A 140 line MATLAB code for topology optimization problems with probabilistic parameters

TL;DR

This paper introduces a compact MATLAB code for topology optimization with probabilistic parameters, utilizing a stochastic sampling approach and adaptive gradient recombination to improve accuracy and efficiency.

Contribution

The paper provides a novel, concise MATLAB implementation for probabilistic topology optimization that enhances gradient approximation through adaptive sampling techniques.

Findings

Efficient performance demonstrated on multiple numerical examples.

Applicable to various stochastic parameters including material failure and load uncertainties.

Code available for download and practical use.

Abstract

We present an efficient 140 line MATLAB code for topology optimization problems that include probabilistic parameters. It is built from the top99neo code by Ferrari and Sigmund and incorporates a stochastic sample-based approach. Old gradient samples are adaptively recombined during the optimization process to obtain a gradient approximation with vanishing approximation error. The method's performance is thoroughly analyzed for several numerical examples. While we focus on applications in which stochastic parameters describe local material failure, we also present extensions of the code to other settings, such as uncertain load positions or dynamic forces of unknown frequency. The complete code is included in the Appendix and can be downloaded from www.topopt.dtu.dk.