Design optimization and virtual testing of a morphing aileron with high actuation bandwidth

Contents lists available at ScienceDirect Aerospace Science and Technology journal homepage: www.elsevier.com/locate/aescte Design optimization and virtual testing of a morphing aileron with high actuation bandwidth Vittorio Cavalieri 1, Alessandro De Gaspari 2,∗ Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156, Milano, Italy article i n f o Editor: Dr Mehdi Ghoreyshi Keywords: Compliant structures Morphing wings Dynamic actuation Aerodynamic shape optimization Topology optimization Dynamic resonant system a b s t r a c t One of the key strategies to make future aviation more sustainable is to improve the aerodynamic efficiency-toweight ratio of aircraft while simultaneously reducing the energy required to actuate onboard control surfaces. This paper presents a novel morphing aileron, designed for a hybrid-electric regional aircraft, developed to replace a conventional aileron while providing multiple benefits. Unlike traditional ailerons, which are restricted to rigid-body rotation, a morphing aileron changes its external shape, enabling greater design flexibility. This shape-changing capability has been exploited to first optimize the external morphed shapes of the aileron that match the aerodynamic performance of the conventional surface, while requiring half the deflection. This results in reduced aerodynamic drag and lower actuation effort. The optimized shapes were then used as targets to design a compliant structure capable of deforming as needed while remaining insensitive to external loads, with the overall actuation force minimized under additional dynamic performance requirements. Virtual testing of the complete device successfully validated its static and dynamic performance. The static validation, carried out in the presence of aerodynamic loads, confirmed the device’s ability to reduce actuation forces under realistic operational conditions. The dynamic validation, conducted in dry conditions, demonstrated the potential of the system to reduce dynamic actuation loads. This implies the potential use of smaller and lighter motor actuators, thus improving the overall system efficiency. 1. Introduction The increasing environmental and economic pressures in the aeronautical industry are driving research toward innovative solutions aimed at enhancing efficiency. Current investigations span multiple disciplines, including aerodynamics, propulsion, and structural design. Among the explored strategies, active flow control techniques have shown potential in suppressing flow separation, thereby improving aerodynamic performance [7]. Hybrid–electric propulsion systems represent a promising path for achieving sustainable aviation, as they can significantly reduce aircraft emissions [8]. Similarly, high–aspect–ratio wings are being studied for their ability to minimize lift–induced drag and improve fuel efficiency [9]. Another promising approach to increase the aerodynamic efficiency–to–weight ratio of aircraft is the integration of morphing devices. Morphing systems enable aircraft wings to adapt to various flight conditions, which can enhance overall mission performance and reduce fuel consumption [10]. While morphing technologies can be applied to high–lift systems [11–13], they also offer the potential to replace conventional control surfaces, such as hinged ∗Corresponding author. E-mail addresses: [email protected] (V. Cavalieri), [email protected] (A. De Gaspari). 1PostDoctoral Researcher. 2Associate Professor. ailerons, which typically introduce aerodynamic discontinuities and disturb laminar flow due to the presence of gaps. In particular, morphing ailerons have shown promise in meeting roll control requirements, even when constrained by limited chord extensions, as commonly found in high aspect ratio wings. Moreover, their functionality extends beyond roll moment increase: morphing trailing edges can also contribute effectively to maneuver load alleviation [14], offering a multi– functional solution within the broader context of next–generation wing design. The design of a morphing aileron falls within the broader concept of variable camber wings, which aim to modify the airfoil curvature to increase lift while minimizing the associated drag increase [15–17]. Different kinds of skin structures can be employed to realize this concept. Segmented skins are based on the relative displacement or rotation of adjacent panels [18,19], while compliant skins exploit the elastic deformation of materials, typically using elastomers or fiber–reinforced composites [20]. Another approach involves flexible skins that take advantage of structural bending deformation, such as corrugated configurations [21,22]. https://doi.org/10.1016/j.ast.2025.111110 Received 29 July 2025; Received in revised form 15 October 2025; Accepted 16 October 2025 Aerospace Science and Technology 168 (2026) 111110 Available online 30 October 2025 1270-9638/© 2025 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). V. Cavalieri and A. De Gaspari Beyond the skin, morphing concepts require suitable internal structures to both enable shape adaptation and withstand aerodynamic loads. Lattice structures offer lightweight and stiff solutions for shape morphing applications [23,24]. Internal configurations based on initially curved beams can achieve large deformations while maintaining high load–bearing capacity [25]. Additionally, bistable composite laminates offer potential for energy–efficient morphing through their ability to maintain shape without continuous actuation [26]. In recent