Stochastic Dynamic Analysis of Large-Scale Nonlinear Structures

Abstract

Stochastic dynamic analysis of structures aims to explore the propagation of uncertainty in dynamic structures, referring to stochastic response and dynamic reliability analyses. For large-scale nonlinear structures, stochastic dynamic analysis is a challenging issue. In this study, a novel direct probability integral method (DPIM) is proposed to synchronously attack the problem of structural stochastic response and dynamic reliability analyses in an efficient and accurate way. The theoretical foundation of DPIM is the probability density integral equation (PDIE), an integral description of probability conservation, which decouples the evolution of probability density from the physical evolution of structure. Firstly, the PDIEs of static and dynamic structures are uniformly derived based on the principle of probability conservation, and then the equivalent differential equations are also highlighted. Then, the formula with Heaviside function for structural reliability estimation is advanced. Moreover, numerical procedures for structural stochastic responses, dynamic reliability and system reliability analyses based on DPIM are demonstrated. Finally, an example of 15-story hysteretic frame building illustrates the high efficiency and accuracy of DPIM for stochastic dynamic analysis.