Geomechanics and Engineering

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A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates

  • Fahsi, Asmaa (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Hebali, Habib (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Chikh, Abdelbaki (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Adda Bedia, E.A. (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2016.05.30
  • Accepted : 2017.03.16
  • Published : 2017.09.25
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Abstract

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

Keywords

References

  1. Abdelhak, Z., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst., Int. J., 18(2), 267-291. https://doi.org/10.12989/sss.2016.18.2.267
  2. Ahouel, M., Houari, M.S.A., Adda Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  3. 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. https://doi.org/10.1177/1099636214526852
  4. Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  5. Ait Atmane, H., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x
  6. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  7. Aizikovich, S.M., Mitrin, B.I., Seleznev, N.M., Wang, Y.C. and Volkov, S.S. (2016), "Influence of a soft FGM interlayer on contact stresses under a beam on an elastic foundation", Struct. Eng. Mech., Int. J., 58(4), 613-625. https://doi.org/10.12989/sem.2016.58.4.613
  8. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  9. Akhavan, H., Hashemi Sh.H., Taher, H.R.D., Alibeigloo, A. and Vahabi, Sh. (2009), "Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis", Comput. Mater. Sci., 44(3), 968-978. https://doi.org/10.1016/j.commatsci.2008.07.004
  10. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  11. Arefi, M. (2015a), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., Int. J., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659
  12. Arefi, M. (2015b), "Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation", Smart Struct. Syst., Int. J., 16(1), 195-211. https://doi.org/10.12989/sss.2015.16.1.195
  13. Arefi, M. and Allam, M.N.M. (2015), "Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation", Smart Struct. Syst., Int. J., 16(1), 81-100. https://doi.org/10.12989/sss.2015.16.1.081
  14. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  15. Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Thermal Stress., 35(8), 677-694. https://doi.org/10.1080/01495739.2012.688665
  16. Bachir Bouiadjra, R., Adda Bedia, E.A. and 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. https://doi.org/10.12989/sem.2013.48.4.547
  17. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., Int. J., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  18. Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., Int. J., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  19. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., Int. J., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091
  20. Becheri, T., Amara, K., Bouazza, M. and Benseddiq, N. (2016), "Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects", Steel Compos. Struct., Int. J., 21(6), 1347-1368. https://doi.org/10.12989/scs.2016.21.6.1347
  21. 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. https://doi.org/10.1016/j.compositesb.2013.12.057
  22. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  23. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  24. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  25. Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., Int. J., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009
  26. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., Int. J., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  27. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  28. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  29. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higherorder 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. https://doi.org/10.1177/1099636213498888
  30. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., Int. J., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  31. Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  32. 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. https://doi.org/10.12989/scs.2013.14.1.085
  33. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., Int. J., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  34. Bouguenina, O., Belakhdar, K., Tounsi, A. and Adda Bedia, E.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., Int. J., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679
  35. Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  36. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  37. 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. https://doi.org/10.1177/1099636211426386
  38. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  39. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., Int. J., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  40. 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. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  41. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  42. Brush, D.O and Almroth, B.O. (1975), Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, NY, USA.
