Stochastic spline fictitious boundary element method for analysis of thin plate bending problems with random fields

Mathematical formulation and computational implementation of the stochastic spline fictitious boundary element method (SFBEM) are presented for stochastic analysis of thin plate bending problems with loadings and structural parameters modeled with random fields. Two sets of governing differential equations with respect to the mean and deviation of deflection are derived by including the first order terms of deviations. These equations are in similar forms to those of deterministic thin plate bending problems, and 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.