Reissner’s mixed variational theorem-based finite cylindrical layer methods for the three-dimensional free vibration analysis of sandwich circular hollow cylinders with an embedded functionally graded material layer

Abstract

Based on Reissner’s mixed variational theorem (RMVT), finite cylindrical layer methods (FCLMs) were developed for the three-dimensional (3D) free vibration analysis of simply supported, functionally graded material (FGM) sandwich circular hollow cylinders. The FGM sandwich cylinder consists of a thick and soft FGM core bounded with two thin and stiff homogeneous material face sheets, in which the material properties of the FGM core are assumed to obey an exponent-law varying exponentially with the thickness coordinate. In this formulation, the FGM sandwich cylinder is divided into a number of equal-thickness cylindrical layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the field variables of each individual layer, respectively. An h-refinement process instead of a p-refinement one is adopted to yield the convergent solutions in this study, and the layerwise linear, quadratic or cubic function distribution through the thickness coordinate is thus assumed for the related field variables. The accuracy and convergence of the RMVT-based FCLMs developed in this article are assessed by comparing their solutions with the exact 3D solutions available in the literature.

A review of theories for the modeling and analysis of functionally graded plates and shells

“…In these models, the plate was divided into a number of finite layers in which trigonometric functions and Lagrange polynomials were respectively used to interpolate the in-plane and transverse variations of the field variables of each individual layer. These models were extended by Wu and Chang [338] and Wu et al [339][340] to the static bending [338], free vibration [339] and buckling [340] of multilayered composite cylinders and sandwich cylinders. A meshless collocation method and an element-free Galerkin method were developed by Wu et al [341] and Wu and Chiu [342] using the differential reproducing kernel interpolation [343] and the RMVT.…”