随机荷载作用下随机结构线性反应的概率密度演化分析

提出了随机荷载作用下随机结构线性静力反应的概率密度演化方法.基于力学平衡方程,导出了随机荷载作用下随机结构反应的状态方程,进而引入扩展状态向量,建立了随机荷载作用下的随机结构静力反应的概率密度演化方程,讨论了其差分数值求解技术.进行了八层框架结构在随机荷载作用下的反应的算例分析.在单一随机参数结构的情况下,与随机结构反应的精确解答进行了对比;对于多个随机参数结构随机反应,则与MonteCarlo分析结果进行了比较.研究表明,本文提出的方法具有很高的精度及良好的实用性.

PROBABILITY DENSITY EVOLUTION OF LINEAR STOCHASTIC STRUTURAL RESPONSE

Probability density evolution method for the analysis of linear stochastic structural static response under random loading is proposed. Based on the mechanical equilibrium equation, the state equation of the stochastic structural responses under random loading is deduced. By introducing the augmented state vector, the probability density evolution equation (PDEE) of the stochastic structural static response is then established. The finite difference method for the PDEE is investigated. Numerical examples are studied for the response of an 8-storey frame structure. In the situation with a single random parameter involved in the structure, comparisons between the results obtained by the proposed method and those obtained by theoretical solution are made. The response of the structure with multiple random parameters are verified by the Monte Carlo method. The studies demonstrate that the proposed method is of high accuray and feasibility.