Figure 12 - from "New Shape Function for the Bending Analysis of Functionally Graded Plate"

Figure 11. Distribution of the normalized values of the transverse shear stresses T;z and Tyz across the thickness of the plate on elastic foundation for different shape functions: (a) a/h = 10,a/b =1,p =2, ko = 100, ky = 10; (b) a/h = 10, a/b =1, p =2, kg = 100, ky = 10. Figure 11. Distribution of the normalized values of the transverse shear stresses Tz and Tyz aCTOSS the

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$Figure 1. Schematic of continuously graded microstructure with metal-ceramic constituents: (a) smoothly graded microstructure; (b) enlarged view; (c) ceramic-metal functionally graded materials (FGM). strength, toughness, and high thermal conductivity. Functionally graded materials, which contain metal and ceramic constituents, improve thermo-mechanical properties between layers, because of which delamination of layers should be avoided due to continuous change between properties of the constituents. By varying the percentage of volume fraction content of the two or more materials, FGM can be formed so that it achieves a desired gradient property in specific directions. Figure 1 shows schematic of continuously graded microstructure with metal-ceramic constituents [4].$

$Figure 2. Different types of functionally graded materials based on nature of gradients: (a) fraction gradient type; (b) shape gradient type; (c) orientation gradient type; (d) size gradient type. Depending on the nature of gradient, functionally graded materials may be grouped into fraction rradient type, shape gradient type, orientation gradient type and size gradient type (Figure 2) [5].$

Figure 3. Geometry of the plate: (a) FGM plate; (b) FGM plate on elastic foundation. The subject of the analysis in this paper are FGM plate (Figure 3a) and FGM plate on elastic foundation (Figure 3b). The plate (length a, width b and height h) is made of functionally graded material consisting of the two constituents, namely, metal and ceramics.

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$Figure 4. The comparison of homogenous plates (ceramic or metal) and FGM plates: (a) volume fraction of the material; (b) homogenous and FGM plates.$

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Table 1. Shear deformation shape functions. This paper proposes a new shape function as follows:

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Milivoje Milanovic, Halit Redzovic

New Shape Function for the Bending Analysis of Functionally Graded Plate

Abstract: The bending analysis of thick and moderately thick functionally graded square and rectangular plates as well as plates on Winkler–Pasternak elastic foundation subjected to sinusoidal transverse load is presented in this paper. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. This paper presents the methodology of the application of the high order shear deformation theory based on the shape functions. A new shape function has been developed and the obtained results are compared to the results obtained with 13 different shape functions presented in the literature. Also, the validity and accuracy of the developed theory was verified by comparing those results with the results obtained using the third order shear deformation theory and 3D theories. In order to determine the procedur...

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