Study on Topology Optimization under Multiple Loading Conditions and Stress Constraints based on EFG Method

Abstract

By choosing the density of particle as the design variables, a new implementation method of topology optimization is presented based on the Element-free Galerkin (EFG) method in this paper, in which the optimal objective is to minimize structural compliance. The advantage of using nodal density is that the displacement and density in the influence domain have the same approximation scheme, and the smoothness of the density field can be improved. Nodal density method presented can prevent the checkerboard from the mathematical model proposed. The topology optimal model based on EFG method under multiple loading cases and stress constraints is proposed, and the sensitivity analysis of optimal design is derived in detail. By using solid isotropic material with penalization (SIMP) method and optimality criteria (OC) method, an algorithm of topology optimization based on the EFG method is presented. The shortcoming of using nodal density can be overcome by introducing the penalty function method. Three topology optimal examples are solved successfully and test the model and algorithm proposed. The results obtained show that the checkerboard phenomenon arisen in topology optimization is not found, and the method proposed is not only effective in suppressing checkerboards but also has better convergence.