Topology optimization using the unsmooth variational topology optimization (UNVARTOP) method: an educational implementation in MATLAB

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 Oliver et al. (Comput Methods Appl Mech Eng 355:779-819, 2019), 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 together with supplementary material.

Automated summary

This paper introduces an efficient and comprehensive MATLAB code for solving two-dimensional structural topology optimization problems, including a variety of different problems such as compliant mechanism synthesis and multi-load compliance. The code includes various improvements and extensions, making it suitable for students and newcomers in the field of topology optimization.