraft of 2.78·10-24, its

overall fatigue life is expected to be 11.9 times longer compared to the passive aircraft with

the largest damage value of 3.32·10-23. This fatigue life improvement to 1190% is significantly

larger than the fatigue life benefit on the active aircraft (12%). In practice however, the factor

11.9 is unlikely to be realized since other components such as control surfaces might reach the

end of their service life earlier. Analogous to the D150 configuration, this difference results

from the lower strain levels on the retrofitted aircraft in general compared to the active aircraft

due to its higher material thicknesses.

(a) (b)

Figure 8.5. Strain and hinge moment collectives during the climb phase of ALLEGRA

110

8.3 Retrofit of passive aircraft with load alleviation
Table 8.2. Fatigue damage overview of retrofitted ALLEGRA
Observed shell
element
Turbulence damage Total fatigue damage
Retrofitted 
aircraft
Passive
aircraft
Retrofitted 
aircraft
Passive
aircraft
Wing root 4.05·10-27 2.74·10-23 2.78·10-24 3.32·10-23
Outer wing section 5.36·10-32 2.83·10-26 4.24·10-27 8.01·10-26
HTP root 9.87·10-34 6.24·10-34 9.87·10-34 6.24·10-34
In general, the maximum benefit of a retrofit is gained if it is implemented on newly delivered 
aircraft.   Depending  on   the   logistics   and  effort   to   implement   the   retrofit,   it   can   still   be 
beneficial for aircraft that have been in operation. The terms logistics and effort implies 
whether the aircraft has to be flown to the manufacturer’s site to undergo the retrofit, and how 
extensive the update of the FCC as well as the subsequent tests are expected to be.
8.4  Load factor threshold for MLA activation
In the fatigue damage accumulations described in Subsection  6.3.3  and  7.3.3, the MLA is 
assumed to always be active. This means that for every commanded vertical load factor other 
than 1.0, the ailerons are deflected by MLA. However, if there is a load factor threshold for 
the MLA, below which it should remain inactive, the effects on the fatigue life of the active 
aircraft are negative. This is because small fluctuations in the load factor below the threshold 
would evoke larger fluctuations in the stresses compared to an aircraft without the MLA 
threshold. Nevertheless, an implementation of such an MLA threshold is potentially beneficial 
in the flight operation. As an example: during take-off, a high maximum lift coefficient is 
desirable since it helps in reducing the take-off roll distance and the take-off speed. However, 
an MLA deflection during take-off means that the lift on a fraction of the lifting surface is 
reduced, and this reduces the overall lift coefficient.
As reference, the ground-air-ground cycle with a maximum load factor of 1.3 is considered, as 
defined in Subsection 6.3.1 and 7.3.1 respectively. For this study, it is assumed that the load 
factor threshold for MLA is higher than 1.3, so that the ailerons of the active aircraft are not 
deflected yet. Without MLA threshold, the ailerons are deflected by -2.5° (trailing edge up) 
according to Equation (5.7). To obtain the total fatigue damage evoked in one reference flight 
cycle, turbulence damage values of the active aircraft from Table 6.10 and Table 7.9 are added 
respectively. Table 8.3 and Table 8.4 list the fatigue damage values resulting from the ground-
air-ground cycle and the resulting total fatigue damage.
111

8 Investigations of load alleviation variations and practical aspects

Table 8.3. Fatigue damage on active D150 with MLA threshold

Observed shell

element

Ground-air-ground cycle

damage

Total fatigue damage

With MLA

threshold

No MLA

threshold

With MLA

threshold

No MLA

threshold

Wing root 1.20·10-11 5.93·10-12 1.20·10-11 5.94·10-12

Outer wing section 4.63·10-11 5.70·10-12 4.63·10-11 5.70·10-12

HTP root 5.50·10-28 2.10·10-27 4.58·10-21 4.58·10-21

Table 8.4. Fatigue damage on active ALLEGRA with MLA threshold

Observed shell

element

Ground-air-ground cycle

damage

Total fatigue damage

With MLA

threshold

No MLA

threshold

With MLA

threshold

No MLA

threshold

Wing root 6.10·10-23 2.97·10-23 6.10·10-23 2.97·10-23

Outer wing section 1.50·10-23 1.24·10-24 1.50·10-23 1.24·10-24

HTP root 4.21·10-38 4.31·10-38 2.26·10-33 2.26·10-33

As apparent, with an MLA threshold, the fatigue damage values on both reference aircraft

increase significantly. On the D150 configuration, an implementation of an MLA threshold

would lead to a shorter fatigue life by a factor of 7.79, resulting from the highest damage

values of 5.94·10-12 without MLA threshold and 4.63·10-11 with the threshold.

