Static analysis of shear deformable functionally graded plates using finite element method

Abstract

Composite materials have been conveniently used in aerospace and other engineering applications for many years because of their excellent strength to weight and stiffness to weight ratios. Recently, an advanced composite materials known as functionally graded material (FGM), with high bending-stretching coupling effect has drawn considerable attention in many engineering applications. The mechanical properties in these materials vary smoothly and continuously in a preferred directions, and are usually made from a mixture of ceramics and metals to achieve the significant requirement of material properties [1]. The ceramic can resist the severe thermal loading in the high temprature environment whereas, the metal is utilized to decrease the large tensile stress on the ceramic surface at the earlier stage of cooling [2].
Due to the wide application of the FGMs structural components in the design of aerospace structures, their static characteristics have fascinated the attention of many researchers in previous years. It is realized from the literature that the amount of such work carried out for isotropic plates are exhaustive and considerable literature are available on composite plates. However, the literature on the analysis of the FGMs plate is inadequate. Reddy [3] presented theoretical formulation and finite element models based on third order shear deformation theory for static and dynamic analysis of the FGM plates. He obtained Navier solutions for a simply supported square plate under sinusoidally distributed load which includes the effect of shear deformation. It is found that in the absence of thermal loading the dynamic response of the FGM plates is intermediate to that of the ceramic and metal plates. Abrate [4] analyzed the problems of free vibrations, buckling, and static deflections of the FGM plates using the classical laminated plate model, the FSDT model, and the HSDT model. It is concluded that the behavior of the FGM plates can be determined without performing a direct analysis. Ferreira et al. [5] performed the static deformations of simply supported FGM plate based on collocation multi quadric radial basis functions by using a higher order shear deformation theory. Talha and Singh [6] analyzed free vibration analysis of FGM plates in which the material properties are graded according to a simple power law distribution of the constituent. Traction free boundary conditions on the top and bottom faces of the plate have been considered in the system equation using HSDT model. They obtained the results by employing a C0 isoparametric finite element model and performed parametric study for varying volume fraction index and the thickness ratio of the FGM plate.
The objective of the present research is to develop a higher order shear deformation theory with a special modification in the transverse displacement which applies additional freedom to the displacements through the thickness and consequently eliminates the over-correction. To implement this theory a suitable C0 continuous isoparametric finite element with thirteen degrees of freedom (DOFs) per node is proposed and developed. The material properties are assumed to be isotropic and vary throughout the thickness, according to a simple power-law function of the position.