STOCHASTIC BOUNDARY ELEMENTS FOR 2-DIMENSIONAL POTENTIAL FLOW IN HOMOGENEOUS-DOMAINS

A stochastic boundary element formulation is presented for the analysi s of two-dimensional steady state potential flow through homogeneous d omains. The operator of the governing differential equation is assumed to be random and is described by a set of correlated random variables . The perturbation method, in conjunction with the boundary element me thod, is employed to derive the systems of equations for the unknown b oundary variables and their respective first and second order derivati ves with respect to the random variables. These quantities are then us ed to calculate the desired response statistics. A general procedure i s developed which is next applied for the specific cases of random geo metric configuration and random material parameter. The random geometr ic configuration is modeled using a finite set of correlated random va riables. The random material parameter is modeled as a homogeneous ran dom field which allows the use of deterministic fundamental solutions and integral representations for homogeneous domains. The random field is first discretized into a set of correlated random variables and th en the general procedure is applied. A transformation of the correlate d random variables into an uncorrelated set is performed to reduce the number of numerical operations. The results for the boundary variable s are used to calculate the response statistics of internal potentials . These calculations require the modeling of the interior of the domai n under consideration. Several models for representing the interior of the domain are presented for both random configuration and random mat erial parameter and their influence on the response statistics is anal ysed. Distributed sources are considered in the present study using th e particular integral approach. A number of numerical examples are pre sented to demonstrate the validity of the present formulations. The re sults obtained from the present analyses are compared with those obtai ned from Monte Carlo simulations with 5000 samples and a good agreemen t of results is observed.