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An ANSYS APDL code for topology optimization of structures with multi-constraints using the BESO method with dynamic evolution rate (DER-BESO)

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Abstract

This paper presents a 390-line code written in ANSYS Parametric Design Language (APDL) for topology optimization of structures with multi-constraints. It adopts the bi-directional evolutionary structural optimization method with the proposed dynamic evolution rate strategy (DER-BESO) to accelerate the iteration convergence. The complete APDL program includes the modules of finite element modeling, element sensitivity calculation, Lagrange multiplier updating, and the element updating module using DER-BESO method. It allows users to conduct the finite element analysis and optimization iterations just in one platform without having to switch repeatedly between the finite element analysis software and the optimization program. Through a cantilever example, the evolution procedure of DER-BSEO is compared to the primary BESO method to show its better performance in convergence speed. Different constraint cases are also considered to examine the robustness of the DER_BESO program. Example extensions for 3D structures and periodic structures with geometric restraints are also presented and discussed. Since ANSYS is a powerful finite element analysis platform, the given code has a perspective of extending to the optimization of large-scale structures or more complicated optimization problems that consider nonlinear or buckling effects.

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Funding

The work described in this paper is fully supported by grants from the National Natural Science Foundation of China (51925802, 51478130) and the China Scholarship Council (201808440070).

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Authors and Affiliations

  1. Guangzhou University-Tamkang University Joint Research Center for Engineering Structure Disaster Prevention and Control, Guangzhou University, Guangzhou, China

    Haidong Lin, An Xu & Ruohong Zhao

  2. Civil, Environmental and Architectural Engineering Department, Bioengineering Research Center (BERC), University of Kansas, 1530 W. 15th Street, Learned Hall, Lawrence, KS, 66045-7609, USA

    An Xu & Anil Misra

Authors
  1. Haidong Lin
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  2. An Xu
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  3. Anil Misra
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  4. Ruohong Zhao
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Corresponding author

Correspondence to An Xu.

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The authors declare that they have no conflict of interest.

Replication of results

The code for the main example, the topology optimization of a 2D cantilever beam, is available as Appendix at the end of this paper. The codes for other examples in this paper will be available on request at xuan@gzhu.edu.cn (An Xu).

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Responsible Editor: Raphael Haftka

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Appendix Complete APDL code for the 2D cantilever example

Appendix Complete APDL code for the 2D cantilever example

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Lin, H., Xu, A., Misra, A. et al. An ANSYS APDL code for topology optimization of structures with multi-constraints using the BESO method with dynamic evolution rate (DER-BESO). Struct Multidisc Optim 62, 2229–2254 (2020). https://doi.org/10.1007/s00158-020-02588-2

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  • DOI: https://doi.org/10.1007/s00158-020-02588-2

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