Structural Engineering and Mechanics

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Mechanical and thermal stability investigation of functionally graded plates resting on elastic foundations

  • Houari, Ali (Departement de Genie Mecanique, Faculte de Technologie, Universite Sidi Bel Abbes) ;
  • Benguediab, Mohamed (Departement de Genie Mecanique, Faculte de Technologie, Universite Sidi Bel Abbes) ;
  • Bakora, Ahmed (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)
  • Received : 2017.05.25
  • Accepted : 2017.09.18
  • Published : 2018.02.25
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Abstract

In present work, both the hyperbolic shear deformation theory and stress function concept are used to study the mechanical and thermal stability responses of functionally graded (FG) plates resting on elastic foundation. The accuracy of the proposed formulation is checked by comparing the computed results with those predicted by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed formulation can achieve the same accuracy of the existing HSDTs which have more number of governing equations.

Keywords

References

  1. Abdelbari, S., Fekrar, A., Heireche, H., Saidi, H., Tounsi, A. and Adda Bedia, E.A. (2016), "An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations", Wind Struct., 22(3), 329-348. https://doi.org/10.12989/was.2016.22.3.329
  2. 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., 18(2), 267-291. https://doi.org/10.12989/sss.2016.18.2.267
  3. Adda Bedia, W., Benzair, A., Semmah, A., Tounsi, A. and Mahmoud, S.R. (2015), "On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity", Brazil. J. Phys., 45(2), 225-233. https://doi.org/10.1007/s13538-015-0306-2
  4. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", J. Civil Struct. Environ., 4(2), 59-64.
  5. 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., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  6. 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
  7. 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., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  8. 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., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  9. Akavci, S.A. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019
  10. Akhavan, H., Hashemi, S.H., Taher, H.R.D., Alibeigloo, A. and Vahabi, S. (2009), "Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis", Comput. Mater. Sci., 44, 968-978. https://doi.org/10.1016/j.commatsci.2008.07.004
  11. Ambartsumian, S.A. (1958), "On the theory of bending plates", Izv. Otd. Tech. Nauk. AN. SSSR, 5, 69-77.
  12. 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., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  13. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  14. 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., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  15. 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., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091
  16. 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
  17. 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., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  18. 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., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  19. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/SEM.2017.62.6.695
  20. 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, 265-275. https://doi.org/10.1007/s40430-015-0354-0
  21. 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., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009
  22. Benbakhti, A., Bachir Bouiadjra, M., Retiel, N. and Tounsi, A. (2016), "A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates", Steel Compos. Struct., 22(5), 975-999. https://doi.org/10.12989/scs.2016.22.5.975
  23. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., Accepted.
  24. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  25. 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
  26. 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, 671-703. https://doi.org/10.1177/1099636213498888
  27. Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614. https://doi.org/10.12989/SSS.2017.19.6.601
  28. 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., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  29. Bouazza, M., Tounsi, A., Adda-Bedia, E.A. and Megueni, A. (2010), "Thermoelastic stability analysis of functionally graded plates: An analytical approach", Comput. Mater. Sci., 49, 865-870. https://doi.org/10.1016/j.commatsci.2010.06.038
  30. 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., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  31. Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  32. 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., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  33. 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., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  34. 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., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  35. 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., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  36. 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., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  37. 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", J. Comput. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  38. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2016), "Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617
  39. 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., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  40. 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., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  41. 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, 2874-2881. https://doi.org/10.1016/j.compstruct.2011.05.017
  42. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  43. 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., 10(3), 357-386. https://doi.org/10.12989/gae.2016.10.3.357
  44. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., AddaBedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., 13(3), 385-410. https://doi.org/10.12989/GAE.2017.13.3.385
  45. 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", Meccan., 49, 795-810. https://doi.org/10.1007/s11012-013-9827-3
  46. Hadji, L., Hassaine Daouadji, T., Ait Amar Meziane, M., Tlidji, Y. and Adda Bedia, E.A. (2016), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., 57(2), 315-325. https://doi.org/10.12989/sem.2016.57.2.315
  47. 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., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  48. 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., 22(3), 473-495. https://doi.org/10.12989/scs.2016.22.3.473
  49. 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", ASCE J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  50. 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., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  51. Javaheri, R. and Eslami, M.R. (2002a), "Thermal buckling of functionally graded plates", AIAA J., 40, 162-169. https://doi.org/10.2514/2.1626
  52. Javaheri, R. and Eslami, M.R. (2002b), "Thermal buckling of functionally graded plates bases on higher order theory", J. Therm. Stress., 25, 603-625. https://doi.org/10.1080/01495730290074333
