WIAS Preprint No. 2873, (2021)

Design of thin micro-architectured panels with extension-bending coupling effects using topology optimization


  • Agnelli, Filippo
  • Nika, Grigor
    ORCID: 0000-0002-4403-6908
  • 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.

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