Design of thin micro-architectured panels with extension-bending coupling effects using topology optimization
- Agnelli, Filippo
- Nika, Grigor
- Constantinescu, Andrei
2020 Mathematics Subject Classification
- 74K20 74P10 74P15 49M41
- Topology optimization, micro-architectured panels, shape morphing, inverse homogenization, level set method
We design thin micro-architectured panels with programmable macroscopic behaviour using inverse homogenization, the Hadamard shape derivative, and a level set method in the diffuse interface context. The optimally designed microstructures take into account the extension-bending effect in addition to in-plane stiffness and out-of-plane bending stiffness. Furthermore, we present numerical examples of optimal microstructures that attain different targets for different volume fractions and interpret the physical significance of the extension-bending coupling. The simultaneous control of the in-plane, out-of-plane and their coupled behaviour enables to shift a flat panel into a dome or saddle shaped structure under the action of an in-plane loading. Moreover, the obtained unit cells are elementary blocks to create three-dimensional objects with shape-morphing capabilities.
- Comput. Methods Appl. Mech. Eng., 391 (2022), Article 114496, DOI 10.1016/j.cma.2021.114496.