Three-Dimensional Elastic Solution of a Transversely Isotropic Functionally Graded Rectangular Plate


Article Preview

Three-dimensional elastic solution of a simply supported, transversely isotropic functionally graded rectangular plate is presented in this paper. Suppose that all elastic coefficients of the material have the same power-law dependence on the thickness coordinate. By introducing two new displacement functions, three equations of equilibrium in terms of displacements are reduced to two uncoupled partial differential equations. Exact solution for a second-order partial differential equation expressed by one of displacement functions is obtained and analytical solution for another fourth-order partial differential equation expressed by another displacement function is found by employing the Frobenius method. The validity of the present solution is first investigated. And the effect of the gradation of material properties on the mechanical behavior of the plate is studied through numerical examples.



Advanced Materials Research (Volumes 591-593)

Edited by:

Liangchi Zhang, Chunliang Zhang, Jeng-Haur Horng and Zichen Chen




G. J. Nie et al., "Three-Dimensional Elastic Solution of a Transversely Isotropic Functionally Graded Rectangular Plate", Advanced Materials Research, Vols. 591-593, pp. 2655-2660, 2012

Online since:

November 2012




[1] A. Alibeigloo: Exact solution for thermo-elastic response of functionally graded rectangular plates. Compos. Struct., Vol. 92 (2010), p.113.


[2] A.H. England: Bending solution for inhomogeneous and laminated elastic plates. J. Elast., Vol. 82 (2006), p.129.

[3] B. Yang, H.J. Ding and W.Q. Chen: Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported. Appl. Math. Model., Vol. 36 (2012), p.488.


[4] Z. Zhong and E.T. Shang: Closed-form solutions of three-dimensional functionally graded plates. Mech. Adv. Mater. Struct., Vol. 15 (2008), p.355.

[5] M. Kashtalyan and J.J. Rushchitsky: Revisiting displacement functions in three-dimensional elasticity of inhomogeneous media. Int. J. of Solids Struct., Vol. 46 (2009), p.3463.


[6] B. Woodward and M. Kashtalyan: Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates. Eur. J. Mech. A-Solid., Vol. 30 (2011), p.705.