Concurrent topology optimization with uniform microstructure for minimizing dynamic response in the time domain

Abstract

This paper aims to develop an efficient concurrent topology optimization approach for minimizing the maximum dynamic response of two-scale hierarchical structures in the time domain. Compared with statics problems, the dynamic response problems usually involve many time steps, which may lead to intensive computational burdens in both dynamic response and sensitivity analyses. This study thus proposes an enhanced decoupled sensitivity analysis method for concurrent topology optimization of the time-domain dynamic response problems. The mode acceleration method is incorporated for efficient dynamic response analysis. The three-field density-based approach is employed for topology optimization of macrostructure and microstructure. A previously proposed aggregation functional is employed to approximate the maximum dynamic response of the structure. The method of moving asymptotes (MMA) is employed to update the design variables. Three numerical examples are presented to demonstrate the effectiveness of the proposed approach. Some discoveries regarding the concurrent topology optimization for dynamics problems are presented and discussed. Furthermore, the potential of the concurrent topology optimization formulation for designing lightweight structures under dynamic loads is also demonstrated.