On the ALLEGRA configuration, the aircraft with MLA threshold would have a fatigue life

that is 2.05 times shorter compared to the aircraft with no threshold. For detailed calculations,

the effect of the high lift devices on the spanwise lift distribution as well as the element

stresses or strains need to be considered.

112

9 Evaluations, conclusions and outlook

9.1 Evaluations

Evaluation of method

An aircraft pre-design method to investigate the influence of load alleviation on structural

mass and fatigue has been developed and discussed. The method has been applied on two

reference aircraft: the conventional D150 configuration and the ALLEGRA configuration with

forward swept wing.

The developed method enables calculations of differences in the structural masses and fatigue

behaviors between the active and passive aircraft. In the structural optimization, the masses

converge according to the criteria defined in Section 3.7. In the last optimization cycle, the

RMS of change in the material thicknesses is below 4.0%. This change is a residual

uncertainty in the material thickness convergence. This uncertainty correlates with the load

case selection algorithm, especially if the dynamic gust loads are dominant. Nevertheless, the

uncertainty is accepted in order to reduce the number of load cases for the structural

optimization to approximately 60. Moreover, a mass convergence to the last kilogram is not

practicable either. Hence, at a certain point of the design process, a freeze of the structural

layout and a definition of target loads are advisable.

In the fatigue analysis, damage due to turbulence and ground-air-ground cycles in a reference

flight mission is obtained. Although the fatigue analysis method cannot provide a quantitative

result (e.g. the aircraft can survive x flight cycles), it enables a comparison between the active

and passive aircraft. With a discretization of the flight mission into three phases (climb, cruise

and descent), an insight into the severeness of turbulence damage in each phase is gained. A

factor of uncertainty in the turbulence damage lies in the random phase distribution during the

generation of the vertical wind speed in the time domain. This means, a different phase

distribution yields another time history of the vertical wind speed that in turn results in

different load collectives. To eliminate this uncertainty in the comparison between the active

and passive aircraft, the time history of the vertical wind speed in each flight phase is identical

for the active and passive aircraft.

The total computing time for the loads and optimization process of the D150 configuration is

40.2Bhours for ten cycles, or 4.02Bhours per cycle in average. In each cycle, an average of

2.52Bhours fall into the gust load calculations. On the ALLEGRA configuration, the

computing time is 35.6Bhours for seven cycles, or 5.09Bhours per cycle in average. The gust

load calculations make up 3.47Bhours per cycle that is longer compared to D150 due to the

larger number of aerodynamic elements (1176 instead of 939). The loads analysis with

MSC.Nastran is run on one processor with 2600BMHz clock frequency. The structural

optimization is carried out using eight processors and 16BGB of allocated RAM. The

computing time of the turbulence and fatigue analysis is relatively short with 10Bminutes.

113

9 Evaluations, conclusions and outlook

Although the dynamic gust analysis requires the majority of the computing time, it is worth

considering since gust loads always appear among the load cases selected for the structural

optimization, see Figure 3.4. This is also the case if the largest bending moments are reached

during maneuvers. In addition, the developed method provides a first insight into how large

the alleviated gust loads are compared to the alleviated maneuver loads. The findings might

help in the decisions of how to retune the control algorithm in the pre-design phase, e.g. to

maximize the mass benefit, that is more cost-efficient compared to doing so at a later stage.

