Concurrent topology optimization for time-domain dynamic stiffness problem of two-scale hierarchical structure
JIANG Xudong1, MA Jiaqi1, TENG Xiaoyan2
1.School of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin 150080, China;
2.School of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China
Abstract:This paper aims to develop an efficient concurrent topology optimization approach with two-scale hierarchical structure for dynamic stiffness problem, which simultaneously realizes macroscopic and microscopic layout optimization. The three-field density-based approach is employed for topological design of macrostructure and microstructure, with an energy-based homogenization method (EBHM) to evaluate the macroscopic effective properties of the microstructure. The HHT-α method is exploited as a time integration scheme to solve the multi-scale structural dynamics problem for the proportional damping system. Based on the discretize-then-differentiate approach with the adjoint method, the sensitivity analysis is conducted on the discretized (both in space and time) topology optimization statement. Accordingly, the consistency errors are avoided, which arise when the adjoint method is used while considering time as a continuous variable. A multiscale topology optimization model is built for minimizing the dynamic compliance under two volume constraints of macrostructure and microstructure. We performed topology optimization of multiscale structures subjected to dynamic loads, such as half-cycle sinusoidal load and half-cycle cosine load. Finally, numerical results obtained from two benchmark examples demonstrate the effectiveness of the proposed method.
江旭东1,马佳琪1,滕晓燕2. 双尺度分级结构时域动刚度问题的并行拓扑优化[J]. 振动与冲击, 2023, 42(15): 31-41.
JIANG Xudong1, MA Jiaqi1, TENG Xiaoyan2. Concurrent topology optimization for time-domain dynamic stiffness problem of two-scale hierarchical structure. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(15): 31-41.
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