  53. Kar, V.R. and Panda, S.K. (2015a), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  54. Kar, V.R. and Panda, S.K. (2015b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Lat. Am. J. Sol. Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691
  55. Kar, V.R. and Panda, S.K. (2016a), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", J. Mech. Sci., 115-116, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014
  56. Kar, V.R. and Panda, S.K. (2016b), "Post-buckling analysis of shear deformable FG shallow spherical shell panel under uniform and non-uniform thermal environment", J. Therm. Stress., 1-15.
  57. Karama, M., Afaq, S. and Mistou, S. (2003), "Mechanical behavior of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity", J. Sol. Struct., 40, 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  58. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircr. Eng. Aerosp. Technol., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  59. Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., In Press.
  60. Kiani, Y., Bagherizadeh, E. and Eslami, M.R. (2011), "Thermal buckling of clamped thin rectangular FGM plates resting on Pasternak elastic foundation (three approximate analytical solutions)", J. Appl. Math. Mech., 91, 581-593.
  61. Klouche, F., Darcherif, L., Sekkal, M., Tounsi, A. and Mahmoud, S.R. (2017), "An original single variable shear deformation theory for buckling analysis of thick isotropic plates", Struct. Eng. Mech., 63(4), 439-446. https://doi.org/10.12989/SEM.2017.63.4.439
  62. Koizumi, M. (1993), "Functionally gradient materials the concept of FGM", Ceram. Trans., 34, 3-10.
  63. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B, 28, 1-4.
  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, 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, 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., 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., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  68. Lee, Y.Y., Zhao, X. and Reddy, J.N. (2010), "Postbuckling analysis of functionally graded plates subject to compressive and thermal loads", Comput. Meth. Appl. Mech. Eng., 199(25-28), 1645-1653. https://doi.org/10.1016/j.cma.2010.01.008
  69. Levinson, M. (1980), "An accurate simple theory of static and dynamics of elastic plates", Mech. Res. Commun., 7, 343-350. https://doi.org/10.1016/0093-6413(80)90049-X
  70. Librescu, L. and Lin, W. (1997), "Postbuckling and vibration of shear deformable flat and curved panels on a non-linear elastic foundation", J. Non-Lin. Mech., 32(2), 211-225. https://doi.org/10.1016/S0020-7462(96)00057-1
  71. Lin, W. and Librescu, L. (1998), "Thermomechanical postbuckling of geometrically imperfect shear-deformable flat and curved panels on a nonlinear foundation", J. Eng. Sci., 36(2), 189-206. https://doi.org/10.1016/S0020-7225(97)00055-4
  72. 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, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  73. Matsunaga, H. (2009), "Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory", Compos. Struct., 90, 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004
  74. 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., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  75. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., In Press.
  76. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/SCS.2017.25.2.157
  77. 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., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  78. Meyers, C.A. and Hyer, M.W. (1991), "Thermal buckling and postbuckling of symmetrically laminated composite plates", J. Therm. Stress., 14, 519-540. https://doi.org/10.1080/01495739108927083
  79. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., 18, 31-38.
  80. Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. https://doi.org/10.12989/SSS.2017.20.3.369
  81. Naderi, A. and Saidi, A.R. (2011), "Exact solution for stability analysis of moderately thick functionally graded sector plates on elastic foundation", Compos. Struct., 93, 629-638. https://doi.org/10.1016/j.compstruct.2010.08.016
  82. Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Gosuedarstvennoe Izadatelstvo Literatim po Stroitelstvu I Arkhitekture, 1, 1-56.
  83. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic metal plates", J. Sol. Struct., 35, 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  84. Raminnea, M., Biglari, H. and Vakili Tahami, F. (2016), "Nonlinear higher order Reddy theory for temperature-dependent vibration and instability of embedded functionally graded pipes conveying fluid-nanoparticle mixture", Struct. Eng. Mech., 59(1), 153-186. https://doi.org/10.12989/sem.2016.59.1.153
  85. Reddy, J.N. (2004), "Mechanics of laminated composite plates and shells: Theory and analysis", 2nd Edition, Boca Raton, CRC Press.
  86. Reissner, E. (1945), "Reflection on the theory of elastic plates", J. Appl. Mech., 38, 1453-1464.
  87. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40, 137-146. https://doi.org/10.2514/2.1622
  88. 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
  89. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94, 195-200. https://doi.org/10.1007/BF01176650
  90. Sugano, Y. (1990), "An analytical solution for a plane thermal stress problem in nonhomogeneous multiply connected regions", JSME Int. J. Ser. A, 33, 136-144.
  91. Swaminathan, K. and Naveenkumar, D.T. (2014), "Higher order refined computational models for the stability analysis of FGM plates: Analytical solutions", Eur. J. Mech. A/Sol., 47, 349-361. https://doi.org/10.1016/j.euromechsol.2014.06.003
  92. 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
  93. 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., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  94. 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
  95. Touratier, M. (1991), "An efficient standard plate theory", J. Eng. Sci., 29, 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  96. Tung, H.V. and Duc, N.D. (2010), "Nonlinear analysis of stability for functionally graded plates under mechanical and thermal loads", Compos. Struct., 92(5), 1184-1191. https://doi.org/10.1016/j.compstruct.2009.10.015
  97. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear analysis of sandwich plates with fgm face sheets resting on elastic foundations", Compos. Struct., 93, 2521-2532. https://doi.org/10.1016/j.compstruct.2011.04.014
  98. Winkler, E. (1867), Die Lehre von der Elasticitaet und Festigkeit, Prag Dominicus.
  99. 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, 2826-2832. https://doi.org/10.1016/j.compstruct.2011.05.022
  100. 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
  101. 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, 869-894. https://doi.org/10.1080/01495739.2013.770356
  102. 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", Meccan., 48, 2019-2035. https://doi.org/10.1007/s11012-013-9720-0
  103. 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, 1119-1138. https://doi.org/10.1080/01495739.2011.606017
  104. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90, 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005
  105. Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., In Press.
  106. 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