Seismic topology optimization considering first-passage probability by incorporating probability density evolution method and bi-directional evolutionary structural optimization

Abstract

This contribution focuses on addressing the challenging problem of dynamic-reliability-based topology optimization (DRBTO) of engineering structures involving uncertainties by synthesizing the probability density evolution method (PDEM) and the bi-directional evolutionary structural optimization (BESO) approach. The considered optimization problem aims at minimizing the first-passage probability under the constraint of material volume. Generally, the double-loop essence of DRBTO involving dynamic reliability evaluation and topology searching makes the computational efforts prohibitively large. To this end, the PDEM is adopted to efficiently assess the first-passage probability of structures under earthquake actions. In particular, by reformulating the first-passage probability under the framework of the PDEM, the sensitivity of the first-passage probability is derived. To further improve the efficiency, a strategy taking advantage of important representative points (IRPs) is employed to achieve a robust estimate of sensitivity of the first-passage probability. The adjoint variable method (AVM) for the sensitivity analysis of transient response considering given modal damping ratios is incorporated to considerably improve the computational efficiency when the reliability sensitivity analysis in terms of multiple design variables is needed. To drive the topology towards the optimum, the above highly efficient reliability assessment and sensitivity analysis are embedded into BESO. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed method, illustrating significant improvement in computational efficiency compared to direct implementation. Additionally, the necessity of introducing seismic reliability in topology optimization is also discussed based on the numerical results.