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Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory

  • Beldjelili, Youcef (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) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2016.01.19
  • Accepted : 2016.04.26
  • Published : 2016.10.25

Abstract

The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.

Keywords

References

  1. Abdelbari, S.A., 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. 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
  3. Ait Atmane, H., Tounsi, A. and Bernard, F. (2016), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., (In press).
  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., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  5. 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
  6. Akavci, S.A. (2007), "Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation", J. Rein Plast Compos., 26, 1907-1913. https://doi.org/10.1177/0731684407081766
  7. 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
  8. 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
  9. 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
  10. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 569-672.
  11. 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
  12. 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
  13. Bao, G. and Wang, L. (1995), "Multiple cracking in functionally graded ceramic/metal coatings", Int. J. Solids Struct., 32, 2853-2871. https://doi.org/10.1016/0020-7683(94)00267-Z
  14. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Beg, O.A. (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
  15. 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
  16. 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
  17. 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, 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  18. 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., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  19. 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
  20. Bever, M.B. and Duwez, P.E. (1972), "Gradients in composite materials", Mater. Sci. Eng., 10, 1-8. https://doi.org/10.1016/0025-5416(72)90059-6
  21. 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., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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. https://doi.org/10.1142/S0219876213500825
  29. Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Tech., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005
  30. Chi, S.H. and Chung, Y.L. (2002), "Cracking in sigmoid functionally graded coating", J. Mech., 18, 41-53.
  31. 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
  32. Chung, Y.L. and Chi, S.H. (2001), "The residual stress of functionally graded materials", J. Chinese Inst. Civil. Hydraulic Eng, 13, 1-9.
  33. Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., 18(2), 395-408. https://doi.org/10.12989/scs.2015.18.2.395
  34. Delale, F. and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. Appl. Mech.- ASME, 50, 609-614. https://doi.org/10.1115/1.3167098
  35. 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., 17(1), 69-81. https://doi.org/10.12989/scs.2014.17.1.069
  36. Duc, N.D. and Cong, P.H. (2013), "Nonlinear postbuckling of symmetric S-FGM plates resting on elastic foundations using higher order shear deformation plate theory in thermal environments", Compos. Struct., 100, 566-574. https://doi.org/10.1016/j.compstruct.2013.01.006
  37. Ebrahimi, F. and Dashti, S. (2015), "Free vibration analysis of a rotating non-uniform functionally graded beam", Steel Compos. Struct., 19(5), 1279-1298. https://doi.org/10.12989/scs.2015.19.5.1279
  38. 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
  39. Erdogan, F. and Chen, YF. (1998), "Interfacial cracking of FGM/metal bonds", (Ed., Kokini, K.), Ceramic Coating.
  40. 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
  41. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F. and Martins, P.A.L.S. (2005), "Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method", Compos. Struct., 69, 449 -457. https://doi.org/10.1016/j.compstruct.2004.08.003
  42. Hadji, L. and Adda Bedia, E.A. (2015a), "Influence of the porosities on the free vibration of FGM beams", Wind Struct., 21 (3), 273-287. https://doi.org/10.12989/was.2015.21.3.273
  43. Hadji, L. and Adda Bedia, E.A. (2015b), "Analyse of the behavior of Functionally graded beams based on neutral surface position", Struct. Eng. Mech., 55(4), 703-717. https://doi.org/10.12989/sem.2015.55.4.703
  44. Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507
  45. 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
  46. 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
  47. Han, S.C., Lee, W.H. and Park, W.T. (2009), "Non-linear analysis of laminated composite and sigmoid functionally graded anisotropic structures using a higher-order shear deformable natural Lagrangian shell element", Compos. Struct., 89, 8-19. https://doi.org/10.1016/j.compstruct.2008.08.006
  48. Han, S.C., Lomboy, G.R. and Kim, K.D. (2008), "Mechanical vibration and buckling analysis of FGM plates and shells using a four-node quasi-conforming shell element", Int. J. Struct. Stab. Dynam, 8(2), 203-229. https://doi.org/10.1142/S0219455408002624
  49. Han, S.C., Park, W.T. and Jung, W.Y. (2015), "A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface", Compos. Struct., 131, 1081-1089. https://doi.org/10.1016/j.compstruct.2015.06.025
  50. 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, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  51. Houari, M.S.A., Tounsi, A., 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, 102-111. https://doi.org/10.1016/j.ijmecsci.2013.09.004
  52. Jin, Z.H. and Paulino, G.H. (2001), "Transient thermal stress analysis of an edge crack in a functionally graded material", Int. J. Fracture, 107, 73-98. https://doi.org/10.1023/A:1026583903046
  53. Jung, W.Y. and Han, S.C. (2013), "Analysis of sigmoid functionally graded material (S-FGM) nanoscale plates using the nonlocal elasticity theory", Math. Probl. Eng., 1-10.
