Green's Function Method for Stability Analysis of Stochastic Structures

The governing equations for the stability analysis of stochastic frame structures with small variations of the material and geometry parameters are established for the means and deviations of responses by including first-order terms. Taking advantage of the similarity between these equations and the governing equations for static analysis, a new Green's function method based on the fundamental solutions for static problems is proposed for the stability analysis of stochastic structures in conjunction with multidomain techniques. The numerical examples presented show that there is good agreement between the results of the proposed method and those from Monte Carlo simulation for small variation situations, and that the new approach is more efficient than the perturbation stochastic FEM. Based on the numerical results, the effects of the covariance type, correlation scale parameter, coefficient of variation, and discretization of random fields, as well as the location of fictitious loads, are investigated. (C) 2014 American Society of Civil Engineers.