The method of fundamental solutions for electroelastic analysis of two-dimensional piezoelectric materials

Abstract

Abstract This paper considers the application of the method of fundamental solutions (MFS) for the numerical solutions of electroelastic analysis of two-dimensional (2D) piezoelectric materials. Accurate simulating of such problem requires solving the coupled mechanical and electrical partial differential equations. In the MFS, the mechanical displacements and electrical potential are approximated by linear combinations of the fundamental solutions of the coupled electroelastic equations, which are expressed in terms of source points located outside the real computational domain. The final coefficients of the fundamental solutions are calculated by enforcing the satisfaction of the corresponding boundary conditions in a least squares sense. Three benchmark numerical examples are well-studied to demonstrate the accuracy and applicability of the method, where the results obtained are compared with the analytical solutions and these of using other numerical methods.