An efficient approach for dynamic-reliability-based topology optimization of braced frame structures with probability density evolution method. (November 2022) - Yang, Jia-Shu; Chen, Jian-Bing; Beer, Michael; Jensen, Hector
Highlights: A novel method for dynamic-reliability-based topology optimization is proposed. An important representative point sieving strategy is inserted into the PDEM. A high-efficient approach for sensitivity of the first-passage probability. Proposed method incorporates the sensitivity of failure probability into SIMP and MMA. Effectiveness is validated by the design optimization of a braced frame structure. Abstract: The present paper explores the feasibility of topology optimization of stochastic dynamical systems in the framework of the probability density evolution method (PDEM). A new method is proposed for solving dynamic-reliability-based topology optimization (DRBTO) problems by combining the PDEM, the ground structure approach and the solid isotropic material with penalization (SIMP) model. In the investigated optimization problems, the first-passage probability is considered as an objective or constraint function. To obtain a clear layout of the optimized structure, the topology of the structure is described by the ground structure approach together with the SIMP model. The PDEM is employed as an efficient approach to assess the first-passage probability. For improved numerical efficiency, an approximate formulation of the first-passage probability based on the important representative points (IRPs) is implemented. On the basis of the approximate formulation of the first-passage probability, a relationship between the sensitivity of the first-passage probability and the transient response is obtained. The adjoint sensitivity analysis of the transient response is introduced to avoid extra numerical efforts. Then, by incorporating the first-passage probability and its sensitivity into the method of moving asymptotes (MMA), the investigated DRBTO problems are solved in an effective manner. The DRBTO of a braced frame structure is presented to demonstrate the availability and effectiveness of the proposed method.