A FEM-based morphing wing concept with periodic cell metamaterial outer surface

A FEM-based morphing wing concept with periodic cell metamaterial outer surface 1Brno University of Technology, Czech Republic, Institute of Solid mechanics, Mechatronics and Biomechanics 2Brno University of Technology, Czech Republic, Institute of Automation and Computer Science 3Brno University of Technology, Czech Republic, Institute of Aerospace Engineering 4Imperial College London, Department of Aeronautics M. Hrstka1, J. Bajer2, J. Navrátil3, P. Zikmund3, Z. Hadaš2, Z. Sharif Khodaei4, F. Aliabadi4, M. Kotoul1 Contents •Introduction and motivation •Design loop •Morphing wing and metamaterials •Aeroelastic optimization •Outer surface and skin structure •Leading edge morphing model •Geometrically exact Timoshenko beam theory and its modification •Results •Conclusion Introduction •BAANG project (Horizon 2020 twinning), https://baang.eu •Building Actions in Smart Aviation with Environmental Gains •Cooperation: BUT, Imperial College, Delf University, TU Wien •Wing morphing concept – improvement of aerodynamic performance of a wing •3D printing (Ti6Al4V) •Multiple flight regimes •Structure health monitoring Design loop Morphing wing and metamaterials •Wing parts characterization – trailing edge, central box, leading edge •Meta-material implementation – lower weight, tailored mechanical properties •Requirements: good flexibility to actuation, high stiffness to resist external loading Aeroelastic optimization •NACA2412 airfoil Outer surface and unit cell •3D printing implementation x y z Leading edge morphing model •Outer surface (skin) and kinematic mechanism •5 DOF •Deflections are not small and large rotations are considered •Geometrically exact beam theory, finite strain •Taylor, Zienkiewicz, Reissner, Simo •Motivation: •Modelling the response of the real shape of the metamaterial is computationaly inefficient •By using the finite strain Timoshenko beam model smaller datafiles are obtained •Ability for using machine learning algorithm for kinematic mechanism design and optimization Geometrically exact beam theory •Geometrically exact beam theory, finite strain, Lagrangian form •Assumptions: planar cross section •Kinematic relations: •Strain measures and stress: Green-Lagrange strain, 2nd Piola Kirchhoff stress •Finite element model of the real structure with repeated unit cell •ANSYS 2023R2 •element: SOLID 186 •NLGEOM, ON Effective stiffnesses identification Parameter Unit value w1[mm] 1.5 h1[mm] 1 wc[mm] 12 hc[mm] 2 tc[mm] 1.2 r1[mm] 0.4 Units in a row [-] 10 Element length [mm] 0.15 E[GPa] 2 μ[-] 0.3 •Symmetric model •Bottom surface: UY=0, UZ=0 on midline •Left surface: symmetry condition UX=0 •Upper surface: MPC contact, ALLDOF constrained •1310114 elements, 337641 nodes •3 loading cases Finite element model settings and boundary conditions x yz Pivot node •Assumptions: •Cross section remain planar •Centerline does not move in the Zdirection Centerline and nodes for data extraction x y z Centerline Cross section Centerline node Upper cross section node Lower cross section node Timoshenko beam finite element Case 1 –axial force FY= 0.5 N in 20 loadsteps Finite element model settings and boundary conditions x y z 𝑭𝒀 Case 2 –bending moment MX= 2.5 Nmm in 20 loadsteps Finite element model settings and boundary conditions x y z 𝑴𝑿 Case 3 –shear force FZ= 25 mN in 20 loadsteps Finite element model settings and boundary conditions x y z 𝑭𝒁 Nonlinear stiffnesses Effective stiffnesses 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Nonlinear stiffnesses Effective stiffnesses 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Results –benchmark study M = 0.2 mNm M = 0.35 mNm M = 0.50 mNm M = 0.95 mNm M = 1.45 mNm M = 2.45 mNm Results –benchmark study M = 2.7 mNm M = 3.45 mNm M = 4.20 mNm M = 4.70 mNm M = 5.0 mNm Conclusions •Leading edge morphing wing model was created by implementing geometrically exact beam theory •Material of the metamaterial was considered as Saint-Venant, linear •Response to the kinematic mechanism topology was studied •FEM model was created from scratch in order to drive all model aspects •Future research: •Develop a model for determination of the airfoil as a output from aeroelastic optimization •Implementation of genetic algorithm •Implementation of machine learning and neural networks Thank you for your attention Acknowledgments: This work was supported by the project BAANG – "Building Actions in Smart Aviation with Environmental Gains" was funded by the European Union Programme Horizon Europe under grant agreement no. 10107909