A state space differential reproducing kernel method for the 3D analysis of FGM sandwich circular hollow cylinders with combinations of simply-supported and clamped edges

Abstract

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) sandwich circular hollow cylinders with combinations of simply-supported and clamped edges and under sinusoidally (or uniformly) distributed loads. The strong formulation of this 3D elasticity problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler–Lagrange equations of this problem and its associated boundary conditions. The primary field variables are expanded as the single Fourier series in the circumferential coordinate, then interpolated in the axial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The present state space DRK solutions can then be obtained by means of the transfer matrix method. In the illustrative examples, three different edge conditions, the simple-simple (SS), simple-clamped (SC), and clamped–clamped (CC) edges, are considered, and the accuracy and convergence of this method are examined by comparing their solutions with the exact 3D ones available in the literature and the solutions using the ANSYS commercial software.