years, pioneering research is exploring the use of multi–stable panels to provide morphing capabilities to composite wings [27,28]. A promising approach for airfoil curvature adaptation is the Fish Bone Active Camber (FishBAC) concept, a bio–inspired design that mimicks the flexible skeletal frame of a fish, with no mechanism or sliding skins [29]. Wind tunnel experiments have demonstrated that a continuous morphing trailing edge based on this concept can outperform traditional hinged flaps in terms of maximum lift–to–drag ratio [30]. Another morphing trailing edge concept is the Translation Induced Camber (TRIC), which allows for both chordwise and spanwise sliding of the bottom skin, using a combination of cross–sectional warping and skin bending to induce both camber and twist morphing [31]. The TRIC concept employs rotary actuators combined with linkages to apply a force to the bottom skin in the chordwise direction. The most technologically mature trailing–edge device characterized by smooth curvature change is the Mission Adaptive Compliant Wing (MACW) flap, whose design was based on the distributed compliance concept. This technology was flight–tested to demonstrate extended laminar flow and reduced fuel consumption compared to conventional flaps. Moreover, it proved to be lighter and required lower actuation forces [32]. Compliant structures, leveraging elastic deformation instead of traditional mechanical linkages and hinges, are well–suited for airfoil camber control [33]. Their design typically involves specialized synthesis methods, often based on genetic algorithms combined with structural parameterizations, such as binary ground structure representation [34] or load path representation [35]. The latter has proven effective for both leading and trailing edge devices [1]. In this context, topology and sizing optimization are jointly addressed to satisfy both structural and kinematic requirements of morphing structures. The design of a morphing device must account for the actuation system needed to realize shape changes. A promising strategy in this regard consists in coupling the actuation system with a sliding skin concept. In [1,2], a solution was introduced in which the sliding motion of the lower skin of a morphing trailing edge is combined with a compliant rib mechanism. Recently, a more general sliding–skins configuration has been proposed, merging the concept of a continuum parallel mechanism [36] either with a robotic system [37] or with an internal auxetic rib structure [38]. The approach adopted in the present work builds upon the first concept described above by introducing a new solution in which the actuation system is combined with the sliding motion of the lower skin only, while removing any internal ribs. The overall morphing structure is therefore optimized to simultaneously fulfill both the structural and kinematic requirements previously described, through the use of collaborative skins. This configuration further reduces weight and simplifies manufacturing, while the combination of a sliding lower skin with a fixed upper skin facilitates integration with wing box architectures and ensures structural continuity. In addition, it prevents any aerodynamic discontinuities, such as gaps or steps, on the upper surface of the airfoils, which would otherwise decrease aerodynamic efficiency. Finally, in this framework of integrated structural and actuator system optimization, minimizing actuation energy can be adopted as a design objective to ensure both lightweight and energy–efficient solutions [3,39]. Several advanced morphing demonstrators are currently being developed within the EU–funded HERWINGT project, supported by the Clean Aviation Joint Undertaking. The high–lift system installed on the project’s reference wing integrates a morphing droop nose and a morphing flap. The droop nose, developed by Politecnico di Milano (PoliMi), builds upon the structural architecture designed and validated in the Clean Sky 2 Airgreen 2 project, which culminated in the successful design and experimental testing of a full–scale demonstrator [4]. The flap, developed by CIRA, is a compliant morphing device obtained through topology optimization [40]. 2D aerodynamic analyses have shown that, in combination with flow control strategies to mitigate flow separation, the droop nose and the morphing flap together can achieve the required high–lift performance [41]. Additionally, the reference wing is equipped with morphing ailerons, whose design and validation are thoroughly discussed in this manuscript. The proposed morphing aileron is designed to reduce aerodynamic drag during maneuvers while also minimizing the required actuation force. Compared to a traditional hinged aileron, drag reduction results from multiple factors. The morphing aileron is seamless, eliminating gaps that contribute to parasitic drag. Furthermore, it can achieve equivalent lift coefficient variations with smaller deflections than a hinged counterpart, further decreasing drag. Smaller deflections also reduce the aerodynamic work performed on the surface, which translates into lower actuation force requirements. This combined reduction of aerodynamic drag and actuation demand represents another novelty of the present work. While the drag reduction improves aerodynamic efficiency, the lower actuation demand specifically enables the installation of more compact and lighter actuation systems, ultimately leading to overall weight savings. Moreover, the intrinsically simple design of the proposed device, together with the use of aeronautical materials and design requirements derived from