Iterative scheme in determination of the probabilistic moments of the structural response in the Stochastic perturbation-based Boundary Element Method

Abstract

The main aim of this work is to present mathematical apparatus, numerical algorithm and computational illustrations of the improved version of the Stochastic perturbation-based Boundary Element Method. It is based on the general order Taylor expansion of all input random parameters and on an iterative algebraic determination of higher order probabilistic moments and characteristics of the structural response. The expected values of both random input parameters and the state functions are analytically expanded first and then they are inserted into all the formulas for higher order statistics, so that linearization procedure inherent for the previous approaches is replaced with the theoretically exact expansion terms. This approach is used in conjunction with the Weighted Least Squares Method applied to determine local polynomial representations of the structural response with respect to the input uncertainty. This new approach is compared with the previous version of the SBEM on the example of both isotropic and composite plane cantilever panels modeled with an uncertainty in their material parameters and parabolic boundary elements and also with the Monte-Carlo simulation scheme. Apparently higher precision in determination of third and fourth probabilistic characteristics is obtained, while the computational effort and time consumption remains the same as for linearized perturbation scheme.