  54. Jung, WY, Han, SC. (2014), "Transient analysis of FGM and laminated composite structures using a refined 8-node ANS shell element", Compos Part B, 56, 372-383. https://doi.org/10.1016/j.compositesb.2013.08.044
  55. Jung, WY, Park, WT, Han, SC. (2014), "Bending and vibration analysis of S-FGM microplates embedded in Pasternak elastic medium using the modified couple stress theory", Int. J. Mech. Sci., 87, 150-162. https://doi.org/10.1016/j.ijmecsci.2014.05.025
  56. 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
  57. Kar, V.R. and Panda, S.K. (2015b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin American Journal of Solids and Structures, 12(11), 1679-7825.
  58. Kar, V.R. and Panda, S.K. (2016), "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
  59. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011
  60. 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. Meth., 11(5), 135007.
  61. Koizumi, M. (1997), "FGM activities in Japan", Composites, 28, 1-4.
  62. Laoufi, I., Ameur, A., 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
  63. 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
  64. Lee, W.H., Han, S.C. and Park, W.T. (2015), "A refined higher order shear and normal deformation theory for E-, P-, and S-FGM plates on Pasternak elastic foundation", Compos. Struct., 122, 330-342. https://doi.org/10.1016/j.compstruct.2014.11.047
  65. Liew, K.M., Kitipornchai, S., Zhang, X.Z. and Lim, C.W. (2003), "Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders", Int. J. Solids Struct., 40, 2355-2380. https://doi.org/10.1016/S0020-7683(03)00061-1
  66. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Exact solutions for free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mater Struct., 16, 576-584. https://doi.org/10.1080/15376490903138888
  67. 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
  68. Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89, 367-373. https://doi.org/10.1016/j.compstruct.2008.08.007
  69. Mansouri, M.H. and Shariyat, M. (2014), "Thermal buckling predictions of three types of high-order theories for the heterogeneous orthotropic plates, using the new version of DQM", Compos. Struct., 113(1), 40-55. https://doi.org/10.1016/j.compstruct.2014.02.032
  70. Mansouri, M.H. and Shariyat, M. (2015), "Biaxial thermo-mechanical buckling of orthotropic auxetic FGM plates with temperature and moisture dependent material properties on elastic foundations", Compos. Part B, 83, 88-104. https://doi.org/10.1016/j.compositesb.2015.08.030
  71. Mantari, J.L. and Guedes Soares, C. (2012), "Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory", Compos. Struct., 94, 1991-2000. https://doi.org/10.1016/j.compstruct.2012.01.005
  72. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  73. Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", 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., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  75. Moradi-Dastjerdi, R. (2016), "Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube", Struct. Eng. Mech., 57(3), 441-456. https://doi.org/10.12989/sem.2016.57.3.441
  76. Moradi, S. and Mansouri, M.H. (2012), "Thermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature", Steel Compos. Struct., 12(2), 129-147. https://doi.org/10.12989/scs.2012.12.2.129
  77. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C. and Jorge, R.M.N. et al. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B, 44, 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089
  78. 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., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  79. Ould Larbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41, 421-433. https://doi.org/10.1080/15397734.2013.763713
  80. Pradhan, K.K. and Chakraverty, S. (2015), "Free vibration of functionally graded thin elliptic plates with various edge supports", Struct. Eng. Mech., 53(2), 337-354. https://doi.org/10.12989/sem.2015.53.2.337
  81. Pradhan, S.C. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound Vib., 321, 342-362. https://doi.org/10.1016/j.jsv.2008.09.018
  82. Quan, T.Q., Tran, P., Tuan, N.D. and Duc, N.D. (2015), "Nonlinear dynamic analysis and vibration of shear deformable eccentrically stiffened S-FGM cylindrical panels with metal-ceramic-metal layers resting on elastic foundations", Compos. Struct., 126, 16-33. https://doi.org/10.1016/j.compstruct.2015.02.056
  83. Rad, A.B. (2015), "Thermo-elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation", Appl. Math. Comput., 256, 276-298. https://doi.org/10.1016/j.amc.2015.01.026
  84. Reddy, J. N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  85. Reddy, J.N. and Cheng, Z.Q. (2001), "Three-dimensional thermomechanical deformations of functionally graded rectangular plates", Eur. J. Mech. A Solids, 20, 841-855.
