An efficient concurrent topology optimization approach for frequency response problems

The purpose of this work is to develop an efficient concurrent topology optimization approach for minimizing frequency response of two-scale hierarchical structures over a given frequency interval. Compared with static problems, frequency response problems usually involve many load steps, which may lead to intensive computational burdens in both frequency response analysis and sensitivity analysis. This study thus proposes an enhanced decoupled sensitivity analysis method for frequency response problems, which is efficient even when plenty of frequency steps are involved and/or damping is considered. Furthermore, a combined method of modal superposition and model order reduction is incorporated for efficient frequency response analysis of two-scale hierarchical structures. A modified threshold Heaviside projection method is used to obtain black-and-white designs and the method of moving asymptotes (MMA) is employed to update the design variables. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach.