Difference Method for Probability Density Evolution Equation of Stochastic Structural Response
Difference Method for Probability Density Evolution Equation of Stochastic Structural Response
复制标题
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Li Jie
中科院分区：
文献类型：
--
作者：
Li Jie
概率密度演化法是一种有前景的随机结构分析方法。研究了随机结构响应的概率密度演化方程的差分法。分别讨论了单侧差分格式和Lax-Wendroff格式的计算性能。两种方案均能满足概率的相容性，并保证随载荷参数的增加而线性增加。以一8层框架结构为例，验证了数值方法的正确性。研究表明，两种方案均具有收敛性和稳定性，并且在不连续点周围存在角点效应。单侧差分格式可以保持计算概率的非负性，而Lax-Wendroff格式通常收敛速度更快。就方差系数而言，单侧格式提供了一个渐近值。相比之下，Lax-Wendroff方案从一开始就能提供一个稳定的值。
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.