Stochastic boundary element method in elasticity

Abstract

The stochastic boundary element method is developed to analyzeelasticity problems with random material and/or geometrical parameters and ran-domly perturbed boundaries. Based on the first-order Taylor series expansion, theboundary integration equations concerning the mean and deviation of the displace-ments are derived, respectively. It is found that the randomness of material param-eters is equivalent to a random body force, so the mean and covariance matricesof unknown boundary displacements and tractions can be obtained. Furthermore,the mean and covariance of displacements and stresses at inner points can also beobtained. Numerical examples show that the proposed stochastic boundary elementmethod gives satisfactory solutions, as compared with those obtained by theoreticalanalysis or other numerical methods.