随机结构静力反应概率密度演化方程的差分方法

随机结构分析的概率密度演化方法是分析随机结构静力反应的一种具有良好前景的方法。本文研究了求解随机结构静力反应概率密度演化方程的差分方法，分别探讨了单边差分格式和Lax-Wendroff格式的计算性态。二者均能满足概率相容性条件并且能够保证均值线性增长。以八层框架结构的静力随机反应为例，对两种差分格式的结果及精确解答进行了具体的比较分析。研究表明，两种差分格式均是收敛和稳定的，在不连续点处存在角点效应．单边差分格式能够保证概率非负性，而Lax-Wendroff格式具有往往更快的收敛速度。就变异系数而言，通常单边差分格式的变异系数随着区间离散数的增长而趋于稳定值，Lax-Wendroff格式则一开始就可得到恒定的值。

Difference Method for Probability Density Evolution Equation of Stochastic Structural Response

Probability density evolution method is a prospective approach for stochastic structural analysis. Difference method for probability density evolution equation of the stochastic structural response was studied. The computational performances of one-sided difference scheme and Lax-Wendroff scheme were discussed, respectively. The two schemes can both satisfy the compatibility of probability and ensure the linear increase with loading parameter increasing. An 8-story frame structure was taken as an example to verify the numerical method. The researches show that the two schemes are both convergent and stable, and there is corner effect around the discontinuous point. The one-sided difference scheme can keep the nonnegativeness of computed probability while the Lax-Wendroff scheme usually has more rapid convergence. As far as the coefficient of variance is concerned, the one-sided scheme provides an asymptotic value. In contrast the Lax-Wendroff scheme can provide a stable value from the beginnings.