Stochastic spline fictitious boundary element method for random vibration analysis of plane elastic problems with structural uncertainties

Abstract

A stochastic spline fictitious boundary element method (SFBEM) is proposed for random vibration analysis of plane elastic problems with both structural and loading uncertainties modeled as random fields and random processes, respectively. Two sets of governing differential equations with respect to the means and deviations of dynamic responses are derived by including the first order terms of deviations. As these equations are in similar forms to those of deterministic plane elastostatic problems, they can be solved by the traditional procedure of SFBEM with deterministic fundamental solutions, leading to the mean and covariance solutions to dynamic responses. To deal with the domain integrals of equivalent loads involved in the covariance solution, the random fields and processes considered are effectively represented by Karhunen–Loeve (KL) expansion in conjunction with the Galerkin projection. Numerical examples indicate that the results of the proposed method agree well with those of Monte-Carlo simulation (MCS) with small variations of structural parameters, and the present approach has higher efficiency than the perturbation stochastic finite element method (FEM) with KL expansion techniques.