Evaluation of results

As described in Chapter 6 and 7, the consideration of load alleviation within the aircraft pre-

design process can simultaneously yield a reduction of wing structural mass and an overall

fatigue life extension. Concerning the wing structural mass reduction on the backward swept

D150 configuration, 130.5Bkg (0.18% of MTOM, 0.32% of OEM) can be saved in total. On

the forward swept ALLEGRA configuration, the wing mass decrease is 410.4Bkg (0.56% of

MTOM, 0.94% of OEM). As a comparison: Wildschek et al. [100] stated in 2013 that on a

large blended wing-body configuration, load alleviation using a feed-forward L∞-optimal

control can yield a mass reduction by 0.5% of the maximum take-off mass. An aspect to be

remarked on is that Wildschek used the elevators, inner, outer spoilers and the ailerons as free

parameters for the controller synthesis. Hence, there were more degrees of freedom available

in tuning the control algorithm. Besides, the deflection rate of the control surfaces were

significantly higher with up to 300°/s that would eliminate potential phase shifts due to a rate

limitation. A further reference is the active load alleviation system on the Lockheed C-5A [80]

documented in 1976. The system was initially developed to extend the fatigue life of the

structure, however it was discarded and a structural modification was introduced. The

structural modification increased the empty mass of the aircraft by 5.5%. However, it cannot

be concluded that the active load alleviation can yield that mass reduction since the structure

of the C-5A is not likely to be completely re-optimized after discarding the load alleviation.

Concerning fatigue, a comparison with literature results is only possible between the

retrofitted and passive aircraft since no data of fatigue comparisons with a separate

optimization of the active aircraft could be found. The retrofitted D150 aircraft is expected to

have a fatigue life improvement by a factor of 2.81 compared to the passive counterpart. For

the ALLEGRA configuration, the fatigue life is expected to increase by a factor of 11.9

through retrofit. However, with the assumptions made, these fatigue results are obtained using

S-N curves with very flat slopes, so that small differences in the load amplitudes result in

huge differences in the fatigue damage accumulation. If S-N curves with steeper slopes are

used, these differences are expected to be smaller. As a comparison, on the Lockheed C-5A

the active load alleviation yields a fatigue life improvement of 25-50%, according to Disney

[17] in 1977. On a business jet configuration investigated by Paletta [69] in 2011, the fatigue

life is extended by 44-67%. Such fatigue life extensions are expected to be more beneficial if

the aircraft undergo many flight cycles on short routes. Otherwise, the benefit of a service life

extension from 30 to e.g. 40 years might be limited due to the availability of newer, more

profitable aircraft.

114

9.2 Conclusions

The investigations featuring the design process serve to gain an insight into the benefits of

load alleviation for a given aircraft in the pre-design phase before it advances to the next

design stage. The analyses cover multiple disciplines (loads, aeroelasticity, aerodynamics,

structure, flight mechanics, control theory, fatigue) and range from loads analysis, structural

optimization to fatigue analysis. The consideration of load alleviation in an early design stage

would also lower the risk of having to change the structure extensively in later stages.

Moreover, dynamic gusts with GLA are worth considering since they give an insight into how

large the alleviated gust loads are compared to the alleviated maneuver loads.

During the investigations, the following aspects emerge and are seen as worth mentioning:

•An implementation of load alleviation can reduce the flight loads, wing structural

mass and extend the wing’s fatigue life in turbulent weather. For ground-air-ground

cycles, the wing of the active aircraft tends to receive more fatigue damage than a

passive one. Overall however, the active aircraft show fatigue life improvement

compared to the passive counterpart. For the reference missions, the fatigue life of the

active aircraft increases by 28% (D150) and 12% (ALLEGRA) respectively – in

addition to the mass benefit.

•The passive aircraft reaches the highest aileron hinge moments during maneuvers.

Gust encounters evoke the largest hinge moments on the active aircraft.

•To maintain the fatigue life improvement of the active aircraft, there must be no

threshold for the MLA. This implies that the MLA has to deflect the ailerons at every

commanded load factor other than 1.0. Otherwise, the active aircraft with MLA

threshold would have a shorter fatigue life compared to the passive counterparts.

•Compared to the passive aircraft, a retrofit yields additional fatigue life – as long as

the passive structure can withstand the alleviated design loads. These alleviated design

loads might evoke new stress peaks due to slightly different ratios between the

bending and torsion moments.

•A fatigue life improvement at one observed position as a result from any measure can

occur simultaneously with a deterioration at another position. Thus, for a global

analysis, several positions should be observed simultaneously, and the highest fatigue

damage value determines the aircraft’s fatigue life.

