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An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates

  • Bellifa, Hichem (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • 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) ;
  • Bousahla, Abdelmoumen Anis (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 : 2016.12.26
  • Accepted : 2017.07.16
  • Published : 2017.10.30
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Abstract

In this article, an efficient and simple refined theory is proposed for buckling analysis of functionally graded plates by using a new displacement field which includes undetermined integral variables. This theory contains only four unknowns, with is even less than the first shear deformation theory (FSDT). Governing equations are obtained from the principle of virtual works. The closed-form solutions of rectangular plates are determined. Comparison studies are carried out to check the validity of obtained results. The influences of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are examined and discussed.

Keywords

References

  1. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Composites:Part B, 39(1), 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026
  2. 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
  3. 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
  4. 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
  5. 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
  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 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
  8. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B- Eng., 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035
  9. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  10. Arefi, M. (2015a), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659
  11. Arefi, M. (2015b), "Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation", Smart Struct. Syst., 16(1), 195-211. https://doi.org/10.12989/sss.2015.16.1.195
  12. 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., 16(1), 81-100. https://doi.org/10.12989/sss.2015.16.1.081
  13. 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
  14. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical postbuckling 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
  15. Baseri, V., Jafari, G.S. and Kolahchi, R. (2016), "Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory", Steel Compos. Struct., 21(4), 883-919. https://doi.org/10.12989/scs.2016.21.4.883
  16. 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
  17. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperaturedependent 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
  18. 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., 21(6), 1347-1368. https://doi.org/10.12989/scs.2016.21.6.1347
  19. 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", Composites: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  20. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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).
  27. 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
  28. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  29. 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
  30. 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
  31. 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
  32. 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
  33. Bodaghi, M. and Saidi, A.R. (2010), "Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory", Appl. Math. Model., 34(11), 3659-3673. https://doi.org/10.1016/j.apm.2010.03.016
  34. 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
  35. 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., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  36. 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., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679
  37. 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
  38. 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
  39. 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, 5-33. https://doi.org/10.1177/1099636211426386
  40. 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
  41. 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
  42. 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
  43. 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
  44. Celebi, K., Yarimpabuc, D. and Keles, I. (2016), "A unified method for stresses in FGM sphere with exponentially-varying properties", Struct. Eng. Mech., 57(5), 823-835. https://doi.org/10.12989/sem.2016.57.5.823
  45. 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
  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., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  47. Darabi, A. and Vosoughi, A.R. (2016), "Hybrid inverse method for small scale parameter estimation of FG nanobeams", Steel Compos. Struct., 20(5), 1119-1131. https://doi.org/10.12989/scs.2016.20.5.1119
  48. 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
  49. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  50. Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature- dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343
  51. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  52. 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., (Accepted).
  53. 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
  54. Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295.
  55. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, 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., (In press).
  56. 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, 795-810. https://doi.org/10.1007/s11012-013-9827-3
  57. Feldman, E. and Aboudi, J. (1997), "Buckling analysis of functionally graded plates subjected to uniaxial loading", Compos. Struct., 38(1-4), 29-36. https://doi.org/10.1016/S0263-8223(97)00038-X
  58. 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., 60(3), 489-505. https://doi.org/10.12989/sem.2016.60.3.489
  59. 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
  60. 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
  61. 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, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  62. 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
  63. 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
  64. Javaheri, R.. and Eslami, M.R. (2002), "Buckling of functionally graded plates under in-plane compressive loading", J. Appl. Math. Mech., 82(4), 277-283.
  65. Javed, S., Viswanathan, K.K., Aziz, Z.A., Karthik, K. and Lee, J.H. (2016), "Vibration of antisymmetric angle-ply laminated plates under higher order shear theory", Steel Compos. Struct., 22(6), 1281-1299. https://doi.org/10.12989/scs.2016.22.6.1281
  66. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircraft Eng. Aerosp.Technol., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  67. Kar, V.R. and Panda, S.K. (2016a), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronautics, 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007
  68. Kar, V.R. and Panda, S.K. (2016b), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115-116, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014
  69. Kar, V.R. and Panda, S.K. (2017), "Post-buckling analysis of shear deformable FG shallow spherical shell panel under uniform and non-uniform thermal environment", J. Therm. Stresses, 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118
