An 89-line code for geometrically nonlinear topology optimization written in FreeFEM
An 89-line code for geometrically nonlinear topology optimization written in FreeFEM
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DOI：
10.1007/s00158-020-02733-x
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发表时间：
2020-09
影响因子：
3.9
通讯作者：
Zhu Benliang;Zhu Benliang;Xianmin Zhang;Hai Li;Junwen Liang;Rixin Wang;Hao Li;S. Nishiwaki
中科院分区：
文献类型：
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作者：
Zhu Benliang;Zhu Benliang;Xianmin Zhang;Hai Li;Junwen Liang;Rixin Wang;Hao Li;S. Nishiwaki
拓扑优化已成为结构构型设计的有力工具。为了进一步推动拓扑优化的发展，在过去的几十年里，为了教育目的，已经出版了许多计算机程序。然而，大多数计算机程序都是基于线性假设构建的。本文基于目前流行的SIMP(带惩罚的固体各向同性材料)方法，用FreeFinal语言编写了89行的非线性拓扑优化程序。不包括用于解释的13行，只需要76行来进行设计参数的初始化、非线性有限元分析、灵敏度计算和更新设计变量。不同的设计问题可以通过修改程序中的几行来解决。完整的课程在附录中列出，仅用于教育目的。
Topology optimization has emerged as a powerful tool for structural configuration design. To further promote the development of topology optimization, many computer programs have been published for educational purposes over the past decades. However, most of the computer programs are constructed based on a linear assumption. This paper presents an 89-line code for nonlinear topology optimization written in FreeFEM based on the popular SIMP (solid isotropic material with penalization) method. Excluding thirteen lines which are used for explanation, only 76 lines are needed for the initialization of the design parameters, nonlinear finite element analysis, sensitivity calculation, and updated design variables. Different design problems can be solved by modifying several lines in the proposed program. The complete program is given in the Appendix and is intended for educational purposes only.