A meshless collocation method for the coupled analysis of functionally graded piezo-thermo-elastic shells and plates under thermal 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, doubly curved functionally graded (FG) piezo-thermo-elastic shells. The material properties of FG shells are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependence on this. In the present formulation, the shape function at each referred node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions. By means of the present DRK interpolation, the essential boundary conditions can be readily applied, exactly like the implementation in the finite element method (FEM). An additional innovation of the present meshless method is that the shape functions for derivatives of the reproducing kernel (RK) functions are determined using a set of differential reproducing conditions, rather than differentiating these RK functions. In the implementation of the DRK interpolation-based collocation method presented in this work, several crucial parameters are discussed, such as the optimal support size and highest-order of the basis functions. The influence of the material-property gradient index on the field variables induced in the FG shells and plates under thermal loads is also studied.