随机结构动力可靠度分析的概率密度演化方法

Probability Density Evolution Method for Dynamic Reliability Analysis of Stochastic Structures

基于随机结构动力反应分析的概率密度演化方法 ,提出了一类新的随机结构动力可靠度分析方法。在随机结构动力反应概率密度演化方程的基础上 ,对于首次超越问题 ,根据所给的首次超越破坏准则施加相应的吸收壁边界条件 ,求解具有吸收壁边界条件的概率密度演化方程并在安全域内积分 ,给出结构的动力可靠度。结合精细时程积分方法和具有 TVD性质的差分格式 ,讨论了计算结构动力可靠度的数值方法。

Based on the probability density evolution method for dynamic response analysis of stochastic structures, a class of new dynamic reliability analysis approaches for stochastic structures is proposed. For the first passage problem, the dynamic reliability can be assessed directly by solving the probability density evolution equation, which is imposed on by an absorbing boundary condition corresponding to the failure criterion, and integrating over the safe domain. Numerical algorithm for the proposed method is studied by combining the precise integration in time domain and the finite difference method with TVD difference schemes. An 8-story frame structure is investigated and the results are compared with those obtained by the Monte Carlo method.