a real aircraft, aims to replace conventional ailerons on actual wings, supporting acceptance by certification authorities. The inherent structural flexibility of the morphing device enables further mass reduction compared to conventional hinged solutions, while also offering the potential to tailor the dynamic response of the system by accounting for dynamic properties during the design phase. Compliant structures have previously been employed as displacement amplification mechanisms in high–frequency active flow control systems [42]. Their use in dynamic applications can reduce peak power requirements, as demonstrated for a flapping–wing micro air vehicle [43]. However, morphing devices used in dynamic applications are typically limited to small–scale unmanned aerial vehicles, which face lower aerodynamic loads and actuation demands. Consequently, piezoelectric actuation is often used in such cases but is generally unsuitable for larger aircraft. An additional novelty of the morphing aileron presented in this work is its high–bandwidth capability, which makes it suitable for installation on modern aircraft incorporating electromechanical actuators and advanced active control systems, including gust load alleviation and flutter suppression technologies. Thus, the flexibility of the structure not only reduces static actuation forces, but also allows for a reduction of dynamic actuation effort by designing the aileron as a dynamic resonant system, and tuning its first vibration mode to lie within or slightly above the target operational bandwidth. As a result, the required dynamic actuation force is minimized, and the static actuation forces become the dominant design driver for the actuation system. This paper presents the optimal design and numerical validation of this morphing aileron. Section 2 introduces the reference wing, outlines the design requirements for the device, and describes the working principle of the actuation system conceived for the morphing concept. The overall design process, conducted at the full–scale level, is detailed in Sections 3 and 4, which cover the aerodynamic shape optimization and the structural optimization, respectively. Section 5 presents the functional and structural assessment performed using a high–fidelity finite element model, including virtual dry dynamic tests of the device. Finally, Section 6 summarizes the main findings of the work. Aerospace Science and Technology 168 (2026) 111110 2 V. Cavalieri and A. De Gaspari Fig. 1. Complete aircraft wing (left) and morphing aileron demonstrator mounted on outermost part of the wing for wind tunnel testing (right). 2. Morphing aileron: Configuration, requirements, and actuation concept The reference configuration considered in this article is based on a high-aspect-ratio strut-braced wing, designed to enhance aerodynamic efficiency and reduce overall fuel consumption in a hybrid-electric regional aircraft. This architecture is adopted as the baseline for integrating the innovative morphing aileron device investigated in this work. The wing is equipped with three independent aileron devices with a total span of approximately five meters. An experimental demonstrator of this morphing device is currently under development for both dry and wind tunnel testing. Due to wind tunnel facility constraints, the demonstrator is limited to the outermost two meters of the aileron span. For this reason, the design of the outermost aileron device is of primary interest. Its root section, located two meters from the wing tip, approximately at the midpoint of the full–span aileron, is selected as the reference airfoil for aerodynamic evaluations and for the definition of the optimal morphing shape. The procedure developed for the shape optimization of this section is then applied to other airfoil locations along the span to reconstruct the complete 3D geometry of the morphing aileron. Fig. 1 shows the complete aircraft wing and the morphing aileron demonstrator attached to the wing box. 2.1. Design requirements General design requirements for the morphing aileron include maintaining a continuous external shape, without steps or gaps, to preserve flow laminarity. Shape changes must be achieved through structural deformation, and therefore the skin is flexible and bends to match the desired geometry, while resisting axial stretching. The lower skin is allowed to slide along the tangential direction of the airfoil surface to accommodate the deformation. The deformable portion of the aileron begins at 70 % of the chord, just aft of the rear spar located at 60 %. This configuration ensures sufficient room for integrating the actuation kinematics. The morphing aileron is designed to minimize the required actuation force and to achieve a dynamic bandwidth of up to 10 Hz, depending on the interaction with the selected electro–mechanical actuators (EMAs). Simultaneously, the morphing aileron is also designed to match or improve the aerodynamic performance of the conventional hinged aileron. In particular, it must provide equivalent increments in lift coefficient across a range of flight conditions, ensuring at least the same roll control authority, alongside drag minimization and reduced structural weight. A reference deflection of ±30◦ is adopted based on the conventional aileron deflection at design maneuvering speed, 𝑉𝐴, corresponding to Mach 0.29 at sea level. In these conditions, the conventional solution exhibits significant flow separation, as illustrated in Fig. 2. The results correspond to a 2◦ angle of attack in the aircraft reference system, with the airfoil geometry including a local wing twist of 0.9◦. Both the minimization of the aerodynamic drag and the minimization of the actuation force are included as objectives from the early stage of the aero–structural shape optimization described in Section 3. The structural integrity of the morphing device, along with its ability to deform as desired, also complies with the design loads defined by CS–25 regulations, which are considered in Section 4.2 during the compliant structure optimization. 