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Topology optimization with wall thickness and piecewise developability constraints for foldable shape-changing structures

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Abstract

Foldable shape-changing structures such as origami, deployable, and 4D printed structures have potentials for enhanced packaging, adaptability, and motion capabilities. Distinct geometric features often found in such foldable shape-changing structures include developability and small wall thickness. In this paper, two geometric constraints are introduced to enable the use of density-based topology optimization in designing piecewise developable thin-walled structures. The proposed developability constraint enforces the normal directions of the surfaces of the structures to lie on a prescribed (small) number of input reference planes, which realizes an optimized structure made of piecewise developable surfaces. The proposed thin-wall constraint simultaneously bounds the minimum and the maximum feature sizes in the structures through two PDE-based filtering operations and an aggregation constraint. Several numerical examples demonstrate the effectiveness of the proposed constraints. While the additional constraints inevitably compromise the structural performance, the ability to control the desired geometric features in topology optimization would benefit the rapidly growing field of foldable shape-changing structures.

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Authors and Affiliations

  1. Toyota Research Institute of North America, 1555 Woodridge Ave., Ann Arbor, MI, 48105, USA

    Yuqing Zhou & Ercan M. Dede

  2. Toyota Central R&D Labs, Inc., Bunkyo-ku, Tokyo, 112-0004, Japan

    Tsuyoshi Nomura

  3. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Kazuhiro Saitou

Authors
  1. Yuqing Zhou
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  2. Tsuyoshi Nomura
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  3. Ercan M. Dede
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  4. Kazuhiro Saitou
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Correspondence to Yuqing Zhou.

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Due to institutional constraints, the source code is unavailable. However, further algorithm details are available upon request to the authors.

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Responsible Editor: Qing Li

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Zhou, Y., Nomura, T., Dede, E.M. et al. Topology optimization with wall thickness and piecewise developability constraints for foldable shape-changing structures. Struct Multidisc Optim 65, 118 (2022). https://doi.org/10.1007/s00158-022-03219-8

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