An efficient concurrent topology optimization approach for frequency response problems

• Published in: Computer methods in applied mechanics and engineering Vol. 347; pp. 700 - 734
• Main Authors: Zhao, Junpeng, Yoon, Heonjun, Youn, Byeng D.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.04.2019; Elsevier BV
• Subjects: Asymptotes; Concurrent topology optimization; Damping; Decoupled sensitivity analysis; Frequencies; Frequency analysis; Frequency response; Frequency response minimization; Mathematical models; Mode superposition method; Model reduction; Multiscale structure; Numerical homogenization; Polymethyl methacrylate; Sensitivity analysis; Sensitivity enhancement; Structural hierarchy; Topology optimization; Frequency response minimization; Multiscale structure; Concurrent topology optimization; Decoupled sensitivity analysis; Numerical homogenization
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.01.004

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. •Concurrent topology optimization for frequency response problems.•Efficient enhanced decoupled sensitivity analysis method for dynamics problems.•Efficient frequency response analysis method for two-scale structures.•Black-and-white designs for both macrostructure and micro unit cell.•Several numerical examples to valid the proposed method.