2.2. Morphing concept and actuation system The morphing aileron architecture is shown in Fig. 3. The complete structure results from the optimization process described in Section 4. It consists of a compliant external skin with variable chordwise thickness, and an internal flexible spar connecting the upper and lower skins. The upper skin is clamped at 70% of the chord via ribs supporting the non–morphing region between the rear spar and the morphing device. In contrast, the lower skin is free to slide in the chord direction. At the same 70% chord location, it is connected to a stringer, which transfers the actuation force from the actuation mechanism to the skin and distributes this force along the span of the aileron, ensuring smooth deformation without introducing anticlastic distortion. The sliding motion of the lower skin occurs along the direction tangent to the airfoil at the attachment point. By applying pull or push forces to the lower skin through this mechanism, the entire structure bends to generate downward or upward deflected shapes, respectively. The actuation system consists of multiple linear motors installed inside the wing–box and attached to the rear spar through an interface plate. At both ends of each motor shaft, a pair of linear guides allows the spanwise movement. Each end of the motor shaft is linked, through a rod, to a linear guide, installed on the ribs, that allow motion along the chordwise direction. The described mechanism converts the spanwise motion of the motor shaft into a controlled chordwise displacement of the lower skin, through the above mentioned stringer connection. The use of linear guides ensures low–friction motion while simultaneously supporting aerodynamic loads acting on the skin. The actuation layout is scalable and modular, making it suitable for implementation across the full span of the morphing device. The proposed kinematic solution was identified as optimal for the 2meter-span ailerons of the reference wing described in Section 2. Specifically, the spanwise actuation system adopted in this work requires a lower force for upward deflection and a similar force for downward deflection, compared to a morphing solution based on a chordwise actuation force applied to the skin. Nevertheless, this configuration may not be suitable for larger ailerons or when trailing–edge twist is also required, as in the system described in [31]. In such scenarios, the morphing aileron structure proposed in this work could still be employed, but would need to be coupled with a different type of actuation. Aerospace Science and Technology 168 (2026) 111110 3 V. Cavalieri and A. De Gaspari Fig. 2. CFD results for the conventional hinged aileron at 2◦ angle of attack: downward deflection of 30◦ (left) and upward deflection of −30◦ (right). Flow is visualized in terms of streamlines and momentum along the chordwise direction. Fig. 3. Morphing aileron configuration. The reference (undeflected) configuration is shown in beige; downward and upward deflected shapes are shown in blue. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3. Aero–structural shape optimization The focus of this section is the first level of the overall design process, which involves the aero–structural shape optimization of the morphing aileron. The objective of this phase is to identify feasible morphing shapes capable of achieving the required aerodynamic performance with minimal actuation effort. This is achieved through a parameterized shape description, aerodynamic simulations, and structural feasibility constraints. The resulting optimal shapes will be used as inputs for the subsequent structural optimization stage, which represents the second level of the overall design process. 3.1. Parameterization method Shape optimization is performed using a parameterization technique that enables shape variation through a limited set of design variables. The original Class/Shape function Transformation (CST) method, proposed by Kulfan [44], has been extended by PoliMi [5] to identify the initial wing shape and to introduce the perturbations associated with morphing. Once the geometries of both the original and the morphing wing surfaces are defined, the CST approach provides an analytical description of each configuration. The comparison between the two allows for the fully analytical computation of axial and bending strains in the skin by evaluating length variation Δ𝐿 and curvature variation Δ𝜅, respectively. The curvature difference function can be also used to estimate the resulting bending stress, assuming suitable values for skin thickness and Young’s modulus, according to Kirchhoff plate theory [45]. This analytical framework also supports the estimation of actuation energy required for morphing. The estimate includes the strain energy required to deform the skin, still calculated analytically, and the aerodynamic work, partially analytical, associated with the skin displacement induced by the morphing deformation [3]. The actuation energy thus depends solely on the skin’s bending strain, thickness, Young modulus, and the pressure distributions before and after morphing. It does not depend on a specific actuator configuration and can be evaluated independently in this phase. Assuming a linear relationship between force and stroke applied to the lower skin, the estimated actuation energy allows computing the force to be applied to the lower skin to achieve the desired stroke. The corresponding stroke is directly evaluated by comparing the original and morphing wing surfaces through the CST analytical approach. It is important to note that this force does not directly represent the actuator load, which depends on actuator placement and kinematic configuration to be defined in later design phases. 