Stochastic spline fictitious boundary element method for modal analysis of plane elastic problems with random fields

Mathematical formulation and computational implementation of the stochastic spline fictitious boundary element method (SFBEM) are presented for modal analysis of plane elastic problems with structural parameters modeled as random fields. Two sets of governing differential equations with respect to the means and deviations of displacement modes are derived by including the first order terms of deviations. These equations are in similar forms to those of deterministic plane elastostatic problems, and can be solved using deterministic elastostatic fundamental solutions, resulting in the means and covariances of the eigenvalues and mode shapes. For the effective treatment of the domain integrals involved in the deviation solution, the random fields considered are represented by Karhunen–Loeve (KL) expansion in conjunction with the Galerkin projection. Numerical examples indicate that the results of the present method are in good agreement with those from the Monte Carlo simulation (MCS) with small variations, and the present approach is more efficient than the perturbation stochastic finite element method (FEM) with the same KL expansion technique.