•A quantitative fatigue prediction in aircraft pre-design is only sensible if the fatigue

relevant parts on the wing are known and modeled – together with the corresponding

stress/strain amplification factors, otherwise the result would practically be infinite

fatigue life.

•On forward swept wing configurations, the short period mode becomes unstable long

before aeroelastic divergence occurs. This is caused by a shift of the aerodynamic

center resulting from the bending-torsion-coupling, and the shift becomes larger with

increasing dynamic pressure. The most effective countermeasure to this would be to

115

9 Evaluations, conclusions and outlook

build the wing as stiff as possible to avoid the wingtip nose-up twist due to bending-

torsion-coupling. Otherwise, aeroelastic tailoring can help in reducing the nose-up

twist to a certain degree by trading bending stiffness against coupling stiffness.

9.3 Discussion of contribution

As elaborated in Section 1.3, the main objective of this thesis it to develop a method that

considers load alleviation in aircraft pre-design and its influence on design loads, structural

mass and fatigue. At this point, it can be concluded that the load alleviation functions for the

aircraft preliminary design stage have been implemented successfully. On one hand, the

algorithms for the MLA and GLA are simple so that they are easily understandable and

transferable to other aircraft configurations. On the other hand, the load alleviation effectively

reduces the wing bending moments without excessively increasing the torsions compared to

the passive counterpart. With load alleviation, a clear trend of decrease in the wing box mass

is obtained. While the mass decrease can be estimated accurately, there are residual

fluctuations in the material thickness distributions between the iteration cycles. Furthermore,

the effect of load alleviation on the fatigue life of the aircraft has also been analyzed

successfully using a reference flight mission. For a more comprehensive investigation

however – e.g. for one aircraft throughout its service life – a distribution of various flight

missions, the turbulence intensities as well as more detailed S-N curves are necessary.

Compared to the state of the art, the developed design process provides an insight into the

influence of load alleviation on the fatigue behavior of the aircraft – alongside its effect on the

wing box mass.

Beside the main objective, several minor aspects have been addressed:

•The developed design process has successfully been applied to a forward swept wing

configuration. It is shown that the forward swept wing configuration has different

sizing load cases and that load alleviation has a larger impact on its wing box mass as

well as fatigue life. Moreover, the potential flight mechanic instability of forward

swept wing configurations due to its aeroelasticity has been investigated, and a

solution to prevent the instability in the flight envelope has been developed.

•In the analyses, elastic aircraft, unsteady aerodynamics, active control as well as

continuous turbulence have been considered. Especially for the fatigue analysis, the

consideration of those aspects gives a more accurate insight into the load collectives of

the particular aircraft compared to standardized load spectra.

•A retrofit of passive aircraft has been investigated successfully. This aspect serves as

comparison of fatigue life extension to literature since no references dealing with

separately optimized active aircraft were found.

116

9.4 Outlook

There are several potential aspects that could be considered in the future. The first one

concerns the design load calculations. In this aspect, the load case variety can be extended to

reproduce the design load cases of a certified aircraft as close as possible. For the wing, this

includes landing, roll and asymmetric load cases as well as gust cases with extended

airbrakes. For the empennage optimization, checked maneuvers and loads caused by airbrake

wake turbulence during landing deceleration can also be considered. However, the latter

cannot be modeled with DLM aerodynamics anymore.

The airbrakes – or spoilers – play a relevant role and can improve the effectiveness of MLA

and GLA. To consider the effect of spoiler deflections with a reliable aerodynamic modeling,

the DLM has to be corrected e.g. based on CFD calculations. CFD can also be used to better

determine the aerodynamic effectiveness of trailing edge control surfaces that is assumed to

be 0.7 in this thesis. For transonic Mach numbers, a DLM correction based on CFD is also

worth considering since e.g. the torsion moments are expected to be affected by local

supersonic areas on the lifting surfaces.

