Dynamic-reliability-based topology optimization of braced frame buildings under near-fault ground motions

Rational and automatic seismic design of building structures is of importance to mitigate earthquake disasters. Topologically optimized frames outperform conventional designs when subjected to earthquake excitations. This study proposes a novel method to address the challenging problem of dynamic-reliability-based topology optimization (DRBTO) for frame-bracing buildings by incorporating direct probability integral method (DPIM) and the sequential approximate integer programming with trust region (SAIP-TR). The considered topology optimization problem aims at minimizing the material volume of braces under the constraint on dynamic reliability. Firstly, to obtain a clear layout of braces, SAIP-TR is introduced to solve the topology optimization expressed as a discrete variable optimization problem. Secondly, in the framework of DPIM, the reliability and reliability sensitivity via an efficient calculation formula are achieved. Meanwhile, a relationship between the reliability sensitivity and the structural response sensitivity is established. Then adjoint sensitivity analysis is adopted to further enhance the efficiency. Finally, the dynamic reliability and its sensitivity are integrated into the SAIP-TR, and the DRBTO problem of a linear braced frame building under stochastic near-fault ground motions is solved to demonstrate the efficacy of the proposed method. The results indicate that fault distance and velocity pulses of near-fault ground motions significantly affect the layout of brace members. In addition, remarkable influences of uncertainties on optimized results are revealed.