Stochastic second-order BEM perturbation formulation

Abstract

This paper presents the stochastic second order moment perturbation approach to the classical deterministic Boundary Element Method (BEM) formulation. Numerous applications of such a formulation in different problems of stochastic mechanics, especially in the field of computational modeling of structural defects in homogeneous and composite materials occurring randomly in solids and engineering structures, were the main reasons to introduce the proposed model. The stochastic boundary element method (SBEM) formulation of the general linear elasticity boundary value has been provided together with an appropriate discretization. The equations describing the expected values and the covariances of stress and strain tensors for points lying on the boundary and inside the region are considered. This set of equations constitutes a formal mathematical statement of the problem and is suitable for computational implementation.