  86. 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., 15, 221-245. https://doi.org/10.12989/scs.2013.15.2.221
  87. Sallai, B., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "Analytical solution for bending analysis of functionally graded beam", Steel Compos. Struct., 19(4), 829-841. https://doi.org/10.12989/scs.2015.19.4.829
  88. Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Tech., 25(9), 2195-2209. https://doi.org/10.1007/s12206-011-0610-x
  89. Shukla, K.K., Kumar, K.V.R., Pandey, R. and Nath, Y. (2007), "Postbuckling response of functionally graded rectangular plates subjected to thermo-mechanical loading", Int. J. Struct. Stab. Dynam., 7, 519-541. https://doi.org/10.1142/S0219455407002381
  90. Sobhy, M. (2015), "Thermoelastic response of FGM plates with temperature-dependent properties resting on variable elastic foundations", International Journal of Applied Mechanics, 7, 1550082. https://doi.org/10.1142/S1758825115500829
  91. Sobhy, M. (2016), "An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment", Int. J. Mech. Sci., 110, 62 -77. https://doi.org/10.1016/j.ijmecsci.2016.03.003
  92. 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., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259
  93. 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., 18(2), 443-465. https://doi.org/10.12989/scs.2015.18.2.443
  94. Thai, H.T. and Vo, T.P. (2013), "A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates", Appl. Math. Model., 37, 3269-3281. https://doi.org/10.1016/j.apm.2012.08.008
  95. Thanga, P.T., Nguyen-Thoia, T. and Lee, J. (2016), "Closed-form expression for nonlinear analysis of imperfect sigmoid-FGM plates with variable thickness resting on elastic medium", Compos. Struct., 143, 143-150. https://doi.org/10.1016/j.compstruct.2016.02.002
  96. 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, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  97. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  98. Vel, S.S. and Batra, R.C. (2003), "Three-dimensional analysis of transient thermal stresses in functionally graded plates", Int. J. Solids Struct., 40, 7181-7196. https://doi.org/10.1016/S0020-7683(03)00361-5
  99. Whitney, J.M. (1969), "The effect of transverse shear deformation on the bending of laminated plates", J. Compos. Mater., 3, 534-547. https://doi.org/10.1177/002199836900300316
  100. Zhang, X.D., Liu, D.Q. and Ge, C. (1994), "Thermal stress analysis of axial symmetry functionally gradient materials under steady temperature field", J. Funct. Grad. Mater., 25, 452-455.
