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An efficient 146-line 3D sensitivity analysis code of stress-based topology optimization written in MATLAB

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A Correction to this article was published on 08 July 2022

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Abstract

This paper presents an efficient and compact MATLAB code for three-dimensional stress-based sensitivity analysis. The 146 lines code includes the finite element analysis and p-norm stress sensitivity analysis based on the adjoint method. The 3D sensitivity analysis for p-norm global stress measure is derived and explained in detail accompanied by corresponding MATLAB code. The correctness of the analytical sensitivity is verified by comparison with finite difference approximation. The nonlinear optimization solver is chosen as the Method of moving asymptotes (MMA). Three typical volume-constrained stress minimization problems are presented to verify the effectiveness of sensitivity analysis code. The MATLAB code presented in this paper can be extended to resolve different stress related 3D topology optimization problems. The complete program for sensitivity analysis is given in the Appendix and is intended for educational purposes. MATLAB code is additionally provided in electronic supplementary material for a simple cantilever beam optimization.

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Acknowledgements

The financial support for this work from National Science Foundation (CMMI-1634261) is gratefully acknowledged. The authors would like to thank Krister Svanberg for providing the MATLAB implementation of his Method of Moving Asymptotes, which was used in this work.

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Authors and Affiliations

  1. Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA, 15261, USA

    Hao Deng, Praveen S. Vulimiri & Albert C. To

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  1. Hao Deng
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  2. Praveen S. Vulimiri
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  3. Albert C. To
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Correspondence to Albert C. To.

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Appendices

Appendix A: MATLAB Program Stress_3D_Sensitivity

The MATLAB code used in this work can be downloaded from: https://github.com/PittAMRL/StressTopOpt.

Appendix B: MATLAB Program Plot_von_Mises

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Deng, H., Vulimiri, P.S. & To, A.C. An efficient 146-line 3D sensitivity analysis code of stress-based topology optimization written in MATLAB. Optim Eng 23, 1733–1757 (2022). https://doi.org/10.1007/s11081-021-09675-3

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