  43. Celebi, K., Yarimpabuc, D. and Keles, I. (2016), "A unified method for stresses in FGM sphere with exponentially-varying properties", Struct. Eng. Mech., Int. J., 57(5), 823-835. https://doi.org/10.12989/sem.2016.57.5.823
  44. Chen, Y.Z. (2015), "A novel solution for thick-walled cylinders made of functionally graded materials", Smart Struct. Syst., Int. J., 15(6), 1503-1520. https://doi.org/10.12989/sss.2015.15.6.1503
  45. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2016), "Thermomechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., Int. J., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617
  46. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., Int. J., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  47. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., Int. J., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  48. Duc, N.D. and Tung, H.V. (2011), "Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations", Compos. Struct., 93(11), 2874-2881. https://doi.org/10.1016/j.compstruct.2011.05.017
  49. Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature- dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., Int. J., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343
  50. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., Int. J., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  51. El-Hassar, S.M., Benyoucef, S., Heireche, H. and Tounsi, A. (2016), "Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory", Geomech. Eng., Int. J., 10(3), 357-386. https://doi.org/10.12989/gae.2016.10.3.357
  52. 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. https://doi.org/10.1007/s11012-013-9827-3
  53. Ghasemabadian, M.A. and Kadkhodayan, M. (2016), "Investigation of buckling behavior of functionally graded piezoelectric (FGP) rectangular plates under open and closed circuit conditions", Struct. Eng. Mech., Int. J., 60(2), 271-299. https://doi.org/10.12989/sem.2016.60.2.271
  54. Ghorbanpour Arani, A., Cheraghbak, A. and Kolahchi, R. (2016), "Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 60(3), 489-505. https://doi.org/10.12989/sem.2016.60.3.489
  55. Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "A refined exponential shear deformation theory for free vibration of FGM beam with porosities", Geomech. Eng., Int. J., 9(3), 361-372. https://doi.org/10.12989/gae.2015.9.3.361
  56. Hadji, L., Hassaine Daouadji, T., Ait Amar Meziane, M., Tlidji, Y. and Adda Bedia, E.A. (2016a), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., Int. J., 57(2), 315-325. https://doi.org/10.12989/sem.2016.57.2.315
  57. Hadji, L., Ait Amar Meziane, M., Abdelhak, Z., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016b), "Static and dynamic behavior of FGM plate using a new first shear deformation plate theory", Struct. Eng. Mech., Int. J., 57(1), 127-140. https://doi.org/10.12989/sem.2016.57.1.127
  58. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  59. Hassaine Daouadji, T. and Hadji, L. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., Int. J., 9(5), 631-644. https://doi.org/10.12989/gae.2015.9.5.631
  60. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., ASCE, 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  61. Hebali, H., Bakora, A., Tounsi, A. and Kaci, A. (2016), "A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates", Steel Compos. Struct., Int. J., 22(3), 473-495. https://doi.org/10.12989/scs.2016.22.3.473
  62. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., Int. J., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  63. 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. https://doi.org/10.12989/scs.2013.15.4.399
  64. Lam, K.Y., Wang, C.M. and He, X.Q. (2000), "Canonical exact solutions for Levy-plates on two parameter foundation using Green's functions", Eng. Struct., 22(3), 364-378. https://doi.org/10.1016/S0141-0296(98)00116-3
  65. Lanhe, W. (2004), "Thermal buckling of a simply supported moderately thick rectangular FGM plate", Compos. Struct., 64(3), 211-218. https://doi.org/10.1016/j.compstruct.2003.08.004
  66. Laoufi, I., Ameur, M., Zidi, M., Adda Bedia, E.A. and Bousahla, A.A. (2016), "Mechanical and hygrothermal behaviour of functionally graded plates using a hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 20(4), 889-911. https://doi.org/10.12989/scs.2016.20.4.889
  67. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  68. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  69. Mantari, J.L. and Granados, E.V. (2015), "A refined FSDT for the static analysis of functionally graded sandwich plates", Thin-Wall. Struct., 90, 150-158. https://doi.org/10.1016/j.tws.2015.01.015
  70. Matsunaga, H. (2009), "Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory", Compos. Struct., 90(1), 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004