  101. Zhou, D. (1993), "A general solution to vibrations of beams on variable Winkler elastic foundation", Comput. Struct., 47, 83-90. https://doi.org/10.1016/0045-7949(93)90281-H
  102. 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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  138. Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method vol.69, pp.2, 2016, https://doi.org/10.12989/sem.2019.69.2.205
  139. Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.019
  140. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.049
  141. Hygrothermal effects on the behavior of reinforced-concrete beams strengthened by bonded composite laminate plates vol.69, pp.3, 2016, https://doi.org/10.12989/sem.2019.69.3.327
  142. A novel refined shear deformation theory for the buckling analysis of thick isotropic plates vol.69, pp.3, 2019, https://doi.org/10.12989/sem.2019.69.3.335
  143. Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load vol.7, pp.1, 2016, https://doi.org/10.12989/acc.2019.7.1.051
  144. Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory vol.16, pp.2, 2019, https://doi.org/10.12989/eas.2019.16.2.177
  145. Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT vol.69, pp.5, 2016, https://doi.org/10.12989/sem.2019.69.5.511
  146. Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT vol.7, pp.2, 2016, https://doi.org/10.12989/anr.2019.7.2.089
  147. Free vibration of imperfect sigmoid and power law functionally graded beams vol.30, pp.6, 2019, https://doi.org/10.12989/scs.2019.30.6.603
  148. Vibration analysis of different material distributions of functionally graded microbeam vol.69, pp.6, 2016, https://doi.org/10.12989/sem.2019.69.6.637
  149. Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities vol.25, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/nhc.25.69
  150. Buckling behavior of rectangular plates under uniaxial and biaxial compression vol.70, pp.1, 2019, https://doi.org/10.12989/sem.2019.70.1.113
  151. Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency vol.134, pp.5, 2016, https://doi.org/10.1140/epjp/i2019-12540-3
  152. A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates vol.70, pp.3, 2019, https://doi.org/10.12989/sem.2019.70.3.325
  153. Improved analytical method for adhesive stresses in plated beam: Effect of shear deformation vol.7, pp.3, 2016, https://doi.org/10.12989/acc.2019.7.3.151
  154. Hygro-thermal effects on wave dispersion responses of magnetostrictive sandwich nanoplates vol.7, pp.3, 2016, https://doi.org/10.12989/anr.2019.7.3.157
  155. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT vol.7, pp.3, 2016, https://doi.org/10.12989/anr.2019.7.3.191
  156. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2016, https://doi.org/10.12989/sem.2019.70.4.407
  157. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2016, https://doi.org/10.12989/gae.2019.18.2.161
  158. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2016, https://doi.org/10.12989/scs.2019.31.5.503
  159. Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.535
  160. Chaotic dynamics of a non-autonomous nonlinear system for a smart composite shell subjected to the hygro-thermal environment vol.25, pp.7, 2019, https://doi.org/10.1007/s00542-018-4206-6
  161. Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment vol.134, pp.7, 2019, https://doi.org/10.1140/epjp/i2019-12581-6
  162. Dynamic analysis of multi-layered composite beams reinforced with graphene platelets resting on two-parameter viscoelastic foundation vol.134, pp.7, 2016, https://doi.org/10.1140/epjp/i2019-12739-2
  163. Vibration analysis of nonlocal porous nanobeams made of functionally graded material vol.7, pp.5, 2019, https://doi.org/10.12989/anr.2019.7.5.351
  164. Bending, buckling and vibration of shear deformable beams made of three-dimensional graphene foam material vol.41, pp.10, 2016, https://doi.org/10.1007/s40430-019-1926-1
  165. Assessment of porosity influence on dynamic characteristics of smart heterogeneous magneto-electro-elastic plates vol.72, pp.1, 2019, https://doi.org/10.12989/sem.2019.72.1.113
  166. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2016, https://doi.org/10.12989/cac.2019.24.4.347
  167. The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory vol.7, pp.6, 2016, https://doi.org/10.12989/anr.2019.7.6.443
  168. Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory vol.17, pp.5, 2016, https://doi.org/10.12989/eas.2019.17.5.447
  169. Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution vol.72, pp.4, 2016, https://doi.org/10.12989/sem.2019.72.4.513