3.2. Formulation of the optimization problem The optimization aims to minimize both the aerodynamic drag coefficient 𝐶𝑑 and the force required by the lower skin 𝐹𝑠𝑘𝑖𝑛 that, as explained above, provides an effective preliminary indicator of the actuation effort. The corresponding multi–objective optimization problem for Aerospace Science and Technology 168 (2026) 111110 4 V. Cavalieri and A. De Gaspari Fig. 4. Design variables defining the structural shape change of the morphing aileron. Fig. 5. Response surfaces of the shape optimization objectives for the downward–deflected morphing aileron. defining optimal morphing shapes is stated as follows: min 𝐱={𝛿𝑇 𝐸 ; Δ𝛽}{𝐶𝑑(𝐱); 𝐹𝑠𝑘𝑖𝑛(𝐱)} such that 𝐶𝑙(𝐱)≥|𝐶𝑙, 𝐻𝑖𝑛𝑔𝑒𝑑 | Δ𝜓𝑤𝑖𝑛𝑔−𝑏𝑜𝑥 ≡[0,0.7] |Δ𝐴(𝐱)|≤𝑘𝑎⋅𝐴 |Δ𝐿𝑈𝑝𝑝𝑒𝑟𝑆𝑘𝑖𝑛(𝐱)|= 0 |Δ𝐿𝐿𝑜𝑤𝑒𝑟𝑆𝑘𝑖𝑛(𝐱)|≤𝑘𝑐⋅𝑐 |Δ𝜅(𝐱)|≤Δ𝜅 𝐱𝑙𝑏 ≤𝐱≤𝐱𝑢𝑏 (1) Here, the design variables 𝐱= {𝛿𝑇 𝐸 ; Δ𝛽} represent the trailing–edge equivalent rotation and the boat–tail angle variation of the airfoil, respectively. They are constrained to vary within the lower and upper bounds 𝐱𝑙𝑏 and 𝐱𝑢𝑏, respectively. The design variables are represented in Fig. 4. The vertex of the equivalent rotation angle is located at the center of the circle tangent to both the upper and lower surfaces where the morphing deformation begins. The two design variables govern a total of four shape parameters, two on the upper surface and two on the lower surface, and these parameters enable the description of all feasible shape variations in the trailing–edge region [5]. The problem formulation includes structural, and aerodynamic constraints. The first constraint ensures that the lift coefficient 𝐶𝑙 is at least equal to that of the fully deflected hinged aileron (𝐶𝑙, 𝐻𝑖𝑛𝑔𝑒𝑑 ), evaluated at the design maneuvering speed (𝑉𝐴) condition at 2◦ angle of attack depicted in Fig. 2. The lift coefficient values for the hinged solutions are 1.5605 and −0.7936 for downward and upward deflections, respectively. The enforcement of this trim condition, combined with the drag minimization, corresponds to maximize the aerodynamic efficiency in the same condition. The second constraint imposes that shape changes do not affect the region within the wing box, defined for 𝜓∈ [0,0.7] of the chord [5]. The remaining structural constraints guarantee feasible morphing behavior: •maximum internal area change Δ𝐴 limited to 𝑘𝑎= 5 %, •zero axial strain in the upper skin, •maximum lower skin stroke limited to 𝑘𝑐= 2.5 % of the chord 𝑐= 1.856 m, •maximum curvature variation Δ𝜅 limited to Δ𝜅= 18. The optimization process is conducted using a Design of Experiments (DOE) approach. Aerodynamic, structural, and actuation results are approximated via response surfaces, built using a Latin hypercube sampling of 40 points in the design space. Each shape is defined analytically using CST, and aerodynamic analyses are performed using the open– source Reynolds–averaged Navier–Stokes (RANS) based CFD solver SU2 [46]. The response surfaces of the objective functions for the downward deflection case, characterized by higher values of drag and required skin force, are presented in Fig. 5. 3.3. Optimization results The solution of the multi–objective problem yields a Pareto front representing the trade–off between drag and required lower skin force. Fig. 6 illustrates the Pareto fronts for downward and upward deflections. Three candidate solutions are highlighted for each deflection case. Their corresponding morphing shapes are shown in Fig. 7. Among the candidate shapes, the final choice was made by prioritizing the minimization of required skin force, while still ensuring competitive aerodynamic performance. Indeed, all the solutions on the Pareto front achieve a drag reduction compared to the conventional hinged aileron, and the additional gain achievable by moving toward the left side of the Pareto front is marginal. Therefore, prioritizing an actuation force reduction is more beneficial, as it allows for the use of smaller and lighter actuators. The selected downward and upward deflection shapes, highlighted in red in the Pareto fronts, are characterized by the optimal variables (𝛿𝑇 𝐸 ,Δ𝛽) = (14◦,25◦) and (𝛿𝑇 𝐸 ,Δ𝛽) = (−15◦,−27◦), and corresponding lower skin strokes of −35.5 mm and 37.9 mm, respectively. These stroke values satisfy the constraints and are used as input for the Aerospace Science and Technology 168 (2026) 111110 5 V. Cavalieri and A. De Gaspari Fig. 6. Pareto fronts of the shape optimization problem for downward (left) and upward (right) deflections. Fig. 7. Highlighted morphing shapes selected from the Pareto fronts for downward (left) and upward (right) deflections. Fig. 8. CFD results at 2◦ AoA: momentum along the chord and streamlines for 14◦ downward (left) and −15◦ upward (right) equivalent deflection of the morphing aileron. subsequent structural optimization and model validation phases. The optimal values of drag coefficient for the selected downward and upward deflections are 𝐶𝑑,𝑑𝑜𝑤𝑛 = 0.02763 and 𝐶𝑑,𝑢𝑝 = 0.01126, while the corresponding values of aerodynamic efficiency are 𝐸𝑑𝑜𝑤𝑛 = 56.5 and 𝐸𝑢𝑝 = −70.5. Fig. 8 compares the aerodynamic flowfields of the selected morphing shapes at the design maneuvering speed. Compared to the results for the hinged aileron (Fig. 2), the morphing shapes exhibit significantly reduced separation and boundary layer detachment. In the following section, a comparison between the aerodynamic behavior of the morphing aileron and the hinged aileron will also be presented, focusing on aerodynamic coefficients, pressure distribution, and actuation loads. This comparison will be based on the actual deformation of the optimized compliant structure, rather than the shape variations prescribed by the CST parameterization. 