Time domain intrusive probabilistic seismic risk analysis of nonlinear shear frame structure

Presented is a time domain intrusive framework for probabilistic seismic risk analysis. Seismic source characterization is mathematically formulated. Methodology for simulating non-stationary seismic motions for given source, path and site is proposed. Both uncertain motions and uncertain structural parameters are characterized as random process/field and represented with Hermite polynomial chaos. Intrusive modeling of Armstrong-Fredrick kinematic hardening based on Hermite polynomial chaos is formulated and incorporated into Galerkin stochastic elastic-plastic FEM. Time-evolving probabilistic structural response is solved through developed stochastic elastic-plastic FEM. Following that, formulation for seismic risk analysis is derived. The framework is illustrated by seismic risk analysis of an eight-story shear frame structure. Uncertainties are propagated from earthquake source into uncertain structural system. Difficulties of choosing intensity measure in the conventional framework are avoided since all the uncertainties and important characteristics (e.g., spectrum acceleration Sa and peak ground acceleration PGA ) of seismic motions are directly carried by the random process excitations in time domain. Stochastic dynamic equations are solved in an intrusive way, circumventing non-intrusive Monte Carlo simulations.