A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures

A mesh free method called point interpolation method (PIM) is presented for static and mode-frequency analysis of two-dimensional piezoelectric structures. In the present method, the problem domain and its boundaries are represented by a set of properly scattered nodes. The displacements and the electric potential of a point are interpolated by the values of nodes in its local support domain using shape functions derived based on a point interpolation scheme. Techniques are discussed to surmount the singularity of the moment matrix. Variational principle together with linear constitutive piezoelectric equations is used to establish a set of system equations for arbitrary-shaped piezoelectric structures. These equations are assembled for all quadrature points and solved for displacements and electric potentials. A polynomial PIM program has been developed in MATLAB with matrix triangularization algorithm (MTA), which automatically performs a proper node enclosure and a proper basis selection. Examples are also presented to demonstrate the accuracy and stability of the present method and their results are compared with the conventional FEM results from ABAQUS as well as the analytical or experimental ones.