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

An edge-based smoothed finite element method (ES-FEM) was recently proposed to significantly improve the accuracy and convergence rate of the standard finite element method for static, free and forced vibration analyses of solids using three-node triangular elements that can be generated automatically for complicated geometries. In this work, it is further extended to static and eigenvalue analyses of two-dimensional piezoelectric structures. In the present ES-FEM, the approximation of the displacement and electric potential fields is the same as in the standard linear FEM, while mechanical strains and electric fields are smoothed over the smoothing domains associated with the edges of the triangles. The system stiffness matrix is then computed via a simple summation over these 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 as experimental ones and (2) the ES-FEM is much more accurate than the linear triangular elements (T3) and often found to be even more accurate than the FEM using quadrilateral elements (Q4) when the same sets of nodes are used.