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

TL;DR

This paper introduces a compact, efficient MATLAB code for 3D stress-based sensitivity analysis in topology optimization, verified through examples and suitable for educational use.

Contribution

A 146-line MATLAB code for 3D stress sensitivity analysis using the adjoint method, including finite element analysis and p-norm stress sensitivity, with verification and practical applications.

Findings

Code accurately computes stress sensitivities

Verified against finite difference approximations

Effective for 3D topology optimization problems

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 only.