For the proposed GLA, the measured angle of attack increment at the nose exactly represents

the change in angle of attack that will hit the wing since 1D turbulence is assumed. However,

in case of a 2D turbulence where the vertical wind changes in lateral direction, the wingtip

does not necessarily experience the same turbulence profile as the aircraft nose. At this point,

a correlation function between the angle of attack increment at the nose and e.g. at the wingtip

should be introduced. Besides, a more sophisticated GLA can be synthesized by optimization,

as described by Wildschek et al. [101]. The optimization objectives can be minimization of

overall stress/strain amplitudes, minimization of wing box mass or minimization of hinge

moments. However, the methods optimizing such control algorithms require that the aircraft’s

dynamics with all possible mass configurations and flight conditions are considered.

Another gust and turbulence sensor that can be used is a light detection and ranging (LIDAR)

sensor. A LIDAR system can detect the wind field up to 300Bm ahead of the aircraft [26]. This

gives the GLA an additional reaction time of approx. 1Bs depending on the weather that affects

the LIDAR signal quality. This additional second opens up further possibilities in the

development of GLA algorithms.

As described in Section 4.3, the GLA in this thesis does not consider feedback quantities of

the structural elasticity. If those are included in the control algorithm however, the damping of

elastic modes can be increased [9] that is beneficial for the fatigue life. Therefore, an

inclusion of a mode damper based on a feedback control algorithm is worth considering – as

long as the turbulence fatigue damage is not significantly outbalanced by the fatigue damage

from ground-air-ground cycles.

117

9 Evaluations, conclusions and outlook

In the structural optimization, aeroelastic tailoring can be considered as well, as described by

Dillinger [16] and by Handojo et al. [37]. However, the simultaneous consideration of a large

number of load cases, dynamic loads and aeroelastic/flight mechanical constraints in one

optimization run with aeroelastic tailoring would create a challenge in computing time and

random-access memory (RAM) requirements.

Concerning fatigue analysis in turbulence, the scenario is that the +1g flight loads stay

constant in the observation period of time, and the turbulence loads are added to the steady

flight loads. This means, load cycles with higher amplitudes have a lower stress/strain ratio

compared to the cycles with lower amplitudes. To take those changes of stress/strain ratios

into account, comprehensive data of S-N curves are necessary, so that an interpolation

between the different stress ratios for the various amplitudes is possible. This will likely result

in steeper slopes of the S-N curves, with it a larger contribution of turbulence loads (high

cycles, low amplitudes) and a smaller contribution of ground-air-ground loads (low cycles,

high amplitudes). Besides, further flight missions as well as a probability distribution of

turbulence intensities can be taken into account. For composite aircraft, a more detailed

fatigue models as applied by Rajpal et al [76] can be considered.

For airlines, one important cost factor is the aircraft inspection interval. However, the

resulting fatigue life extension of active aircraft does not ensure the possibility to increase the

inspection interval yet. For this aspect, further analyses of aircraft systems such as control

surface actuators are necessary, especially since the active aircraft deflect the control surfaces

significantly more often.

Moreover, the potential benefit through fatigue life extension also needs to be assessed while

considering the expected distribution of the flight mission duration. As an example: if an

aircraft only flies long distances, the expected service life can be extended from 30 to 40

years. Within 40 years however, there might be newer, more profitable aircraft so that the

benefit of the longer service life is reduced. On the other hand, if an aircraft only flies short

distances, the initial expected service life might be e.g. 15 years, and its extension to 20 years

might be more beneficial.

For the pre-design stage, a consideration of a more comprehensive design load spectrum and

aerodynamic modeling is expected to have the largest impact on the design. For the fatigue

analysis, it is advisable to take probability distributions of turbulence intensities and various

flight missions into account.

118

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Appendix

Visualization of gust and maneuver loads in the 2D envelopes

(a) (b)

Figure A-1. 2D gust and maneuver load envelopes of active D150 (a) and active ALLEGRAG(b)

