A stochastic boundary element method for piezoelectric problems

In this paper, the stochastic boundary element method of piezoelectric problems with randomness of material parameters and randomness of applied loads is proposed. By using the method of first-order Taylor expansion, each random quantity is written into the sum of the mean and deviation. The boundary integral equations corresponding to the means and deviations of the displacements and electric potential are derived, respectively. It is demonstrated that the randomness of material parameters can be transformed into the equivalent random body forces and equivalent random charge density, so that the fundamental solutions of deterministic piezoelectric problems can be used in boundary integral equations of the means or deviations due to the similarity between the governing equations with randomness and those of deterministic piezoelectric problems. Finally, several numerical examples are performed to verify the validity of the proposed stochastic boundary element method.