**Commenced**in January 2007

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**Edition:**International

**Paper Count:**32119

##### Thermo-mechanical Deformation Behavior of Functionally Graded Rectangular Plates Subjected to Various Boundary Conditions and Loadings

**Authors:**
Mohammad Talha,
B. N. Singh

**Abstract:**

This paper deals with the thermo-mechanical deformation behavior of shear deformable functionally graded ceramicmetal (FGM) plates. Theoretical formulations are based on higher order shear deformation theory with a considerable amendment in the transverse displacement using finite element method (FEM). The mechanical properties of the plate are assumed to be temperaturedependent and graded in the thickness direction according to a powerlaw distribution in terms of the volume fractions of the constituents. The temperature field is supposed to be a uniform distribution over the plate surface (XY plane) and varied in the thickness direction only. The fundamental equations for the FGM plates are obtained using variational approach by considering traction free boundary conditions on the top and bottom faces of the plate. A C0 continuous isoparametric Lagrangian finite element with thirteen degrees of freedom per node have been employed to accomplish the results. Convergence and comparison studies have been performed to demonstrate the efficiency of the present model. The numerical results are obtained for different thickness ratios, aspect ratios, volume fraction index and temperature rise with different loading and boundary conditions. Numerical results for the FGM plates are provided in dimensionless tabular and graphical forms. The results proclaim that the temperature field and the gradient in the material properties have significant role on the thermo-mechanical deformation behavior of the FGM plates.

**Keywords:**
Functionally graded material,
higher order shear deformation theory,
finite element method,
independent field variables.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334540

**References:**

[1] M. Koizumi, The concept of FGM, Proceedings of the Second International symposium onFGM, vol. 34, pp. 3−10, 1993.

[2] M. Koizumi, FGM activities in Japan, Composites Part B, vol. 28B, pp. 1−4, 1997.

[3] E. Reissner,The Effect of transverse shear deformation on the bending of elastic plates, J. appl. Mech., vol. 12 Trans, A69−A77, 1945.

[4] Mindlin, R. D. Influence of rotatory inertia and shear on flexural vibrations of isotropic elastic plates, J. Appl. Mech., vol. 73, pp. 31−38, 1951.

[5] R. B. Nelson, and D. R. Larch, A refined theory of laminated orthotropic plates, J. appl. Mech., vol. 41, pp. 177-183, 1974.

[6] Reissner, E. On Transverse bending of plates including the effect of transverse shear deformation., Int. J. Solids Struct., 1975, 11, 569-573.

[7] K. H. Lo, R. M. Christensen, and E. M. Wu, A high-order theory of plate deformation-part I: homogeneous plates., J. appl. Mech., vol. 44, pp.663-668, 1977.

[8] J. N. Reddy, A simple higher-order theory for laminated composite plates. J. appl. Mech, vol.51, pp. 745-752,1984.

[9] J. N. Reddy, Analysis of functionally graded plates, Int. J. Numer. Method Engng., vol.47, pp. 663−684, 2000.

[10] S. Abrate, Free vibration buckling and static deflections of functionally graded plates, Compos. Scie. and Tech., vol. 66, pp.2383−2394, 2006.

[11] PARK, Jae-Sang. and KIM, Ji-Hwan. Thermal postbuckling and vibration analyses of functionally graded plates,J. Sound vibr., vol. 289, pp.77−93, 2006.

[12] Wu. Lanhe, Thermal buckling of a simply supported moderately thick rectangular FGM plate, Compo. Struct., vol. 64, pp. 211−218, 2004.

[13] A. R. Saidi, and E. Jomehzadeh, On the analytical approach for the bending/stretching of linearly elastic functionally graded rectangular plates with two opposite edges simply supported, Proc. IMechE, Part C., 2009, 223, 1873−1884.

[14] Wu. Lanhe, Thermal buckling of a simply supported moderately thick rectangular FGM plate,Compo. Struct., vol. 64, pp.211−218, 2004.

[15] A. J. M, Ferreira, R.C, Batra, C.M.C, Roque, L.F, Qian, and P.A.L.S, Martins, Static analysis of functionally graded plates using third order shear deformation theory and a meshless method,Compo. Struct., vol. 69, pp. 449−457, 2005.

[16] J. Yang, and H. S. Shen,Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments, J. Sound Vibr., vol. 255, pp. 579−602, 2000.

[17] L.F, Qian. R. C. Batra, and L. M. Chen, Static and dynamic deformations of thick functionally graded elastic plates by using higher order shear and normal deformable plate theory and meshless local Petrov-Galerkin method , Composite Part B, pp.685−697, 2004.

[18] E. Efraim,a nd M. Eisenberger, Exact vibration analysis of variable thickness annular isotropic and FGM plates, J. Sound Vibr., vol. 299, pp. 720−738, 2007.

[19] M. H. Naei, A. Masoumi, and A. Shamekhi, Buckling analysis of circular functionally graded material plate having variable thickness under uniform compression by finite-element method,Proc. IMechE, Part C, vol. 221 pp. 1241−1247, 2007.

[20] H. M. Navazi, and H. Haddadpour, Aero-thermoelastic stability of functionally graded plates, Compos. Struct., vol. 80, pp. 580−587, 2007.

[21] J. N. Reddy, and Z. Q. Cheng, Frequency of functionally graded plates with three-dimensional asymptotic approach, J. of Engg. Mech., vol. 129 (8), pp. 896−900, 2003.

[22] T. M. Nguyen, K. Sab, and G. Bonnet, First-order shear deformation plate models for functionally graded materials,Compos. Struct., vol. 83, pp. 25−36, 2008.

[23] K. M. Liew, K. C. Hung, and M. K. Lim, A continuum three-dimensional vibration analysis of thick rectangular plates, Int. J. Solids Struct., vol. 30 (24), pp. 3357−3379, 1993

[24] H. Matasunaga, Analysis of functionally graded plates, Compos. Struct., vol. 82, pp. 499−512, 2008.

[25] Y. S. Touloukian, Thermophysical properties of high temprature solid materials., MacMillan, New York, 1967.

[26] X.I. Huang, and H. S. Shen, Nonlinear vibration and dynamic response of functionally graded plates in thermal environments Int. J. Solids and Struct., vol. 41, pp. 2403-2427, 2004.

[27] Mohammad Talha, B. N. Singh, "Static response and free vibration analysis of FGM plates using higher order shear deformation theory," App. Math. Model., vol. 34, pp. 3991-4011, 2010.