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A discontinuous phase field approach to variational growth-based topology optimization

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Abstract

Numerical instabilities cause the well-known problem of checkerboarding during topology optimization: elements that possess material are periodically neighbored to elements that are material-free. Furthermore, such numerical solutions depend on the finite element mesh and no reasonable processing techniques exist for manufacture. Thus, integral- or gradient-based regularization techniques are usually applied during topology optimization. In this paper, a novel approach to regularization is derived for a recently published variational approach to topology optimization that is based on material growth. The presented approach shares some similarities with the discontinuous Galerkin method and completely removes consideration of additional nodal quantities or complex integration schemes. The derivation and numerical treatment of the resulting phase field equation as well as exemplary numerical results are presented.

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Acknowledgment

We thank U. Hoppe for helpful discussions and critical remarks.

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Authors and Affiliations

  1. Insitute of Mechanics, Bergische Universität Wuppertal, Wuppertal, Germany

    Philipp Junker

  2. Insitute of Mechanics of Materials, Ruhr-Universität Bochum, Bochum, Germany

    Klaus Hackl

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  1. Philipp Junker
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  2. Klaus Hackl
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Correspondence to Philipp Junker.

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Junker, P., Hackl, K. A discontinuous phase field approach to variational growth-based topology optimization. Struct Multidisc Optim 54, 81–94 (2016). https://doi.org/10.1007/s00158-016-1398-1

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  • DOI: https://doi.org/10.1007/s00158-016-1398-1

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