用MATLAB编写的146行三维应力拓扑灵敏度分析程序optimization
An efficient 146-line 3D sensitivity analysis code of stress-based topology optimization written in MATLAB
摘要：
本文提出了一种高效和紧凑的MATLAB代码的三维应力为基础的灵敏度分析。146行代码包括有限元分析和基于伴随方法的p范数应力灵敏度分析。推导了p-范数整体应力测度的三维灵敏度分析，并给出了相应的MATLAB程序。通过与有限差分近似的比较，验证了解析灵敏度的正确性。采用移动渐近线法（MMA）求解非线性最优化。以三个典型的体积约束应力最小化问题为例，验证了灵敏度分析程序的有效性。本文提出的MATLAB程序可以扩展到解决不同应力相关的三维拓扑最优化问题。灵敏度分析的完整程序见附录，仅用于教育目的。
英文摘要：
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.
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