#### Vol. 2, No. 1, 2007

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### Yen-Ling Chung and Wei-Ting Chen

Vol. 2 (2007), No. 1, 63–86
##### Abstract

We analyze functionally graded material (FGM) plates with two opposite edges simply supported and the other two edges free subjected to a uniform load. Even though an FGM plate is a kind of composite material, if the Young’s modulus of the FGM plates varies along the thickness direction and the Poisson’s ratio is constant in the whole FGM plate, the bending and in-plane problems in FGM plates under transverse load only are uncoupled. Therefore, the analytical solution to the bending problem of FGM plates is obtained in this study by Fourier series expansions, which agrees very well with a finite element calculation. Results show that the maximum tensile stresses are located at the bottom of the FGM plates. However, the maximum compressive stresses move to the inside of the FGM plates. The coefficients ${A}_{11},{B}_{11},{C}_{11}$ defined in this paper relate to the area and to the first and the second moments of the area under the $E\left(z\right)$ curve from $z=-h∕2$ to $z=h∕2$. The parameter ${Q}_{11}$, representing the location of the centroid of the area under the $E\left(z\right)$ curve, is related to the location of the neutral surfaces, and ${S}_{11}$ represents the bending stiffness of the FGM plates.

##### Keywords
FGM plate, Fourier series expansion, finite element analysis