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http://dx.doi.org/10.12989/scs.2015.18.2.443

Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory  

Tebboune, Wafa (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Houari, Mohammed Sid Ahmed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de Genie Civil)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Publication Information
Steel and Composite Structures / v.18, no.2, 2015 , pp. 443-465 More about this Journal
Abstract
In this paper, an efficient and simple trigonometric shear deformation theory is presented for thermal buckling analysis of functionally graded plates. It is assumed that the plate is in contact with elastic foundation during deformation. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns. It is assumed that the mechanical and thermal non-homogeneous properties of functionally graded plate vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain-displacement relations, the equilibrium and stability equations of plates made of functionally graded materials are derived. The boundary conditions for the plate are assumed to be simply supported on all edges. The elastic foundation is modelled by two-parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effects of thermal loading types and variations of power of functionally graded material, aspect ratio, and thickness ratio on the critical buckling temperature of functionally graded plates are investigated and discussed.
Keywords
functionally graded materials; buckling; plate theory; elastic foundations;
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Times Cited By KSCI : 9  (Citation Analysis)
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1 Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703.   DOI
2 Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013) "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104.   DOI   ScienceOn
3 Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33.   DOI
4 Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Methods, 11(6), 1350082.   DOI
5 Cheng, Z.Q. and Batra, B.C. (2000), "Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plate", J. Sound Vib., 229(4), 879-895.   DOI   ScienceOn
6 Cheng, Z.Q. and Kitipornchai, S. (1999), "Membrane analogy of buckling and vibration of inhomogeneous plates", ASCE J. Eng. Mech., 125(11), 1293-1267.   DOI
7 Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., Int. J., 17(1), 69-81.   DOI
8 El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247.   DOI   ScienceOn
9 Fekrar, A., El Meiche, N., Bessaim, A., Tounsi, A. and Adda Bedia, E.A. (2012), "Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory", Steel Compos. Struct., Int. J., 13(1), 91-107.   DOI   ScienceOn
10 Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810.   DOI
11 Hadji, L., Ait Atmane, H., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2011), "Free vibration of functionally graded sandwich plates using four-variable refined plate theory", Appl. Math. Mech., 32(7), 7925-7942.
12 Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383.   DOI
13 Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E., 40(8), 2791-2799.   DOI
14 Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 467-479.
15 Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates based on higher order theory," J. Therm. Stress., 25(1), 603-625.   DOI
16 Kaci, A., Tounsi, A., Bakhti, K. and Adda Bedia, E.A. (2012), "Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates", Steel Compos. Struct., Int. J., 12(6), 491-504.   DOI   ScienceOn
17 Kitipornchai, S., Yang, J. and Liew, K.M. (2006), "Random vibration of the functionally graded laminates in thermal environments", Comput. Method. Appl. Mech. Eng., 195(9-12), 1075-1095.   DOI
18 Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solid. Struct., 40(6), 1525-1546.   DOI
19 Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct, Int. J., 15(4), 399-423.   DOI
20 Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Methods, 11(5), 1350077.   DOI
21 Klouche Djedid, I., Benachour, A., Houari, M.S.A., Tounsi, A. and Ameur, M. (2014), "A n-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., Int. J., 17(1), 21-46.   DOI
22 Koizumi, M. (1993), "The concept of FGM", Ceram Trans, Funct Gradient Mater, 34, 3-10.
23 Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 641-650.   DOI
24 Noda, N., Hetnarski, R.B. and Tanigawa, Y. (2003), Thermal Stresses, (Second Edition), Taylor & Francis, New York, NY, USA.