4. Compliant structure optimization The design of the compliant structure is achieved through a combined topology and sizing optimization process. Once actuated, the structure must be capable of producing external shapes that closely approximate the target configurations obtained from the aerodynamic shape optimization described in the previous section. The overall structural layout consists of an internal support structure connected to a variable–thickness skin. The behavior of the device is governed both by the topology of the internal structure and by the thickness distribution of the skin. The internal structure supports the skin in sustaining loads and plays a crucial role in achieving the desired deformation. In this concept, the actuation system is connected directly to the skin and drives its sliding motion, as described in Section 2.2. Aerospace Science and Technology 168 (2026) 111110 6 V. Cavalieri and A. De Gaspari Fig. 9. Finite element model and optimization variables for the structural design of the morphing aileron. 4.1. Design optimization methodology The design approach adopted in this study is specifically tailored for trailing–edge devices. It assumes a simplified structural configuration compared to a full load path representation, omitting internal points. As a result, the internal structure is composed of elements that directly connect the upper and lower skins. This choice offers two primary advantages: it reduces architectural complexity, thus simplifying manufacturing and lowering stress levels compared to the load path configurations used in leading–edge devices [6], and it reduces the number of design variables, as no internal point coordinates are included. An illustrative finite element model of the morphing aileron and its optimization variables is shown in Fig. 9. The finite element (FE) model is developed using Abaqus software, selected for its advanced nonlinear analysis capabilities. The structure is modeled using 4–node quadrilateral shell elements with a finite–strain formulation, both for the skin and the internal structure. A surface– to–surface tie constraint is employed to model the connection between the skin and internal structure. The model represents a spanwise section of the device, thus excluding 3D effects which will be addressed at a later stage in the design process. The internal structure spans the entire section and represents compliant spars. Boundary conditions are used to model the interface between the skin and the wing. The upper skin is clamped, while the lower skin is free to slide along a direction tangent to the airfoil surface at the point where morphing deformation begins. In the reference configuration, the lower skin is clamped and the actuator is locked. During actuation, the prescribed displacement at the lower skin is enforced. This stroke is determined from the CST–based geometric description, corresponding to the length variation of the lower skin. The design variables for the optimization problem, illustrated in Fig. 9, are: •Beam sizes (real variables): in–plane dimensions of the internal structural elements. •Boundary sizes (real variables): thicknesses of the boundary segments into which the skin is partitioned. •Boundary arclength (real variables): non–dimensional arclength positions on the upper and lower skins where internal beams may be connected. •Beam destination (integer variables): integer variables indicating which destination points the internal beams are connected to. •Beam existence (binary variables): used to activate or deactivate internal beams. The simplicity of this approach, compared to the complete load path representation method [47], lies in the non–use of internal points. As a result, load paths connect only output points, simplifying the connectivity definition. Each load path is fully defined by two attachment points, and its presence or absence is governed by a binary variable (1 or 0), without requiring filtering techniques. The topology is thus controlled by the combined use of the boundary arclength, beam destination, and beam existence variables. In parallel, the use of beam and boundary size variables addresses the sizing problem. Using arclength–based positions as design variables offers significant advantages. A single scalar value suffices to define a point along the skin, whose coordinates can be reconstructed through the CST. Furthermore, since these arclength positions are continuous variables, the formulation is inherently mesh– independent. 