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Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading

Published online by Cambridge University Press:  03 June 2015

A. Behravan Rad
A. Behravan Rad*
Affiliation:
Department of Mechanical Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran
*
*Corresponding author. Email: behravanrad@gmail.comEmail: abehravanrad@aol.com
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Abstract

In this paper, the static analysis of functionally graded (FG) circular plates resting on linear elastic foundation with various edge conditions is carried out by using a semi-analytical approach. The governing differential equations are derived based on the three dimensional theory of elasticity and assuming that the mechanical properties of the material vary exponentially along the thickness direction and Poisson’s ratio remains constant. The solution is obtained by employing the state space method (SSM) to express exactly the plate behavior along the graded direction and the one dimensional differential quadrature method (DQM) to approximate the radial variations of the parameters. The effects of different parameters (e.g., material property gradient index, elastic foundation coefficients, the surfaces conditions (hard or soft surface of the plate on foundation), plate geometric parameters and edges condition) on the deformation and stress distributions of the FG circular plates are investigated.

Keywords

15A1615A1865D3274B0574G15Functionally graded circular plateelastic foundationdifferential quadrature methodstate-space method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 2 , April 2012 , pp. 205 - 222
Copyright
Copyright © Global-Science Press 2012

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References

[1] Chen, W., Liang, S. and Zhong, T., On the DQ analysis of geometrically nonlinear vibration of immovably simply supported beams, J. Sound. Vib., 206(5) (1997), pp. 745–748.Google Scholar
[2] Reddy, J. N., Wang, C. M. and Kitipornchai, S., Axisymmetric bending of functionally graded circular and annular plates, Euro. J. Mech. Solids., 18(2) (1999), pp. 185–199.Google Scholar
[3] Chen, W., Shu, C. and He, W., The DQ solution of geometrically nonlinear bending of orthotropic rectangular plates by using Hadamard and SJT product, Comput. Struct., 74(1) (2000), pp. 65–74.CrossRefGoogle Scholar
[4] Yang, J. and Shen, H. S., Dynamic response of initially stressed functionally graded rectangular thin plates, Comp. Struct., 54 (2001), pp. 497–508.Google Scholar
[5] Ma, L. S. and Wang, T. J., Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory, Int. J. Solids. Struct., 41(1) (2004), pp. 85–101.CrossRefGoogle Scholar
[6] Vel, S. S. and Batra, R. C., Three-dimensional exact solution for the vibration of functionally graded rectangular plates, J. Sound. Vib., 272 (2004), pp. 703–730.CrossRefGoogle Scholar
[7] Chen, C. S., Nonlinear vibration of a shear deformable functionally graded plate, Comp. Struct., 68 (2005), pp. 295–302.CrossRefGoogle Scholar
[8] Serge, A., Free vibration, buckling, and static deflections of functionally graded plates, Comp. Sci. Tech., 66 (2006), pp. 2383–2394.Google Scholar
[9] Park, J. S. and Kim, J. H., Thermal post buckling and vibration analyses of functionally graded plates, J. Sound. Vib., 289 (2006), pp. 77–93.CrossRefGoogle Scholar
[10] Nie, G. J. and Zhong, Z., Axisymmetric bending of two-directional functionally graded circular and annular plates, Acta. Mech. Solid. Sin., 20(4) (2007), pp. 289–295.CrossRefGoogle Scholar
[11] Nie, G. J. and Zhong, Z., Semi-analytical solution for three-dimensional vibration of functionally graded circular plates, Comput. Meth. Appl. Mech. Eng., 196 (2007), pp. 4901–4910.Google Scholar
[12] Li, X. Y., Ding, H. J. and Chen, W. Q., Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk , Int. J. Solids. Struct., 45(1) (2008), pp. 191–210.Google Scholar
[13] Nie, G. J. and Zhong, Z., Vibration analysis of functionally graded sectorial plates with simply supported radial edges, Comp. Struct., 84 (2008), pp. 167–176.Google Scholar
[14] Huang, Z. Y., Lu, C. F. and Chen, W. Q., Benchmark solution for functionally graded thick plates resting on Winkler-Pasternak elastic foundations, Comp. Struct., 85 (2008), pp. 95–104.Google Scholar
[15] Wang, Y., Xu, R. Q. and Ding, H. J., Free axisymmetric vibration of FGM plates, Appl. Math. Mech., 30(9) (2009), pp. 1077–1082.CrossRefGoogle Scholar
[16] Malekzadeh, P., Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations, Comp. Struct., 89 (2009), pp. 367–373.CrossRefGoogle Scholar
[17] Hosseini, H., Akhavan, H., Rokni, D. T., Daemi, N. H. and Alibeigloo, A., Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundation, Mater. Design., 31(4) (2010), pp. 1871–1880.Google Scholar
[18] Nie, G. J. and Zhong, Z., Dynamic analysis of multi-directional functionally graded annular plates, Appl. Math. Model., 34(3) (2010), pp. 608–616.CrossRefGoogle Scholar
[19] Alibeigloo, A., Three-dimensional exact solution for functionally graded rectangular plate with integrated surface piezoelectric layers resting on elastic foundation, Mech. Adv. Mater. Struct., 17(3) (2010), pp. 1–14.CrossRefGoogle Scholar
[20] Malekzadeh, P., Shahpari, S. A. and Ziaee, H. R., Three-dimensional free vibration of thick functionally graded annular plates in thermal environment, J. Sound. Vib., 329 (2010), pp. 425–442.CrossRefGoogle Scholar
[21] Shu, C., Differential Quadrature and Its Application in Engineering, Springer Publication, New York, 2000.CrossRefGoogle Scholar
[22] Zong, Z. and Zhang, Y., Advanced Differential Quadrature Methods, CRC Press, New York, 2009.Google Scholar