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Stress and Strain Analysis of Functionally Graded Rectangular Plate with Exponentially Varying Properties

DOI: 10.1155/2013/206239

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Abstract:

The bending of rectangular plate made of functionally graded material (FGM) is investigated by using three-dimensional elasticity theory. The governing equations obtained here are solved with static analysis considering the types of plates, which properties varying exponentially along direction. The value of Poisson’s ratio has been taken as a constant. The influence of different functionally graded variation on the stress and displacement fields was studied through a numerical example. The exact solution shows that the graded material properties have significant effects on the mechanical behavior of the plate. 1. Introduction Recently, a new category of composite materials known as functionally graded materials (FGMs) has attracted the interest of many researchers. The FGMs are heterogeneous composite materials in which the mechanical properties vary continuously in certain direction. FGMs are used in many engineering applications such as aviation, rocketry, missiles, chemical, aerospace, and mechanical industries. Therefore, composites that are made of FGMs were considerably attractive in recent years. Several studies have been performed to analyze the behavior of functionally graded beam, plates, and shells. Hadi et al. [1, 2] studied an Euler-Bernoulli and Timoshenko beam made of functionally graded material subjected to a transverse loading at which Young’s modulus of the beam varies by specific function. Reddy [3] has analyzed the static behavior of functionally graded rectangular plates based on his third-order shear deformation plate theory. Cheng and Batra [4] have related the deflections of a simple supported functionally graded polygonal plate given by the first-order shear deformation theory and a third-order shear deformation theory to an equivalent homogeneous Kirchhoff plate. Cheng and Batra [5] also presented results for the buckling and steady state vibrations of a simple supported functionally graded polygonal plate based on Reddy’s plate theory. Loy et al. [6] studied the vibration of functionally graded cylindrical shells by using Love’s shell theory. Analytical 3D solutions for plates are useful because provided benchmark results to assess the accuracy of various 2D plate theories and finite element formulations. Cheng and Batra [7] used the method of asymptotic expansion to study the 3D thermoelastic deformations of a functionally graded elliptic plate. Recently, Vel and Batra [8] have presented an exact 3D solution for the thermoelastic deformation of functionally graded simple supported plates of finite dimensions. Reiter et al.

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