Thermo-Elastic Analysis of Non-Uniform Functionally Graded Circular Plate Resting on a Gradient Elastic Foundation

Subject Areas : Engineering

A  Behravan Rad ¹ (Engineering Department ,Zamyad Company,15Km Karaj Old Road, P.O 1386183741, Tehran, Iran)

Received: 2016-09-20 Accepted : 2016-12-14 Published : 2017-03-30

Keywords: Circular plate, Functionally graded, Gradient foundation, Thermo-mechanical, Semi-analytical, Non-uniform,

Abstract :

Present paper is devoted to stress and deformation analyses of heated variable thickness functionally graded (FG) circular plate with clamped supported, embedded on a gradient elastic foundation and subjected to non-uniform transverse load. The plate is coupled by an elastic medium which is simulated as a Winkler- Pasternak foundation with gradient coefficients in the radial and circumferential directions during the plate deformation. The temperature distribution is assumed to be a function of the thickness direction. The governing state equations are derived in terms of displacements and temperature based on the 3D theory of thermo-elasticity. These equations are solved using a semi-analytical method to evaluate the deformation and stress components in the plate. Material properties of the plate except the Poisson's ratio are assumed to be graded continuously along the thickness direction according to an exponential distribution. A parametric study is accomplished to evaluate the effects of material heterogeneity indices, foundation parameters, temperature difference between the top and bottom surfaces of the plate and thickness to radius ratio on displacements and stresses. The results are reported for the first time and the new results can be used as a benchmark solution for the future researches.

References:

[1] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Axisymmetric bending of functionally graded circular and annular plates, European Journal of Mechanics A/Solids 18(2): 185-189.
[2] Najafizadeh M. M., Heydari H. R., 2008, An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression, International Journal of Mechanical Science 50(3): 603-612.
[3] Ma L. s., Wang T. J., 2003, Nonlinear bending and post buckling of functionally graded circular plates under mechanical and thermal loadings, International Journal of Solids & Structures 40: 3311-3330.
[4] Khorshidvand A. R., Jabbari M., Eslami M. R., 2012, Thermo elastic buckling analysis of functionally graded circular plates integrated with oiezoelectric layers, Journal of Thermal Stress 35: 695-717.
[5] Kiani Y., Eslami M. R., 2013, An exact solution for thermal buckling of annular FGM plates on an elastic medium, Composites Part: B Engineering 45: 101-110.
[6] Gaikwad K. R., 2013, Analysis of thermo-elastic deformation of a thin hollow circular disk due to partially distributed heat supply, Journal of Thermal Stress 36: 207-224.
[7] Golmakani M.E., Kadkhodayan M., 2014, An investigation into the thermo elastic analysis of circular and annular FGM plates, Mechanics of Advanced Materials and Structures 21(1): 1-13.
[8] Fallah F., Noseir A., 2015, Thermo - mechanical behavior of functionally graded circular sector plates, Acta Mechanica 226: 37-54.
[9] Gunes R., Reddy J. N., 2008, Nonlinear analysis of functionally graded circular plates under different loads and boundary conditions, International Journal of Structural Stability and Dynamic 8(1): 131-159.
[10] Prakash T., Ganapathi M., 2006, Asymmetric flexural vibration and thermo-elastic stability of functionally graded circular plates using finite element method, Composite Part: B Engineering 37(7-8): 642-649.
[11] Gomshei M. M., abbasi V., 2013, Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method, Journal of Mechanical Science and Technology 27 (4): 1031-1039.
[12] Afsar A. M., Go J., 2010, Finite element analysis of thermo-elastic field in a rotating FGM circular disk, Applied Mathematical Modeling 34: 3309-3320.
[13] Leu S-Y., Chien L-c., 2015, Thermoelastic analysis of functionally graded rotating disks with variable thickness involving non-uniform heat source, Journal of Thermal Stress 38: 415-426.
[14] Safaeian Hamzehkolaei N., Malekzadeh P., Vaseghi J., 2011, Thermal effect on axisymmetric bending of functionally graded circular and annular plates using DQM, Steel and Composite Structures 11(4): 341-358.
[15] Malekzadeh P., Golbahar Haghighi M.R., Atashi M.M., 2011, Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment, Meccanica 47(2): 321-333.
[16] Sepahi O., Forouzan M.R., Malekzadeh P., 2011, Thermal buckling and post buckling analysis of functionally graded annular plates with temperature dependent material properties, Materials & Design 32(7): 4030-4041.
[17] Sepahi O., Forouzan M.R., Malekzadeh P., 2010, Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM, Composite Structures 92: 2369-2378.
[18] Jabbari M., Shahryari E., Haghighat H., Eslami M.R., 2014, An analytical solution for steady state three dimensional thermo elasticity of functionally graded circular plates due to axisymmetric loads, European Journal of Mechanics A/Solids 47: 124-142.
[19] Nie G.J., Zhong Z., 2007, Semi-analytical solution for three-dimensional vibration of functionally graded circular plates, Computational Methods in Applied Mechanics and Engineering 196: 4901-4910.
[20] Yu Li X., Li P.D., Kang G.Z., Pan D.Z., 2013, Axisymmetric thermo-elasticity field in a functionally graded circular plate of transversely isotropic material, Mathematics and Mechanics of Solid 18(5): 464-475.
[21] Behravan Rad A., 2012, 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 4(2): 205- 222.
[22] Behravan Rad A., Alibeigloo A., 2013, Semi-analytical solution for the static analysis of 2D functionally graded circular and annular circular plates resting on elastic foundation, Mechanics of Advanced Materials and Structures 20(7): 515-528.
[23] Behravan Rad A., 2012, Static response of 2D functionally graded circular plate with gradient thickness and elastic foundations to compound loads, Structural Engineering and Mechanics 44(2):139-161.
[24] Shu C., 2000, Differential Quadrature and Its Application in Engineering, Springer, New York.
[25] Zong Z., Zhang Y., 2009, Advanced Differential Quadrature Methods, CRC Press, New York.