Stochastic design optimization of nonlinear structures under random seismic excitations using incremental dynamic analysis

The increasing demand for mitigating earthquake hazards has prompted substantial research attention towards performance-based seismic design of civil structures. Nevertheless, there remains limited exploration into optimizing complex structures while accounting for seismic uncertainties. This study seeks to address this gap by introducing an effective approach for optimizing designs of nonlinear structures under random seismic excitations. The key innovation lies in approximating structural failure probability through incremental dynamic analysis (IDA), leading to the development of a novel double-loop optimization method tailored for designing nonlinear structures exposed to stochastic seismic loading conditions. In the outer loop, geometric variables of structures are optimized using sequential quadratic programming; within the inner loop, IDA is adopted for structural analysis to quantify seismic uncertainty, and the resulting failure probability is then served as the optimization constraint for the outer loop. To validate its accuracy and efficacy, numerical investigations have been performed on two representative case studies utilizing OpenSees: a reinforced concrete column and a three-story steel frame. The findings affirm that IDA can precisely estimate failure probabilities associated with nonlinear structures experiencing random ground motions and demonstrate that this proposed methodology can effectively determine optimal geometries aimed at enhancing structural resilience against earthquakes across various levels of failure probabilities and bound constraints.