RMVT-based meshless collocation and element-free Galerkin methods for the approximate 3D analysis of multilayered composite and FGM circular hollow cylinders

Abstract

A meshless collocation (MC) and an element-free Galerkin (EFG) method, using the differential reproducing kernel (DRK) interpolation, are developed for the approximate three-dimensional (3D) analysis of simply supported, multilayered composite and functionally graded material (FGM) circular hollow cylinders under mechanical loads. The strong and weak formulations of this 3D elasticity problem are derived on the basis of the Reissner mixed variational theorem (RMVT). The former consists of the Euler–Lagrange equations of this problem and its associated boundary conditions, while the latter represents a weighted residual integral in which the differentiation is equally distributed among the primary field variables and their variations. An earlier proposed DRK interpolation is used to construct the primary field variables where the Kronecker delta properties are satisfied, and the boundary and continuity conditions related to the primary variables themselves can be directly applied. The system equations of both the RMVT-based MC and EFG methods are obtained using these strong and weak formulations, respectively, in combination with the DRK interpolation. In the illustrative examples, the accuracy and convergence rate of the present MC and EFG methods are examined, and some guidance for using these methods is suggested.