Concurrent design of composite macrostructure and cellular microstructure with respect to dynamic stress response under random excitations

Abstract This paper proposes a concurrent topology optimization method of macrostructural material distribution and periodic microstructure considering dynamic stress response under random excitations. The optimization problem is the minimization of the dynamic stress response of the macrostructure subject to volume constraints in both macrostructure and microstructure. To ensure the safety of the macrostructure, a new relaxation method is put forward to establish a relationship between the dynamic stress limit and the mechanical properties of microstructure. The sensitivities of the dynamic stress response with respect to the design variables in two scales, i.e., macro and micro scales, are derived. Then, the aforementioned optimization problem is solved by the bi-directional evolutionary structural optimization (BESO) method. Finally, several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.