A FEM-based mo phing wing concep wi h pe iodic
cell me ama e ial ou e su ace
1B no Uni e si y o Technology, Czech Republic, Ins i u e o Solid mechanics, Mecha onics and Biomechanics
2B no Uni e si y o Technology, Czech Republic, Ins i u e o Au oma ion and Compu e Science
3B no Uni e si y o Technology, Czech Republic, Ins i u e o Ae ospace Enginee ing
4Impe ial College London, Depa men o Ae onau ics
M. H s ka1, J. Baje 2, J. Na á il3, P. Zikmund3, Z. Hadaš2, Z. Sha i Khodaei4, F. Aliabadi4, M. Ko oul1
Con en s
•In oduc ion and mo i a ion
•Design loop
•Mo phing wing and me ama e ials
•Ae oelas ic op imiza ion
•Ou e su ace and skin s uc u e
•Leading edge mo phing model
•Geome ically exac Timoshenko beam heo y and i s modi ica ion
•Resul s
•Conclusion
In oduc ion
•BAANG p ojec (Ho izon 2020 winning), h ps://baang.eu
•Building Ac ions in Sma A ia ion wi h En i onmen al Gains
•Coope a ion: BUT, Impe ial College, Del Uni e si y, TU Wien
•Wing mo phing concep – imp o emen o ae odynamic pe o mance o a wing
•3D p in ing (Ti6Al4V)
•Mul iple ligh egimes
•S uc u e heal h moni o ing
Design loop
Mo phing wing and me ama e ials
•Wing pa s cha ac e iza ion – ailing edge, cen al box, leading edge
•Me a-ma e ial implemen a ion – lowe weigh , ailo ed mechanical p ope ies
•Requi emen s: good lexibili y o ac ua ion, high s i ness o esis ex e nal loading
Ae oelas ic op imiza ion
•NACA2412 ai oil
Ou e su ace and uni cell
•3D p in ing implemen a ion
x
y
z
Leading edge mo phing model
•Ou e su ace (skin) and kinema ic mechanism
•5 DOF
•De lec ions a e no small and la ge o a ions a e conside ed
•Geome ically exac beam heo y, ini e s ain
•Taylo , Zienkiewicz, Reissne , Simo
•Mo i a ion:
•Modelling he esponse o he eal shape o he me ama e ial is compu a ionaly ine icien
•By using he ini e s ain Timoshenko beam model smalle da a iles a e ob ained
•Abili y o using machine lea ning algo i hm o kinema ic mechanism design and op imiza ion
Geome ically exac beam heo y
•Geome ically exac beam heo y, ini e s ain, Lag angian o m
•Assump ions: plana c oss sec ion
•Kinema ic ela ions:
•S ain measu es and s ess: G een-Lag ange s ain, 2nd Piola Ki chho s ess
•Fini e elemen model o he eal s uc u e wi h epea ed uni cell
•ANSYS 2023R2
•elemen : SOLID 186
•NLGEOM, ON
E ec i e s i nesses iden i ica ion
Pa ame e Uni alue
w1[mm] 1.5
h1[mm] 1
wc[mm] 12
hc[mm] 2
c[mm] 1.2
1[mm] 0.4
Uni s in a ow [-] 10
Elemen leng h [mm] 0.15
E[GPa] 2
μ[-] 0.3
•Symme ic model
•Bo om su ace: UY=0, UZ=0 on midline
•Le su ace: symme y condi ion UX=0
•Uppe su ace: MPC con ac , ALLDOF cons ained
•1310114 elemen s, 337641 nodes
•3 loading cases
Fini e elemen model se ings and bounda y condi ions
x
yz
Pi o node
•Assump ions:
•C oss sec ion emain plana
•Cen e line does no mo e in he Zdi ec ion
Cen e line and nodes o da a ex ac ion
x
y
z
Cen e line
C oss sec ion
Cen e line node
Uppe c oss sec ion node
Lowe c oss sec ion node
Timoshenko beam ini e elemen
Case 1 –axial o ce
FY= 0.5 N in 20 loads eps
Fini e elemen model se ings and bounda y condi ions
x
y
z
𝑭𝒀
Case 2 –bending momen
MX= 2.5 Nmm in 20 loads eps
Fini e elemen model se ings and bounda y condi ions
x
y
z
𝑴𝑿
Case 3 –shea o ce
FZ= 25 mN in 20 loads eps
Fini e elemen model se ings and bounda y condi ions
x
y
z
𝑭𝒁
Nonlinea s i nesses
E ec i e s i nesses
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Nonlinea s i nesses
E ec i e s i nesses
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Resul s –benchma k s udy
M = 0.2 mNm M = 0.35 mNm M = 0.50 mNm
M = 0.95 mNm M = 1.45 mNm M = 2.45 mNm
Resul s –benchma k s udy
M = 2.7 mNm M = 3.45 mNm M = 4.20 mNm
M = 4.70 mNm M = 5.0 mNm
Conclusions
•Leading edge mo phing wing model was c ea ed by implemen ing geome ically exac beam
heo y
•Ma e ial o he me ama e ial was conside ed as Sain -Venan , linea
•Response o he kinema ic mechanism opology was s udied
•FEM model was c ea ed om sc a ch in o de o d i e all model aspec s
•Fu u e esea ch:
•De elop a model o de e mina ion o he ai oil as a ou pu om ae oelas ic op imiza ion
•Implemen a ion o gene ic algo i hm
•Implemen a ion o machine lea ning and neu al ne wo ks
Thank you o you a en ion
Acknowledgmen s:
This wo k was suppo ed by he p ojec BAANG – "Building Ac ions in Sma A ia ion wi h
En i onmen al Gains" was unded by he Eu opean Union P og amme Ho izon Eu ope unde g an
ag eemen no. 10107909
