## Mechanical behavior of functionally graded material plates under transverse load-part. I: Analysis.(English)Zbl 1121.74396

Summary: An elastic, rectangular, and simply supported, functionally graded material (FGM) plate of medium thickness subjected to transverse loading has been investigated. The Poisson’s ratios of the FGM plates are assumed to be constant, but their Young’s 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 $$Eh^{3}/12(1 - \nu ^{2})$$, while the expressions of the bending stiffness of FGM plates are more complicated combination of material properties.

### MSC:

 74K20 Plates 74E05 Inhomogeneity in solid mechanics

### Keywords:

FGM plate; Fourier series expansion; analytical solution
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