A DRK Interpolation-Based Collocation Method for the Analysis of Functionally Graded Piezoelectric Hollow Cylinders under Electro-Mechanical Loads

Abstract

A meshless collocation method based on the differential reproducing kernel (DRK) interpolation is developed for the three-dimensional (3D) coupled analysis of simply-supported, functionally graded (FG) piezoelectric hollow cylinders. The material properties of FG hollow cylinders are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. In the present formulation, the shape function for the reproducing kernel (RK) interpolation function at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions. By means of this DRK interpolation, the essential boundary conditions can be readily applied, exactly like the implementation in the finite element method (FEM). An additional innovation of this meshless method is that the shape functions for derivatives of the RK interpolation functions are determined using a set of differential reproducing conditions, rather than directly differentiating them. In the implementation of the DRK interpolation-based collocation method presented in this work, some crucial parameters are discussed, such as the optimal support size and the highest-order of the basis functions. The influence of the material-property gradient index on the field variables induced in the FG hollow cylinders is also studied.