4.2. Optimization problem and results The primary goal of the morphing device is to achieve the optimal shapes required for the desired aerodynamic performance. However, being an aeronautical component, the device must also satisfy structural requirements under each considered load condition. Specifically, the structure must withstand aerodynamic loads without significant deformation, regardless of whether the configuration is morphing or not. Additionally, the structure must comply with typical strength verifications in terms of allowable stress. The attempt to achieve the target shapes resulting from shape optimization is formalized as the minimization of the least–square error (LSE) between the deformed shape, obtained via finite element analysis under actuation, and the desired target shape. The minimization of LSE, evaluated at a set of skin control points, represents the kinematic requirement associated with morphing. On the other hand, the structural requirement related to load-bearing capacity can be formulated as the minimization of the strain energy, assuming a fixed lower skin. Alternatively, the required stiffness can be promoted by minimizing the displacements at the skin control points, which can be formalized as the minimization of the LSE between the deformed shape under aerodynamic loads and the undeformed, unloaded configuration. The selected objective functions for this optimization problem are: Aerospace Science and Technology 168 (2026) 111110 7 V. Cavalieri and A. De Gaspari •Minimization of the kinematic LSE in both downward and upward deflection configurations, under the corresponding aerodynamic loads (Mach = 0.29, h = 0 m; AoA = 8deg for downward deflection and AoA = -4deg for upward deflection), when the mechanism is actuated. •Minimization of the structural LSE to preserve the undeformed airfoil shape, under aerodynamic loads corresponding to the most critical flight condition (Mach = 0.45, h = 0 m, AoA = 4°), when the mechanism is not actuated. A lower constraint is imposed on the frequency of the first vibration mode 𝑓1 to ensure a dynamic behavior compatible with a 10 Hz actuation bandwidth. This prevents the device from acting as a low–pass filter, which could delay the control response. The natural frequency is computed assuming boundary conditions that allow the lower skin to slide freely, thereby promoting the design of a dynamic resonant system capable of following fast control commands. The objective and constraint functions are evaluated through nonlinear finite element analyses in Abaqus. Constraints on maximum strain are not included in the optimization, as CST–based estimates indicate that the strain levels required to achieve the target curvature changes are non–critical. Therefore, strains are verified only for the final optimal solution. The optimization problem for the definition of the optimal structure is formulated as: min 𝐱𝐿𝑆𝐸𝑖(𝐱), 𝑖 = 1,2,3 𝐫𝑖(𝐱) = 𝟎, 𝑖 = 1,2,3 𝑓1≥𝑓 𝐱𝑙𝑏 ≤𝐱≤𝐱𝑢𝑏 (2) where the design variables 𝐱 define the topology and sizing of the structure. The objective functions correspond to the LSE values for the three configurations: downward and upward deflections (kinematic requirements) and undeformed configuration (structural requirement). The residual equations 𝐫𝑖(𝐱) = 0 ensure equilibrium in the nonlinear analyses. The constraint on the first mode frequency 𝑓1 guarantees compliance with the bandwidth requirement, with 𝑓= 10 Hz. The multi–objective nature of the problem makes it suitable for a multi–point design optimization strategy, seeking a trade–off between the different deflected shapes associated with different flight conditions. The aerodynamic loads for the selected configurations are obtained from 2D CFD simulations of CST–defined target shapes. In the finite element model, these loads are applied as pressure distributions on the skin, and remain normal to the deformed surface throughout the morphing process. The undeformed shape pressure field is applied at the start of the analysis, and the pressures are linearly increased until they match those associated with the final target shape. When the deformed shape obtained by optimization converges to the target shape, the applied aerodynamic loads can be considered accurate. The boundary conditions used to enforce lower skin motion correspond to the length variations derived from the CST evaluation, as described in Section 3.3. The reaction force required to enforce the skin motion represents the actuation force needed to achieve the desired shape under aerodynamic loads. Although actuation force is not explicitly minimized in this multi–objective problem, the formulation, based on tracking target shapes defined by the optimization problem of Eq. (1), implicitly favors designs that lead to lower actuation loads. Moreover, for a given optimal shape, the actuation force depends on the local thickness distribution, which will be further refined through a local optimization step aiming to reduce force while preserving shape quality, as defined later in Eq. (3). The multi–objective problem is solved using a controlled, elitist genetic algorithm, which promotes both high–fitness individuals and those that contribute to population diversity. Parent selection is performed through binary tournament selection: each parent is chosen as the best of two randomly selected candidates. Genetic diversity is introduced through crossover and mutation operators, which are designed to handle both continuous, discrete and binary design variables. For size–related variables, crossover exchanges variables of the same type (boundary or beam) between parents with a certain probability, while mutation replaces a variable with a randomly selected value within bounds. For topology–related variables, crossover may exchange beams between parents, and mutation may alter a beam’s destination or toggle its presence in the model. Structural integrity rules are enforced to prevent overlapping or intersecting beams, although beams may share common end points on the skins. The initial population