Concurrent design of composite macrostructure and cellular microstructure under random excitations

In this paper, a method for the concurrent topology optimization of macrostructural material distribution and periodic microstructure under random excitations is proposed. The sensitivity analysis of dynamic response with respect to design variables in two scales, i.e., macro and micro scales, is presented. The corresponding concurrent topology optimization of macrostructure and microstructure is established, where the objective function is to minimize the displacement response mean square (RMS) of the prescribed degree of freedom while volume constraints are applied to the macromaterial distribution and phase materials. The optimization problem is solved using a bi-directional evolutionary structural optimization (BESO) method. Several examples are presented to demonstrate the effectiveness of the proposed method.