Concurrent multiscale topology optimization: A hybrid approach

Abstract

This paper presents a hybrid approach for multiscale topology optimization of structures. The topological shape of both macro-structure and micro-structure are concurrently optimized, based on the solid isotropic material with penalization (SIMP) technique in combination with finite element method (FEM). The material is assumed to have periodically patterned micro-structures, such that the effective properties can be evaluated via energy-based homogenization method (EBHM). In every iteration, the effective properties of material are passed to the macroscopic problem, and the macroscopic behavior (e.g. strain energy) is transferred back to the micro-scale problem, where the unit cell representing the micro-structure of material is determined for the next iteration. It is found that the update process can be done separately, i.e., the sensitivity of macro-scale design variables is not required during the update of micro-scale design variables, and vice versa. Hence, the proposal is that the macro-structure is updated by the gradient-free Proportional Topology Optimization (PTO) algorithm to utilize the computational efficiency of PTO. The micro-structure is still updated by the common gradient-based algorithm, namely Optimality Criteria (OC). Three benchmark numerical examples are investigated, demonstrating the feasibility and efficiency of the proposed hybrid approach.