The joint probability density function of nonlinear dynamic stochastic response of structures
结构动力非线性随机反应的联合概率分布

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.