A three-dimensional solution for the problem of transversely loaded, all-round clamped rectangular plates of arbitrary thickness is presented within the linear, small deformation theory of elasticity. The Ritz minimum energy principle is employed to derive the governing equation of the plate made of functionally graded materials. In theory, if we employ an infinite number of terms in the displacement series, the exact solution can be determined. However, a practical limit always exists due to numerical implementation. The solution has a validity comparable to some higher order theories. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The displacements and stresses of the plate for different values of the power-law exponent are investigated.
Three-Dimensional Flexure of Rectangular Plates Made of Functionally Graded Materials
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Elishakoff, I., and Gentilini, C. (January 18, 2005). "Three-Dimensional Flexure of Rectangular Plates Made of Functionally Graded Materials." ASME. J. Appl. Mech. September 2005; 72(5): 788–791. https://doi.org/10.1115/1.1985429
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