A stochastic variational formulation for nonlinear dynamic analysis of structure

Abstract

In this paper, stochastic structural parameters and random dynamic excitation are introduced directly into the dynamic functional variational formulations. Based on the instantaneous minimum potential energy principle and the small parameter perturbation technique, a unified nonlinear stochastic variational formulation of dynamic analysis for random structure and the relevant incremental stochastic finite element method are also developed. With the aid of incremental recurrence equations, the transient nonlinear analysis of structures with stochastic parameters under random excitation may be obtained conveniently. The results of a numerical example show that the approaches presented in this paper have the advantages of simple and convenient program implementation, and are accurate and effective for the nonlinear dynamic analysis of random structures.