STATIC ANALYSIS OF TWO DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR PLATE UNDER COMBINED AXISYMMETRIC BOUNDARY CONDITIONS

Abstract

This paper is concerned with the theoretical analysis of static behavior of the two-directional functionally graded circular plate embedded on two parameter elastic foundation (Winkler- Pasternak type) under axisymmetric transverse and shear loads by using semi-analytical method. This method gives an analytical solution in the thickness and approximate solution in the radius directions by employing the state-space based differential quadrature method. The governing state equations are derived based on 3D theory of elasticity, and assuming the material properties of the plate except the Poisson’s ratio varies continuously throughout the thickness and radius directions in the form of an exponential function. The stresses and displacements distribution are obtained by expanding the state variables and solving these state equations. The effects of foundation stiffnesses, material heterogeneity indices, loads ratio and the plate geometric parameter on the deformations and stresses distribution of the FG circular plate are investigated in numerical examples. The main foundings are: i- the mechanical behavior of the plate with the softer (metal rich) surface supported by elastic foundation differ significantly from that of the plate with the harder (ceramic rich) surface subjected to the same foundation.ii- the effecte of shear interaction on in-plain stresses is much more than the other stress components.The results are reported for the first time and are discussed in detail

Keywords

• FG Circular Plate, Elastic Foundation, Elasticity, State - Space, DQ Method

References

1. [1] Nemat-Alla M., Reduction of thermal stresses by developing two-dimensional functionally graded material, International Journal of Solids and Structures, 2003, 40, 7339-7356.
2. [2] Nie, G. J. and Zhong, Z., Axisymmetric bending of two-directional functionally graded circular and annular plates, Acta Mechanica Solid Sincia, 2007, 2(4), 289-295.
3. [3] Lu C.F., Lim C.W., Chen W.Q., Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions, International Journal of Numerical Methods in Engineering, 2009, 79, 25 – 44.
4. [4] Nie, G. J. and Zhong, Z., Dynamic analysis of multi-directional functionally graded annular plate, Applied Mathematical Modeling, 2010, 34(3), 608–616.
5. [5] Alibeigloo, A., Three-dimensional exact solution for functionally graded rectangular plate with integrated surface piezoelectric layers resting on elastic foundation, Mechanics of Advanced Materials and Structures, 2010, 17, 183 – 195.
6. [6] Shariyat, M., Alipour, M.M., Differential transform vibration and modal stress analyses of circular plates made of two directional functionally graded materials resting on elastic foundations, Archive of Applied Mechanics, DOI: 10. 1007/500419-010-0484-X
7. [7] Yun, W., Rongqiao X., Hojiang D., Three-dimensional solution of axisymmetric bending of functionally graded circular plates, Composite Structures, 2010, 92, 1683 – 1693.
8. [8] Golmakani, M.E., Kadkhodayan M., Non linear bending analysis of annular FGM plates using higher – order shear deformation plate theories, Composite Structures, 2011, 93, 973 – 982.

9. [9] Akgoz B. and Civalek O., Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameter elastic foundations, Steel and Composite Structures, 2011, 11(5), 403-421.
10. [10] Malekzadeh P., Golbahar Haghighi M.R., Atashi M.M., Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment, meccanica, 2011, 47(2), 321-333
11. [11] Yas M. H., Tahouneh V., 3-D free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM), Acta Mechanica, 2012, 223(1), 43–62.
12. [12] Jodaei A., Jalal M., Yas M.H., Free vibration analysis of functionally graded annular plates by state-spaced based differential quadrature method and comparative modeling by ANN, Compsites Part B, Engineering, 2012, 43, 340-353.
13. [13] Ponnusamy P. and Selvamani R., Wave propagation in a generalized thermoelastic plate embedded in elastic medium, Interaction and Multiscale Mechanics, 2012, 5(1), 13–26.
14. [14] Eftekhari S. A., Jafari A. A., Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates, Applied Mathematics and Mechanics, 2012, 33(1), 81 – 98.
15. [15] Amini M. H., Soleimani M., Altafi A., Rastgoo A., Effects of geometric nonlinearity on free and forced vibration analysis of moderately thick annular functionally graded plate, Mechanics of Advanced Materials and Structures, DOI:10.1080/15376494.2012.676711
16. [16] Golmakani M.E., Kadkhodayan M., An investigation into the thermoelastic analysis of circular and annular FGM plates, Mechanics of Advanced Materials and Structures, DOI: 10.1080/15376494.2012.677101
17. [17] Behravan Rad A., Semi-analytical solution for functionally graded solid circular and annular plates resting on elastic foundations subjected to axisymmetric transverse loading, Advances in Applied Mathematics and Mechanics, 2012, 4(2), 205 – 222.4
18. [18] Shu, C., Differential Quadrature and Its Application in Engineering, Springer Publication, New York, 2000.