Topology optimization for minimizing the maximum dynamic response in the time domain using aggregation functional method

• Published in: Computers & structures Vol. 190; pp. 41 - 60
• Main Authors: Zhao, Junpeng, Wang, Chunjie
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.10.2017; Elsevier BV
• Subjects: Adjoint variable method; Agglomeration; Aggregates; Aggregation functional; Dynamic response; Free vibration; Mathematical analysis; Model reduction method; Numerical integration; Operators (mathematics); Optimization; Sensitivity analysis; Time domain analysis; Topology; Topology optimization; Vibration; Dynamic response; Topology optimization; Aggregation functional; Adjoint variable method; Model reduction method
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2017.05.002

•The overall maximum dynamic in the time domain is minimized.•The possible non-differentiability of the overall maximum dynamic response is demonstrated.•The max operator in objective function is replaced by an aggregation functional.•Differentiate-then-discrete approach can be used for sensitivity analysis.•Numerical examples demonstrate the effectiveness of the proposed method. This paper develops an efficient approach to solving dynamic response topology optimization problems in the time domain. The objective is to minimize the maximum response of the structure over the complete vibration phase. In order to alleviate the difficulties due to the max operator in the objective function, an aggregation functional is proposed and employed to transform the original problem formulation into one that is computational tractable. The main advantage of the proposed aggregation functional over the existing aggregation functions, such as KS function and the p-norm function is that, for the dynamic response problems in the time domain, the differentiate-then-discretize approach can now be used for adjoint sensitivity analysis, instead of the discretize-then-differentiate approach, which is tightly coupled with the numerical integration schemes of the primal analysis and is more cumbersome. In addition to the solution method, some issues of dynamic response topology optimization problems in the time domain are discussed. The reason why the maximum dynamic response may occur in the free vibration phase for transient load is uncovered. A strategy to reduce the maximum dynamic response over the complete vibration phase is proposed. Numerical examples demonstrate the effectiveness of the proposed method.