Topology optimization of periodic mechanical structures with orthotropic materials based on the element-free Galerkin method

Abstract

A topology optimization (TO) algorithm for periodic mechanical structures with orthotropic materials is established by using the element-free Galerkin method (EFGM) and imposing periodic constraints on design subdomains. The effectiveness of the presented TO algorithm is verified by two numerical examples compared with the finite element method (FEM). The comparisons demonstrate that the EFGM periodic structures without using any filtering techniques have smoother boundaries and fewer intermediate relative densities. These optimal periodic structures can be manufactured by 3D printing from the extracted "*.stl" files. The effects of the number of design subdomains, Poisson's ratio factor, and off-angle on minimum compliance and periodic structures are studied, and reasonable ranges of parameters are recommended to improve the mechanical performance of periodic structures. The results indicate that the increase of the number of design subdomains in any direction leads to inevitable stiffness loss, but the minimum compliance can be further reduced by decreasing Poisson's ratio factor and adjusting off-angle properly for specific number of design subdomains. Optimal periodic structures with orthotropic materials are of better mechanical performance to resist deformation and reduce von Mises stress than those with isotropic materials.