Two-scale dynamic optimal design of composite structures in the time domain using equivalent static loads

In this paper, a method for the concurrent topology optimization of macrostructural material distribution and periodic microstructure under dynamic loading based on the equivalent static loads (ESLs) in the time domain is proposed. The sensitivity analysis of the maximal dynamic strain energy with respect to design variables in two scales, i.e., macro and micro scales, is presented. The corresponding concurrent topology optimization model of macrostructure and microstructure is established, where the objective is to minimize the maximal dynamic strain energy of the macrostructure subject to volume constraints on the macromaterial distribution and phase materials. The optimization problem is solved using a bi-directional evolutionary structural optimization (BESO) method. The results of several examples demonstrate that the proposed method is effective for the concurrent topology optimization under dynamic loading.