Hindawi Publishing Corporation Modelling and Simulation in Engineering Volume 2012, Article ID 159806, 10 pages doi:10.1155/2012/159806 Research Article A New Hyperbolic Shear Deformation Theory for Bending Analysis of Functionally Graded Plates Tahar Hassaine Daouadji, 1, 2 Abdelaziz Hadj Henni, 1, 2 Abdelouahed Tounsi, 2 and Adda Bedia El Abbes 2 1 Departement of Civil Engineering, Ibn Khaldoun University of Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algeria 2 Laboratoire des Mat´ eriaux et Hydrologie, Universit´ e de Sidi Bel Abbes, BP 89 Cit´ e Ben M’hidi, 22000 Sidi Bel Abbes, Algeria Correspondence should be addressed to Tahar Hassaine Daouadji, daouadjitah@yahoo.fr Received 16 May 2012; Accepted 3 August 2012 Academic Editor: Guowei Wei Copyright © 2012 Tahar Hassaine Daouadji et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Theoretical formulation, Navier’s solutions of rectangular plates based on a new higher order shear deformation model are presented for the static response of functionally graded plates. This theory enforces traction-free boundary conditions at plate surfaces. Shear correction factors are not required because a correct representation of transverse shearing strain is given. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concern flexural behavior of FG plates with metal-ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fractions profiles, aspect ratios, and length to thickness ratios. Results are verified with available results in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded plates. 1. Introduction The concept of functionally graded materials (FGMs) was first introduced in 1984 by a group of material scientists in Japan, as ultrahigh temperature-resistant materials for aircraft, space vehicles, and other engineering applications. Functionally graded materials (FGMs) are new composite materials in which the microstructural details are spatially varied through nonuniform distribution of the reinforce- ment phase. This is achieved by using reinforcement with different properties, sizes, and shapes, as well as by inter- changing the role of reinforcement and matrix phase in a continuous manner. The result is a microstructure that produces continuous or smooth change on thermal and mechanical properties at the macroscopic or continuum level (Koizumi, 1993 [1]; Hirai and Chen, 1999 [2]). Now, FGMs are developed for general use as structural components in extremely high-temperature environments. Therefore, it is important to study the wave propagation of functionally graded materials structures in terms of nondestructive evaluation and material characterization. Several studies have been performed to analyze the mechanical or the thermal or the thermomechanical responses of FG plates and shells. A comprehensive review is done by Tanigawa (1995) [3]. Reddy (2000) [4] has analyzed the static behavior of functionally graded rectangular plates based on his third-order shear deformation plate theory. Cheng and Batra (2000) [5] have related the deflections of a simply supported FG polygonal plate given by the first-order shear deformation theory and third-order shear deformation theory to that of an equivalent homogeneous Kirchhoff plate. The static response of FG plate has been investigated by Zenkour (2006) [6] using a generalized shear deformation theory. In a recent study, S ¸ims ¸ek (2010) [7] has studied the dynamic deflections and the stresses of an FG simply supported beam subjected to a mov- ing mass by using Euler Bernoulli, Timoshenko, and the parabolic shear deformation beam theory. S ¸ims ¸ek (2010) [8],