Abstract 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 S a and peak ground acceleration P G A ) 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.

中文翻译：

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非线性剪切框架结构时域侵入概率地震风险分析

摘要 提出了一种用于概率地震风险分析的时域侵入式框架。地震源表征是用数学公式表达的。提出了模拟给定震源、路径和地点的非平稳地震运动的方法。不确定运动和不确定结构参数都被表征为随机过程/场，并用 Hermite 多项式混沌表示。建立了基于 Hermite 多项式混沌的 Armstrong-Fredrick 运动硬化的侵入式建模，并将其合并到 Galerkin 随机弹塑性有限元中。通过开发的随机弹塑性有限元法解决了随时间演变的概率结构响应。随后，推导出地震风险分析的公式。该框架通过八层剪力框架结构的地震风险分析来说明。不确定性从震源传播到不确定的结构系统中。由于地震运动的所有不确定性和重要特征（例如频谱加速度S a 和峰值地面加速度PGA ）直接由时域中的随机过程激励携带，因此避免了在常规框架中选择强度度量的困难。随机动态方程以侵入式方式求解，绕过非侵入式蒙特卡罗模拟。地震运动的频谱加速度 S a 和峰值地面加速度 PGA ) 由时域中的随机过程激励直接携带。随机动态方程以侵入式方式求解，绕过非侵入式蒙特卡罗模拟。地震运动的频谱加速度 S a 和峰值地面加速度 PGA ) 由时域中的随机过程激励直接携带。随机动态方程以侵入式方式求解，绕过非侵入式蒙特卡罗模拟。