结构动力非线性随机反应的联合概率分布

在密度演化理论基本思想的框架下，对广义密度 演化方程进行推广，导出了结构不同反应量的联合概率密度函数演化方程. 结合确定性结构 非线性动力反应分析与二维偏微分方程求解的有限差分方法，可以获取结构不同反应量的联 合概率密度函数的数值解答. 分析实例表明：结构反应的联合概率密度函数呈丘陵状不规则 分布，而不同反应量之间的相关系数是时变的.

The joint probability density function of nonlinear dynamic stochastic response of structures

In nonlinear dynamic response analysis and reliability evaluation of structures, it is of paramount importance to capture the joint probability density function for various response quantities. In the present paper, following the basic line of density evolution, the generalized density evolution equation is extended to a two-dimensional partial differential equation governing the joint probability density function. The numerical algorithm combines the deterministic dynamic response analysis and the finite difference method. Numerical example is given for a ten-story frame structure with stochastic parameters subjected to random ground motions. The investigations show that the joint probability density function is irregular like a hilly country, while the coefficient of covariance varies with time.