Static Analysis of Functionally Graded Annular Plate Resting on Elastic Foundation Subject to an Axisymmetric Transverse Load Based on the Three Dimensional Theory of Elasticity

Subject Areas : Engineering

A Behravan Rad ^{1 *} , A Alibeigloo ² , S.S Malihi ³

1 - Department of Mechanical Engineering, Islamic Azad University, Karaj Branch
2 - Department of Mechanical Engineering, Engineering Faculty, Tarbiat Modares University
3 - Department of Mechanical Engineering, Islamic Azad University, Karaj Branch

Received: 2010-05-02 Accepted : 2010-11-03 Published : 2010-09-30

Keywords: Elastic foundation, FGM annular Plate, Semi-Analytical Method, differential quadrature, state space,

Abstract :

In this paper, static analysis of functionally graded annular plate resting on elastic foundation with various boundary conditions is carried out by using a semi-‍analytical approach‍ (SSM‍-DQM). The differential governing equations are presented based on the three dimensional theory of elasticity. The plate is assumed isotropic at any point, while material properties to vary exponentially through the thickness direction and the Poisson’s ratio remain constant. The system of governing partial differential equations can be writhen as state equations by expanding the state variables and using the state space method (SSM) about thickness direction and applying the one dimensional differential quadrature method (DQM) along the radial direction. Interactions between the plate and two parameter elastic foundations are treated as boundary conditions. The stresses and displacements distributions are obtained by solving these state equations. In this study, the influences of the material property graded index, the elastic foundation coefficients (Winkler-Pasternak), the thickness to radius ratio, and edge supports effect on the bending behavior of the FGM annular plate are investigated and discussed in details.

References:

[1] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Symmetric bending of functionally graded circular and annular plates. European Journal of Mechanics A/Solids 18(2):185-199.

[2] Yang J., Shen H.S., 2001, Dynamic response of initially stressed functionally graded rectangular thin plates, Composite Structures 54: 497-508.

[3] Ma L.S., Wang T.J., 2004, Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory, International Journal of Solids and Structures 41(1): 85-101.

[4] Vel S.S., Batra R.C., 2004, Three-dimensional exact solution for the vibration of functionally graded rectangular plates, Journal of Sound and Vibration 272: 703-730.

[5] Chen C.S., 2005, Nonlinear vibration of a shear deformable functionally graded plate, Composite Structures 68:295-302.

[6] Serge A.., 2006, Free vibration buckling and static deflections of functionally graded plates, Composite Science and Technology 66: 2383-2394.

[7] Park J.S., Kim J.H., 2006, Thermal postbuckling and vibration analyses of functionally graded plates, Journal of Sound and Vibration 289: 77-93.

[8] Nie G.J., Zhong Z.., 2007, Axisymmetric bending of two-directional functionally graded circular and annular plates, Acta Mechanica Solid Sincia 20(4): 289-295.

[9] Nie G.J., Zhong Z.., 2007, Semi-analytical solution for three-dimensional vibration of functionally graded circular plates, Computer Methods in Applied Mechanics and Engineering 196:4901-4910.

[10] Li X.Y., Ding H.J., Chen W.Q., 2008, Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk, International Journal of Solids and Structures 45(1): 191-210.

[11] Nie G.J., Zhong Z., 2008, Vibration analysis of functionally graded sectorial plates with simply supported radial edges, Composite Structures 84:167-176.

[12] Huang Z.Y., Lu C.F., Chen W.Q., 2008, Benchmark solution for functionally graded thick plates resting on Winkler- Pasternak elastic foundations, Composite Structures 85: 95-104.

[13] Wang Y., Xu R.Q., Ding H.J., 2009, Free axisymmetric vibration of FGM plates, Applied Mathematics and Mechanics 30 (9): 1077-1082.

[14] Malekzadeh P., 2009, Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations, Composite Structures 89: 367-373.

[15] Hosseini Hashemi Sh., Akhavan H., Rokni D.T., Daemi H., Alibeigloo N., 2010, Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundation, Materials and Design 31(4): 1871-1880.

[16] Nie G.J., Zhong Z., 2010, Dynamic analysis of multi-directional functionally graded annular plates, Applied Mathematical Modeling 34(3): 608-616.

[17] Shu C., 2000, Differential Quadrature and Its Application in Engineering, Springer Publication, New York.