A 262-line Matlab code for the level set topology optimization based on the estimated gradient field in the body-fitted mesh

Abstract

Topology optimization is an influential technique engineers and designers employ to achieve desirable material distribution within a designated domain. This educational article introduces a concise and efficient Matlab code, comprising only 262 lines, developed explicitly for the Level Set topology optimization based on the estimated Gradient Field (GFLS) in the body-fitted mesh. Unlike conventional level set methods that rely on the upwind scheme employed in the structured meshes, the proposed algorithm adopts the per-cell linear estimation of the discrete gradient vectors in the body-fitted mesh framework to obtain the velocity field and update the level set function. The Matlab code, named GFLS262, consists of a 62-line main program, 41-line finite element analysis function, and 48-line sub-functions, enabling the implementation of the GFLS method in 2D scenarios. Additionally, a 111-line function describes an improved mesh generator incorporated in the code to facilitate the generation of body-fitted meshes. The superiority of this innovative approach over the previous optimization methods with invariant meshes is demonstrated through various benchmark examples. For ease of access and further learning, the educational Matlab code is available on the website and can also be found in the Appendix section of this article.