  70. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016a), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., 5(4), 205-221. https://doi.org/10.12989/amr.2016.5.4.205
  71. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2016b), "Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247.
  72. Kar, V.R. and Panda, S.K. (2015), "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
  73. 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).
  74. 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., (In press).
  75. Koizumi, M. (1993), "The concept of FGM Ceramic transactions", Funct .Grad. Mater., 34, 3-10.
  76. 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
  77. 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), 889-912. https://doi.org/10.12989/scs.2016.20.4.889
  78. Mahdavian, M. (2009), "Buckling analysis of simply-supported functionally graded rectangular plates under non-uniform inplane compressive loading", J. Solid Mech., 1(3), 213-225.
  79. 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
  80. Mahmoud, S.R., Abd-Alla, A.M., Tounsi, A. and Marin, M. (2015), "The problem of wave propagation in magneto-rotating orthotropic non-homogeneous medium", J. Vib. Control, 21(16), 3281-3291. https://doi.org/10.1177/1077546314521443
  81. Mantari, J.L. and Granados, E.V. (2015), "Dynamic analysis of functionally graded plates using a novel FSDT", Compos. Part B- Eng., 75, 148 -155. https://doi.org/10.1016/j.compositesb.2015.01.028
  82. 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
  83. 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).
  84. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., (Accepted).
  85. 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
  86. Merazi, M., Hadji, L., Daouadji, T.H., Tounsi, A. and Adda Bedia, E.A. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305
  87. Merdaci, S., Tounsi, A. and Bakora, A. (2016), "A novel four variable refined plate theory for laminated composite plates", Steel Compos. Struct., 22(4), 713-732. https://doi.org/10.12989/scs.2016.22.4.713
  88. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18 (1), 31-38.
  89. Mohammadi, M., Saidi, A.R. and Jomehzadeh, E. (2010a), "Levy solution for buckling analysis of functionally graded rectangular plates", Appl. Compos. Mater., 17(2), 81-93. https://doi.org/10.1007/s10443-009-9100-z
  90. Mohammadi, M., Saidi, A.R. and Jomehzadeh, E. (2010b), "A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges", Proc. Inst. Mech. Engrs. Part C J. Mech. Eng. Sci., 224(9), 1831-1841. https://doi.org/10.1243/09544062JMES1804
  91. Mouaici, F., Benyoucef, S., Ait Atmane, H., Tounsi, A. (2016), "Effect of porosity on vibrational characteristics of nonhomogeneous plates using hyperbolic shear deformation theory", Wind Struct., 22(4), 429-454. https://doi.org/10.12989/was.2016.22.4.429
  92. 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., (In press).
  93. Najafizadeh, M.M. and Heydari, H.R. (2007), "Higher-order theory for buckling of functionally graded circular plates", AIAA J., 45(6), 1153. https://doi.org/10.2514/1.12146
  94. Najafizadeh, M.M. and 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", Int. J. Mech. Sci., 50(3), 603-612. https://doi.org/10.1016/j.ijmecsci.2007.07.010
  95. Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higherorder shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  96. Panda, S.K. and Singh, B.N. (2009), "Thermal post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method", Compos. Struct., 91(3), 366 - 374. https://doi.org/10.1016/j.compstruct.2009.06.004
  97. Panda, S.K. and Singh, B.N. (2010a), "Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method", Proc. IMechE Part C: J. Mech. Eng. Sci., 224(4), 757-769.
  98. Panda, S.K. and Singh, B.N. (2010b), "Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel", Int. J. Mech. Mater. Des., 6(2), 175-188. https://doi.org/10.1007/s10999-010-9127-1
  99. Panda, S.K. and Singh, B.N. (2011), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM", Finite Elem. Anal. Des., 47(4), 378-386. https://doi.org/10.1016/j.finel.2010.12.008
  100. Panda, S.K. and Singh, B.N. (2013a), "Post-buckling analysis of laminated composite doubly curved panel embedded with SMA fibers subjected to thermal environment", Mech. Adv. Mater. Struct., 20(10), 842-853. https://doi.org/10.1080/15376494.2012.677097
  101. Panda, S.K. and Singh, B.N. (2013b), "Thermal postbuckling behavior of laminated composite spherical shell panel using NFEM", Mech. Based Des. Struc., 41(4), 468-488. https://doi.org/10.1080/15397734.2013.797330
  102. Panda, S.K. and Singh, B.N. (2013c), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29(1), 47-57. https://doi.org/10.1016/j.ast.2013.01.007
  103. Panda, S.K. and Singh, B.N. (2013d), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers", Nonlinear Dynam., 74(1-2), 395-418. https://doi.org/10.1007/s11071-013-0978-5
  104. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermomechanical loading", Int. J. Appl. Comput. Math., 1(3), 475-490 https://doi.org/10.1007/s40819-015-0035-9
  105. Raminnea, M., Biglari, H. and Vakili Tahami, F. (2016), "Nonlinear higher order Reddy theory for temperaturedependent 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
  106. Reddy, J.N. (2004), "Mechanics of Laminated Composite Plates and Shells: Theory and Analysis", CRC, 2004.
  107. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-72.
  108. 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., 11(2), 289-307. https://doi.org/10.12989/gae.2016.11.2.289
  109. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., (Accepted).
  110. Sepiani, H.A., Rastgoo, A., Ebrahimi, F. and Ghorbanpour Arani, A. (2010), "Vibration and buckling analysis of two-layered functionally graded cylindrical shell, considering the effects of transverse shear and rotary inertia", Mater. Des., 31(3), 1063-1069. https://doi.org/10.1016/j.matdes.2009.09.052
  111. Shariat, B.A.S. and Eslami, M.R. (2005), "Buckling of functionally graded plates under in plane compressive loading based on the first order plate theory", Proceedings of the 5th International Conference on Composite Science and Technology 2005, American University of Sharjah, United Arab Emirates.
  112. 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/Solids, 47, 349-361. https://doi.org/10.1016/j.euromechsol.2014.06.003
  113. 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
  114. 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. Tech., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  115. 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
  116. 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., 58(3), 515-532. https://doi.org/10.12989/sem.2016.58.3.515
  117. Turan, M., Adiyaman, G., Kahya, V. and Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Struct. Eng. Mech., 58(3), 423-442. https://doi.org/10.12989/sem.2016.58.3.423
  118. Yang, J., Liew, K.M. and Kitipornchai, S. (2005), "Second-order statistics of the elastic buckling of functionally graded rectangular plates", Compos. Sci. Technol., 65(7-8), 1165-1175. https://doi.org/10.1016/j.compscitech.2004.11.012
  119. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  120. 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
  121. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygrothermo-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
  122. 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).

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