An edge-based smoothed finite element method for analysis of two-dimensionalpiezoelectric structures

Abstract

An edge-based smoothed finite element method (ES-FEM) was recently proposed tosignificantly improve the accuracy and convergence rate of the standard finite elementmethod for static, free and forced vibration analyses of solids using three-node triangularelements that can be generated automatically for complicated geometries. In this work, it isfurther extended to static and eigenvalue analyses of two-dimensional piezoelectricstructures. In the present ES-FEM, the approximation of the displacement and electricpotential fields is the same as in the standard linear FEM, while mechanical strains andelectric fields are smoothed over the smoothing domains associated with the edges of thetriangles. The system stiffness matrix is then computed via a simple summation overthese smoothed domains. The results of several numerical examples show that:(1) the ES-FEM is in a good agreement with the analytical solutions as well asexperimental ones and (2) the ES-FEM is much more accurate than the lineartriangular elements (T3) and often found to be even more accurate than theFEM using quadrilateral elements (Q4) when the same sets of nodes are used.