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.

本文提出了一种高效紧凑的 MATLAB 代码，用于基于三维应力的灵敏度分析。146行代码包括有限元分析和基于伴随法的p范数应力敏感性分析。派生并详细解释了 p 范数全局应力测量的 3D 灵敏度分析，并附有相应的 MATLAB 代码。通过与有限差分近似的比较，验证了解析灵敏度的正确性。非线性优化求解器被选为移动渐近线方法 (MMA)。提出了三个典型的体积约束应力最小化问题来验证灵敏度分析代码的有效性。本文中提供的 MATLAB 代码可以扩展到解决不同应力相关的 3D 拓扑优化问题。完整的敏感性分析程序在附录中给出，用于教育目的。MATLAB 代码在电子补充材料中额外提供，用于简单的悬臂梁优化。