is randomly generated within the allowed design space. Boundary arclength variables are selected partly at random and partly from a predefined set of optimal active points on the skin. This set is derived from the union of active points identified for each morphing shape and correspond to locations that allow to better fit curvature difference between morphing and undeformed shapes, identified through a dedicated minimization process [1]. The genetic algorithm returns a Pareto set of optimal solutions. Among these, a final design is selected for further refinement. In this second step, a local optimization using a sequential quadratic programming algorithm adjusts the skin thickness distribution to reduce actuation force while preserving the achieved shape. The corresponding problem is: min 𝐱max 𝑖|𝐹𝑖(𝐱)|, 𝑖 = 1,2 𝐿𝑆𝐸𝑖(𝐱)≤𝐿𝑆𝐸𝑖, 𝑖 = 1,2,3 𝐫𝑖(𝐱) = 𝟎, 𝑖 = 1,2,3 𝑓1≥𝑓 𝐱𝑙𝑏 ≤𝐱≤𝐱𝑢𝑏 (3) The objective is to minimize the peak force required on the lower skin for both downward or upward deflection cases, which allows for smaller actuators and contributes to mass savings. The LSE constraints ensure that shape quality is not degraded from the global optimization results. Other constraints remain unchanged from Eq. (2). In this sizing optimization, the topology (including internal spar placement) is kept fixed. The structural configuration of the final optimal design is shown in Fig. 10, together with the deformed shapes and corresponding maximum principal strain contours. Shape quality comparisons are provided in Fig. 11. A modal analysis of the final optimized design is conducted for two different boundary conditions: with sliding and fixed lower skin. The corresponding first–mode frequencies are 10.9 Hz and 51.5 Hz, respectively. The former satisfies the minimum dynamic constraint included in the optimization, while the latter ensures that the actuation command remains in phase with the structural response within the bandwidth of interest, as further discussed in Section 5.2. 4.3. Comparison between morphing and hinged aileron The aerodynamic advantage of the morphing aileron over a conventional hinged solution is demonstrated by comparing their aerodynamic performance at the design maneuvering speed. Fig. 12 shows the lift coefficient and the efficiency as functions of the angle of attack, while Fig. 13 represents the polar curves. The 𝐶𝑙−𝛼 curves shows that the constraint on the lift coefficient is satisfied, since for positive deflection morphing 𝐶𝑙 is higher than the hinged one, whereas they are equal for negative deflections. The morphing configurations exhibit significantly lower drag, nearly an order of magnitude less in the case of downward deflection, while achieving the same variations in lift coefficient as the hinged configurations. This results in a clear improvement in aerodynamic efficiency, as shown in the graph at the bottom of Fig. 12, where the 14◦ downward morphing configuration is compared with the 30◦ hinged configuration, and the −15◦ upward morphing configuration is Aerospace Science and Technology 168 (2026) 111110 8 V. Cavalieri and A. De Gaspari Fig. 10. Optimal solution from the structural optimization problem (in gray) and downward/upward deformed shapes with contours of maximum principal strain. Fig. 11. Comparison between deformed and target shapes for downward (left) and upward (right) deflection. compared with the −30◦ hinged configuration. The efficiency difference between the morphing and hinged solutions is highlighted across the full range of angles of attack. Validation of the morphing aileron also includes the aerodynamic analysis of the deformed shapes obtained from the finite element simulations, to verify that the lift coefficient requirements are met by the actual structural solution. To this end, CFD analyses are performed and the results are compared with those of the corresponding target shapes. This comparison, carried out at the same design conditions used for the structural optimization described in Section 4.2, shows minor differences in lift and drag coefficients, leading to an efficiency reduction of about 1 % of the deformed shape compared to the target. Nonetheless, the aerodynamic efficiency of the deformed shape remains about three times higher than that of the hinged aileron (2.8 and 3.3 for downward and upward deflections, respectively). In Fig. 14, the pressure coefficient distributions of the deformed and target shapes are compared, alongside the distribution for the hinged aileron. Once the aerodynamic performance of the designed morphing solution has been validated, an actuation force comparison with the corresponding hinged solution can also be performed. The total actuation force required for the morphing aileron consists of two contributions: a structural component needed to deform the structure, and an aerodynamic component needed to counteract the aerodynamic loads. This total force is obtained through finite element analyses of the optimized structure under aerodynamic loads. The structural contribution is estimated as the force required to achieve the morphing deformation in the absence of aerodynamic loads. The aerodynamic contribution is then computed as the difference between the total force and this structural component. In contrast, for the conventional hinged aileron, the actuation force is entirely due to aerodynamic loads. It is estimated based on the hinge moment of a rigidly rotated aileron, assuming an internal actuation mechanism, as external modifications of the aerodynamic surfaces are not permitted on the reference wing. Fig. 12. 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