A radial point interpolation method for simulation of two-dimensional piezoelectric structures

Abstract

A meshfree, radial point interpolation method (RPIM) is presented for the analysis of piezoelectric structures, in which the fundamental electrostatic equations governing piezoelectric media are solved numerically without mesh generation. In the present method, the problem domain is represented by a set of scattered nodes and the field variable is interpolated using the values of nodes in its support domain based on the radial basis functions with polynomial reproduction. The shape functions so constructed possess a delta function property, and hence the essential boundary conditions can be implemented with ease as in the conventional finite element method (FEM). The method is successfully applied to determine deflections or electric potentials of a bimorph beam and mode shapes and natural frequencies of transducers. The present results agree well with those of experiments as well as the FEM by ABAQUS. Some shape parameters are also investigated thoroughly for the future convenience of applying the RPIM for smart materials and structures without the use of elements.