Topology optimization using the unsmooth variational topology optimization (UNVARTOP) method. An educational implementation in Matlab

TL;DR

This paper provides an educational MATLAB implementation of the UNVARTOP method for 2D and 3D topology optimization, including various problem types, with detailed instructions and code for students and newcomers.

Contribution

It offers a comprehensive, easy-to-understand MATLAB code for topology optimization using UNVARTOP, extending to multiple problem types and dimensions, with implementation guidance.

Findings

Efficient MATLAB code for 2D and 3D topology optimization

Extensions to heat conduction and multi-load problems

Improved algorithms for constraint handling and topology updates

Abstract

This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis and multi-load compliance problems. The Unsmooth Variational Topology Optimization (UNVARTOP) method, developed by the authors in a previous work, is used in the topology optimization code, based on the finite element method (FEM), to compute the sensitivity and update the topology. The paper also includes instructions to improve the bisection algorithm, modify the computation of the Lagrangian multiplier by using an Augmented Lagrangian to impose the constraint, implement heat conduction problems and extend the code to three-dimensional topology optimization problems. The code, intended for students and newcomers in topology optimization, is included as an appendix (Appendix A) and it can be downloaded from https://github.com/DanielYago together with supplementary material.