STOCHASTIC BOUNDARY ELEMENTS IN ELASTOSTATICS

A stochastic boundary element formulation for the treatment of boundar y value problems in two-dimensional elastostatics that involve a rando m operator is presented. A general perturbation procedure is formulate d for the set of correlated random variables governing the response of the solid. This procedure is then specialized for the cases of (a) ra ndom geometry and (b) random material properties. The problems involvi ng a random configuration are analyzed using the random variable model , and those with a random material property are analyzed using the ran dom field model. The random field is first discretized into a set of c orrelated random variables, which are then transformed into an uncorre lated set to simplify the analysis. The derivatives of the boundary el ement matrices appearing in the systems of equations from the perturba tion of the random variables are derived analytically. The direct solu tion methods are used to obtain the response variables and their first - and second-order derivatives, respectively. Quadratic, conforming bo undary elements are employed in the boundary element discretization an d the strongly singular terms of the boundary element matrices and the ir first- and second-order derivatives are obtained using the conditio ns associated with rigid body motions of the solid. The present formul ation has been evaluated for a number of example problems through comp arisons with the solutions obtained by Monte Carlo simulation. A good agreement of the results is observed.