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Novel implementation of extrusion constraint in topology optimization by Helmholtz-type anisotropic filter

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Abstract

In this paper, a novel implementation of extrusion constraint in topology optimization is proposed based on Helmholtz-type anisotropic filter approach. The main idea is to set a far larger filter feature size along the extrusion direction than other directions, and thus, the density field is kept constant along the extrusion direction. The Helmholtz-type anisotropic filter can be easily implemented by adding a few more parameters to the isotropic one. Three illustrative examples, including 3D cantilever, spherical frame, and S-shape curved shell, are carried out to verify the effectiveness and robustness of the proposed method. Example results corroborate that the proposed method is suitable for both regular and irregular meshes regardless of geometrical complexity. Compared with the traditional variable mapping method, the proposed method needs less manual setup in the preprocessing of the analysis model for implementing extrusion constraint in topology optimization, which can be easily integrated into the solid isotropic materials with penalization (SIMP) topology optimization or commercial topology optimization software.

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Funding

This work was supported by National Natural Science Foundation of China (No.11825202, No.11902065), China Postdoctoral Science Foundation (No. 2019M651107), and LiaoNing Revitalization Talents Program (No. XLYC1802020).

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Authors and Affiliations

  1. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Bo Wang, Yan Zhou, Kuo Tian & Guangming Wang

Authors
  1. Bo Wang
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  2. Yan Zhou
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  3. Kuo Tian
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  4. Guangming Wang
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Corresponding author

Correspondence to Kuo Tian.

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The authors declare that there are no conflict of interest.

Replication of results

In order to make the replication of results easier, a code written in Matlab is provided. This code is available at the GitHub repository https://github.com/zy12000/TOP3D-EXTRUSION. Interested readers can download the code and learn to run it. It is modified from top88, top82 (Andreassen et al. 2011), and top3d (Liu and Tovar 2014) for implementing our method for FE models with structured meshes.

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Responsible Editor: Qing Li

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Wang, B., Zhou, Y., Tian, K. et al. Novel implementation of extrusion constraint in topology optimization by Helmholtz-type anisotropic filter. Struct Multidisc Optim 62, 2091–2100 (2020). https://doi.org/10.1007/s00158-020-02597-1

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  • DOI: https://doi.org/10.1007/s00158-020-02597-1

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