An elastic, rectangular, and simply supported, functionally graded material (FGM) plate of medium thickness subjected to transverse loading has been investigated. The PoissonÕs ratios of the FGM plates are assumed to be constant, but their YoungÕs moduli vary continuously throughout the thickness direction according to the volume fraction of constituents defined by power-law, sigmoid, or exponential function. Based on the classical plate theory and Fourier series expansion, the series solutions of power-law FGM (simply called P-FGM), sigmoid FGM (S-FGM), and exponential FGM (E-FGM) plates are obtained. The analytical solutions of P-, S-and E-FGM plates are proved by the numerical results of finite element method. The closed-form solutions illustrated by Fourier series expression are given in Part I of this paper. The closed-form and finite element solutions are compared and discussed in Part II of this paper. Results reveal that the formulations of the solutions of FGM plates and homogeneous plates are similar, except the bending stiffness of plates. The bending stiffness of a homogeneous plate is Eh 3 /12(1 À m 2 ), while the expressions of the bending stiffness of FGM plates are more complicated combination of material properties.

The formulations of the complete solutions to the rectangular simply supported plates with power-law, sigmoid, and exponential FGMs have been derived in Part I. In this part, we focus on the numerical solutions evaluated directly from theoretical formulations and calculated by finite element method using MARC program. The effects of loading conditions, the change of PoissonÕs ratio, and the aspect ratio on the mechanical behavior of an FGM plate are discussed. Besides, a comparison of the results of P-FGM, S-FGM, and E-FGM is investigated. Finite element modelsIn the numerical calculation, consider a square FGM plate with the ratio of width to thickness equal to 50, i.e., a = b = 100 cm, h = 2 cm. The plate is simply supported on its four sides and is subjected to the transverse load, as shown in Fig. 1. The PoissonÕs ratio of the FGM plate is assumed to be constant in the whole plate. Take m = 0.3. The YoungÕs moduli at the top and bottom surfaces of the FGM plate are assumed to be E 2 and E 1 , respectively. However, the YoungÕs modulus at any point on the FGM plate varies continuously in the thickness direction based on the volume fraction of the constituents. 0020-7683/$ -see front matter Ó

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