Stochastic spline fictitious boundary element method in elastostatic problems with random fields

Mathematical formulation and computational implementation of the stochastic spline fictitious boundary element method (SFBEM) are presented for the analysis of plane elasticity problems with material parameters modeled with random fields. Two sets of governing differential equations with respect to the means and deviations of structural responses are derived by including the first order terms of deviations. These equations, being in similar forms to those of deterministic elastostatic problems, can be solved using deterministic fundamental solutions. The calculation is conducted with SFBEM, a modified indirect boundary element method (IBEM), resulting in the means and covariances of responses. The proposed method is validated by comparing the solutions obtained with Monte Carlo simulation for a number of example problems and a good agreement of results is observed.