  71. Meftah, A., Bakora, A., Zaoui, F.Z., Tounsi, A. and Adda Bedia, E.A. (2017), "A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Steel Compos. Struct., Int. J., 23(3), 317-330. https://doi.org/10.12989/scs.2017.23.3.317
  72. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., Int. J., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  73. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2017), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater. [In press]
  74. Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  75. Merdaci, S., Tounsi, A. and Bakora, A. (2016), "A novel four variable refined plate theory for laminated composite plates", Steel Compos. Struct., Int. J., 22(4), 713-732. https://doi.org/10.12989/scs.2016.22.4.713
  76. Meyers, C.A. and Hyer, M.W. (1991), "Thermal buckling and postbuckling of symmetrically laminated composite plates", J. Therm. Stress., 14(4), 519-540. https://doi.org/10.1080/01495739108927083
  77. Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  78. Pradhan, K.K. and Chakraverty, S. (2015), "Free vibration of functionally graded thin elliptic plates with various edge supports", Struct. Eng. Mech., Int. J., 53(2), 337-354. https://doi.org/10.12989/sem.2015.53.2.337
  79. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solids Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  80. Rajabi, M., Soltani, N. and Eshraghi, I. (2016), "Effects of temperature dependent material properties on mixed mode crack tip parameters of functionally graded materials", Struct. Eng. Mech., Int. J., 58(2), 217-230. https://doi.org/10.12989/sem.2016.58.2.217
  81. Reddy, J.N. (1984), Energy Principles and Variational Methods in Applied Mechanics, John Wiley, New York, NY, USA.
  82. Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15(2), 221-245. https://doi.org/10.12989/scs.2013.15.2.221
  83. Saidi, H., Tounsi, A. and Bousahla, A.A. (2016), "A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations", Geomech. Eng., Int. J., 11(2), 289-307. https://doi.org/10.12989/gae.2016.11.2.289
  84. 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. https://doi.org/10.1016/j.compstruct.2012.11.018
  85. Sohn, K.J. and Kim, J.H. (2008), "Structural stability of functionally graded panels subjected to aero-thermal loads", Compos. Struct., 82(3), 317-325. https://doi.org/10.1016/j.compstruct.2007.07.010
  86. Sugano, Y. (1990), "An analytical solution for a plane thermal stress problem in nonhomogeneous multiply connected regions: Unaxisymmetric steady-state thermal stresses in a nonhomogeneous hollow circular plate", JSME Int. J. Ser A, 33(2), 136-144.
  87. Tagrara, S.H., Benachour, A., Bachir Bouiadjra, M. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., Int. J., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259
  88. Taibi, F.Z., Benyoucef, S., Tounsi, A., Bachir Bouiadjra, R., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 17(2), 99-129. https://doi.org/10.1177/1099636214554904
  89. Tebboune, W., Benrahou, K.H., Houari, M.S.A. and Tounsi, A. (2015), "Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory", Steel Compos. Struct., Int. J., 18(2), 443-465. https://doi.org/10.12989/scs.2015.18.2.443
  90. Thai, H.T. and Kim, S.E. (2013), "Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation", Int. J. Mech. Sci., 75, 34-44. https://doi.org/10.1016/j.ijmecsci.2013.06.007
  91. 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. https://doi.org/10.1016/j.ast.2011.11.009
  92. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., Int. J., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  93. Trinh, T.H., Nguyen, D.K., Gan, B.S. and Alexandrov, S. (2016), "Post-buckling responses of elastoplastic FGM beams on nonlinear elastic foundation", Struct. Eng. Mech., Int. J., 58(3), 515-532. https://doi.org/10.12989/sem.2016.58.3.515
  94. Tung, H.V. and Duc, N.D. (2010), "Thermoelastic stability of thick imperfect functionally graded plates", Vietnam J. Mech., 32(1), 47-58. https://doi.org/10.15625/0866-7136/32/1/316
  95. Xiang, S., Jin, Y.X., Bi, Z.Y., Jiang, S.X. and Yang, M.S. (2011), "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93(11), 2826-2232. https://doi.org/10.1016/j.compstruct.2011.05.022
  96. 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. https://doi.org/10.1016/j.compositesb.2014.02.014
  97. Yaghoobi, H. and Torabi, M. (2013), "Exact solution for thermal buckling of functionally graded plates resting on elastic foundations with various boundary conditions", J. Therm. Stress., 36(9), 869-894. https://doi.org/10.1080/01495739.2013.770356
  98. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005
  99. Zenkour, A.M. and Sobhy, M. (2011), "Thermal buckling of functionally graded plates resting on elastic foundations using the trigonometric theory", J. Therm. Stress., 34(11), 1119-1138. https://doi.org/10.1080/01495739.2011.606017
  100. 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. https://doi.org/10.1016/j.ast.2014.02.001

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