Mechanical Optimizations with Variable Mesh Size, Using Differential Evolution Algorithm

Structural problems are a common topic among several optimization works; with the use of finite element analysis (FEA), the aim of these works is to improve the mechanical behavior of the distinct elements or bodies involved in these optimization problems. However, the impact of the meshing discretization on the outcome of the optimization process has not been studied in previous works. The present work investigates the effect of mesh element size on the mechanical optimization of two cases of study; the first one is about a modal optimization on a cantilever beam, and the second one is about a cellular beam, where the aim is to reduce the weight of the beam under static load. In these two optimization problems, variables commonly used in the literature were employed, while additionally including the mesh size as an extra variable. The computational framework is implemented on MATLAB R2022a, and the modal and weight optimizations are carried out through APDL (ANSYS Parametric Design Language) executed in batch mode. The results demonstrate that the consideration of the mesh size element can improve the computational time that is required to perform this mechanical optimization, achieving a 96% percentage of time reduction instead of making the analysis with the finest element size (in case 1) and a 90 percent time reduction for the second case of study.