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 of different response quantities. In the present paper, under the basic thoughts of density evolution, the generalized density evolution equation is extended to derive a two-dimensional partial differential equation governing the joint probability density function. The numerical algorithm is outlined combining the deterministic dynamic response analysis and the finite difference method. Numerical example is conducted to analyze 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 hilly country, while the coefficient of covariance is time variant.Keywords: nonlinear, dynamic response, probability density evolution method, joint probability density function, coefficient of covariance