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.

拓扑优化已成为结构配置设计的强大工具。为了进一步促进拓扑优化的发展，在过去的几十年中，出于教育目的已经发布了许多计算机程序。但是，大多数计算机程序都是基于线性假设构造的。本文基于流行的SIMP（带有罚分的固体各向同性材料）方法，提出了用FreeFEM编写的用于非线性拓扑优化的89行代码。除用于说明的13条线外，设计参数的初始化，非线性有限元分析，灵敏度计算和更新的设计变量仅需要76条线。可以通过在建议的程序中修改几行来解决不同的设计问题。