Generalized finite difference method for electroelastic analysis of three-dimensional piezoelectric structures

Abstract

This short communication makes the first attempt to apply the generalized finite difference method (GFDM), a newly-developed meshless collocation method, for the numerical solutions of three-dimensional (3D) piezoelectric problems. In the present method, the entire computational domain is divided into a set of overlapping subdomains in which the local Taylor series expansion and moving-least square approximation are applied to construct the local systems of linear equations. By satisfying the coupled mechanical and electrical governing equations, a sparse and banded stiffness matrix can be established which makes the method very attractive for large-scale engineering simulations. Preliminary numerical experiments are presented to demonstrate the applicability and accuracy of the present method, where the results obtained are compared with the analytical solutions with very good agreement.