  170. Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation vol.12, pp.24, 2019, https://doi.org/10.1007/s12517-019-4871-5
  171. Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer vol.134, pp.12, 2016, https://doi.org/10.1140/epjp/i2019-12662-6
  172. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2016, https://doi.org/10.12989/scs.2019.33.5.699
  173. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  174. Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model vol.33, pp.6, 2016, https://doi.org/10.12989/scs.2019.33.6.805
  175. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2016, https://doi.org/10.12989/was.2019.29.6.371
  176. Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method vol.26, pp.1, 2020, https://doi.org/10.1177/1077546319876389
  177. Variational approximate for high order bending analysis of laminated composite plates vol.73, pp.1, 2016, https://doi.org/10.12989/sem.2020.73.1.097
  178. Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle vol.73, pp.2, 2016, https://doi.org/10.12989/sem.2020.73.2.209
  179. Nonlinear Vibration Analysis of Sigmoid Functionally Graded Sandwich Plate with Ceramic-FGM-Metal Layers vol.8, pp.1, 2016, https://doi.org/10.1007/s42417-018-0058-8
  180. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2016, https://doi.org/10.1140/epjp/s13360-020-00137-w
  181. Effect of Microstructure and Surface Energy on the Static and Dynamic Characteristics of FG Timoshenko Nanobeam Embedded in an Elastic Medium vol.61, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.61.97
  182. Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle vol.8, pp.2, 2016, https://doi.org/10.12989/anr.2020.8.2.135
  183. A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates vol.25, pp.2, 2020, https://doi.org/10.12989/sss.2020.25.2.197
  184. Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.147
  185. A refined HSDT for bending and dynamic analysis of FGM plates vol.74, pp.1, 2020, https://doi.org/10.12989/sem.2020.74.1.105
  186. Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading vol.8, pp.3, 2016, https://doi.org/10.12989/anr.2020.8.3.203
  187. Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories vol.74, pp.2, 2020, https://doi.org/10.12989/sem.2020.74.2.175
  188. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2016, https://doi.org/10.12989/sss.2020.25.4.409
  189. Mixture rule for studding the environmental pollution reduction in concrete structures containing nanoparticles vol.9, pp.3, 2016, https://doi.org/10.12989/csm.2020.9.3.281
  190. Active vibration control of nonlinear stiffened FG cylindrical shell under periodic loads vol.25, pp.6, 2016, https://doi.org/10.12989/sss.2020.25.6.643
  191. Dynamic behavior of axially functionally graded simply supported beams vol.25, pp.6, 2016, https://doi.org/10.12989/sss.2020.25.6.669
  192. Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures vol.36, pp.3, 2016, https://doi.org/10.1007/s00366-019-00742-z
  193. Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM vol.75, pp.5, 2020, https://doi.org/10.12989/sem.2020.75.5.633
  194. Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam vol.26, pp.3, 2016, https://doi.org/10.12989/sss.2020.26.3.361
  195. 2D magnetic field effect on the thermal buckling of metal foam nanoplates reinforced with FG-GPLs lying on Pasternak foundation in humid environment vol.135, pp.11, 2016, https://doi.org/10.1140/epjp/s13360-020-00905-8
  196. Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory vol.23, pp.3, 2016, https://doi.org/10.1177/1099636219845841
  197. Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions vol.23, pp.3, 2016, https://doi.org/10.1177/1099636219851281
  198. Stress Distribution on the Cracked Sandwich Plate with Non Linear Thermal and Moisture Concentration vol.32, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/nhc.32.45
  199. Analysis of porosity effect on free vibration and buckling responses for sandwich sigmoid function based functionally graded material plate resting on Pasternak foundation using Galerkin Vlasov’ vol.23, pp.5, 2021, https://doi.org/10.1177/1099636220904340
  200. Modeling of memory-dependent derivative in a functionally graded plate vol.31, pp.4, 2016, https://doi.org/10.1080/17455030.2019.1606962
  201. Wave dispersion of nanobeams incorporating stretching effect vol.31, pp.4, 2016, https://doi.org/10.1080/17455030.2019.1607623
  202. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2016, https://doi.org/10.12989/scs.2021.40.3.355