Selected modes of the reference aircraft

Table A-1. Selected modes of the D150 configuration at operating empty mass

Mode Frequency

Active aircraft Passive aircraft

First symmetric wing bending 2.86 Hz 2.83 Hz

Second symmetric wing bending 9.32 Hz 9.16 Hz

First symmetric wing torsion 21.88 Hz 21.31 Hz

First symmetric HTP bending 8.41 Hz 8.41 Hz

First VTP bending 10.08 Hz 10.06 Hz

First vertical fuselage bending 5.46 Hz 5.45 Hz

Table A-2. Selected modes of the ALLEGRA configuration at operating empty mass

Mode Frequency

Active aircraft Passive aircraft

First symmetric wing bending 3.22 Hz 3.13 Hz

Second symmetric wing bending 9.86 Hz 9.41 Hz

First symmetric wing torsion 23.60 Hz 22.51 Hz

First symmetric HTP bending 8.57 Hz 8.55 Hz

First VTP bending 2.42 Hz 2.42 Hz

First vertical fuselage bending 4.58 Hz 4.57 Hz

127

Appendix

Flutter curves of the D150 configuration

(a)

(b)

Figure A-2. Flutter curves of the passive (a) and active (b) D150 configuration

128

Appendix

The flutter speed of the D150 configuration occurs between 356 and 358Bm/s TAS. In Figure

A-2, two highlighted flutter curves near each other are visible on both aircraft. Using a

manual mode tracking, the dominant modes of the flutter phenomena are identified as the

symmetric and antisymmetric HTP torsion, see Figure A-3. Under vacuum condition, those

elastic modes have frequencies ranging from 21.2 to 21.3BHz. At the flutter points, the flutter

frequencies of both aircraft range between 17.6 and 17.8BHz. Furthermore, as apparent in

Figure A-3, the fuselage has no relevant participation in the modes.

(a)

(b)

Figure A-3. Symmetric (a) and antisymmetric (b) HTP torsion mode of the D150 configuration

129

Appendix

Flutter curves of the ALLEGRA configuration

(a)

(b)

Figure A-4. Flutter curves of the passive(a) and active (b) ALLEGRA configuration

130

Appendix

On the ALLEGRA configuration, the flutter point occurs between 269 and 270Bm/s TAS. In

Figure A-4, the curves leading to the flutter point on both aircraft are highlighted. Using a

manual mode tracking, the dominant mode at the flutter speed is the VTP bending, see Figure

A-5. Under vacuum condition, the frequency of the elastic mode is 2.42BHz for both active

and passive aircraft. At the flutter points, the flutter frequency of both aircraft is 2.87BHz.

Moreover, from Figure A-5 it is apparent that there is no coupling with the fuselage.

Figure A-5. VTP bending mode of the ALLEGRA configuration

131

Appendix

Turbulence fatigue analysis of the D150 configuration

Table A-3. Turbulence fatigue damage per hour on D150

Flight phase Observed shell

element

Retrofitted

aircraft

Passive aircraft Active aircraft

Climb

Wing root 1.09·10-15 1.54·10-12 2.56·10-15

Outer wing section 2.76·10-23 8.59·10-16 2.68·10-22

HTP root 1.15·10-23 3.17·10-24 1.41·10-23

Cruise

Wing root 3.19·10-26 6.23·10-23 1.03·10-25

Outer wing section 2.33·10-32 2.65·10-26 4.14·10-31

HTP root 8.27·10-36 3.71·10-36 1.22·10-35

Descent

Wing root 1.18·10-14 3.06·10-12 1.79·10-14

Outer wing section 4.02·10-22 1.41·10-15 8.16·10-21

HTP root 3.70·10-20 5.34·10-21 9.15·10-21

Turbulence fatigue analysis of the ALLEGRA configuration

Table A-4. Turbulence fatigue damage per hour on ALLEGRA

Flight phase Observed shell

element

Retrofitted

aircraft

Passive aircraft Active aircraft

Climb

Wing root 3.11·10-27 1.85·10-23 7.35·10-26

Outer wing section 1.26·10-31 5.24·10-26 2.21·10-29

HTP root 6.11·10-24 5.77·10-34 1.07·10-33

Cruise

Wing root 5.50·10-38 5.44·10-35 5.51·10-37

Outer wing section 3.91·10-43 5.98·10-38 8.55·10-41

HTP root 5.71·10-46 3.94·10-46 1.00·10-45

Descent

Wing root 5.61·10-27 4.00·10-23 3.09·10-26

Outer wing section 6.49·10-33 1.47·10-26 1.05·10-30

HTP root 1.49·10-33 7.87·10-34 3.65·10-33

132