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MATLAB implementations of velocity field level set method for topology optimization: an 80-line code for 2D and a 100-line code for 3D problems

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Abstract

This paper presents MATLAB implementations of the velocity field level set method for topology optimization. An 80-line code and a 100-line code are provided for 2D and 3D static compliance minimization problems, respectively. The velocity field level set method inherits the implicit topology and shape representation of the standard level set method but advances the design boundaries with a velocity field constructed from the velocity design variables and basis functions. Therefore, it can achieve structural designs with relatively clear and smooth material boundaries. Moreover, it allows general mathematical programming algorithms to be conveniently employed to handle more constraints when solving the optimization problem. In the presented codes, the method of moving asymptotes is used as the optimizer. For simplification, the presented MATLAB code is in a basic version. Some modifications and extensions are given in the examples to show the validity and efficiency of the codes. Further adaption of the current codes can also be made to fulfill various requirements.

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Acknowledgements

The support of the National Science Foundation of China (12002076, 11872140) and China Postdoctoral Science Foundation (2019TQ0047) is gratefully acknowledged.

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Authors and Affiliations

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

    Yaguang Wang & Zhan Kang

Authors
  1. Yaguang Wang
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  2. Zhan Kang
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Correspondence to Zhan Kang.

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The authors declare that they have no conflict of interest.

Replication of results

The MATLAB codes are given in Appendices and can also be downloaded in the supplementary material. The MMA algorithm we use here is Version September 2007 (and a small change August 2008) developed by Professor Krister Svanberg (krille@math.kth.se).

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Responsible Editor: Zhen Luo

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Appendices

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Wang, Y., Kang, Z. MATLAB implementations of velocity field level set method for topology optimization: an 80-line code for 2D and a 100-line code for 3D problems. Struct Multidisc Optim 64, 4325–4342 (2021). https://doi.org/10.1007/s00158-021-02958-4

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  • DOI: https://doi.org/10.1007/s00158-021-02958-4

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