A radial point interpolation method for simulation of two-dimensionalpiezoelectric structures

Abstract

A meshfree, radial point interpolation method (RPIM) is presented for theanalysis of piezoelectric structures, in which the fundamental electrostaticequations governing piezoelectric media are solved numerically without meshgeneration. In the present method, the problem domain is represented by a set ofscattered nodes and the field variable is interpolated using the values of nodes inits support domain based on the radial basis functions with polynomialreproduction. The shape functions so constructed possess a delta functionproperty, and hence the essential boundary conditions can be implemented withease as in the conventional finite element method (FEM). The method issuccessfully applied to determine deflections or electric potentials of a bimorphbeam and mode shapes and natural frequencies of transducers. The present resultsagree well with those of experiments as well as the FEM by ABAQUS. Someshape parameters are also investigated thoroughly for the future convenience ofapplying the RPIM for smart materials and structures without the use ofelements.