25 Sadoune, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., Int. J., 17(3), 321-338.   DOI
26 Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Cosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR, 1-56. [in Russian]
27 Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", ASME J. Appl. Mech., 51(4), 745-752.   DOI
28 Reddy, J.N. and Cheng, Z.Q. (2002), "Frequency correspondence between membranes and functionally graded spherical shallow shells of polygonal plan form", Int. J. Mech. Sci., 44(5), 967-985.   DOI
29 Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87.   DOI   ScienceOn
30 Sobhy, M. (2014), "Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions", Acta Mech., 225(9), 2521-2538.   DOI
31 Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220.   DOI
32 Whitney, J.M. and Pagano, N.J. (1970), "Shear deformation in heterogeneous anisotropic plates", J. Appl. Mech., 37(), 1031-1036.   DOI
33 Woo, J., Meguid, S.A., Stranart, J.C. and Liew, K.M. (2005), "Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells", Int. J. Mech. Sci., 47(8), 1147-1171.   DOI
34 Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48(8), 2019-2035.   DOI   ScienceOn
35 Yaghoobi, H. and Fereidoon, A. (2014), "Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory", Compos.: Part B, 62, 54-64.   DOI
36 Yaghoobi, H. and Torabi, M. (2013a), "Exact solution for thermal buckling of functionally graded plates resting on elastic foundations with various boundary conditions", J. Therm. Stresses, 36(9), 869-894.   DOI
37 Yaghoobi, H. and Torabi, M. (2013b), "Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation", Appl. Math. Model., 37(18-19), 8324-8340.   DOI
38 Yamanouchi, M., Koizumi, M., Hirai, T. and Shiota, I. (1990), "On the design of functionally gradient materials", Proceedings of First International Symposium on Functionally Gradient Materials, Sendai, Japan, October.
39 Yang, J., Liew, K.M. and Kitipornchai, S. (2005a), "Second-order statistics of the elastic buckling of functionally graded rectangular plates", Compos. Sci. Technol., 65(7-8), 1165-1175.   DOI
40 Yang, J, Liew, K.M. and Kitipornchai, S. (2005b), "Stochastic analysis of compositionally graded plates with system randomness under static loading", Int. J. Mech. Sci., 47(10), 1519-1541.   DOI
41 Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51(11-12), 869-880.   DOI
42 Zenkour, A. and Sobhy, M. (2013), "Dynamic bending response of thermoelastic functionally graded plates resting on elastic foundations", Aerosp. Sci. Technol., 29(1), 7-17.   DOI
43 Zenkour, A.M. and Sobhy, M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos. Struct., 93(1), 93-102.   DOI   ScienceOn
44 Zenkour, A.M. and Sobhy, M. (2011), "Thermal buckling of functionally graded plates resting on elastic foundations using the trigonometric theory", J. Therm. Stresses, 34(11), 1119-1138.   DOI
45 Zenkour, A. and Sobhy, M. (2012), "Elastic foundation analysis of uniformly loaded functionally graded viscoelastic sandwich plates", J. Mech., 28(3), 439-452.   DOI
46 Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34.   DOI
47 Ameur, M., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2011), "A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations", KSCE J. Civil Eng., 15(8), 1405-1414.   과학기술학회마을   DOI   ScienceOn
48 Abdelaziz, H.H., Ait Atmane, H., Mechab, I., Boumia, L., Tounsi, A. and Adda Bedia, E.A. (2011), "Static analysis of functionally graded sandwich plates using an efficient and simple refined theory", Chinese J. Aeronaut., 24(4), 434-448.   DOI
49 Ait Atmane, H., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6(2), 113-121.   DOI
50 Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318.   DOI
51 Avramidis, I.E. and Morfidis, K. (2006), "Bending of beams on three-parameter elastic foundation", Int. J. Solids Struct., 43(2), 357-375.   DOI
52 Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Therm. Stresses, 35(8), 677-694.   DOI
53 Bachir Bouiadjra, R., Adda Bedia, E.A., Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 48(4), 547-567.   DOI
54 Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283.   DOI
55 Benachour, A., Daouadji, H.T., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B, 42(6), 1386-1394.   DOI
56 Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A., Ait Atmane, H. and Adda Bedia, E.A. (2010), "Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations", Mech. Compos. Mater., 46(4), 425-434.   DOI