Structural Engineering and Mechanics

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Improved HSDT accounting for effect of thickness stretching in advanced composite plates

  • Bouhadra, Abdelhakim (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, civil Engineering Department) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, civil Engineering Department) ;
  • Bousahla, Abdelmoumen Anis (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, civil Engineering Department) ;
  • Benyoucef, Samir (Materials 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 : 2017.11.21
  • Accepted : 2018.01.29
  • Published : 2018.04.10
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Abstract

In this article, a higher shear deformation theory (HSDT) is improved to consider the influence of thickness stretching in functionally graded (FG) plates. The proposed HSDT has fewer numbers of variables and equations of motion than the first-order shear deformation theory (FSDT), but considers the transverse shear deformation influences without requiring shear correction coefficients. The kinematic of the present improved HSDT is modified by considering undetermined integral terms in in-plane displacements and a parabolic distribution of the vertical displacement within the thickness, and consequently, the thickness stretching influence is taken into account. Analytical solutions of simply supported FG plates are found, and the computed results are compared with 3D solutions and those generated by other HSDTs. Verification examples demonstrate that the developed theory is not only more accurate than the refined plate theory, but also comparable with the HSDTs which use more number of variables.

Keywords

References

  1. Abdelaziz, H.H., Ait Amar Meziane, M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/SCS.2017.25.6.693
  2. Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  3. 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.
  4. 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
  5. Huffington, N.J. (1963), "Response of elastic columns to axial pulse loading", AIAA J., 1(9), 2099-2104. https://doi.org/10.2514/3.2000
  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, 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035
  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. Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567
  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. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., In Press.
  13. Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., Accepted.
  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. Baseri, V., Jafari, G.R.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. 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), "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
  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., 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
  20. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017a), "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
  21. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017b), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  22. Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F., Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. https://doi.org/10.12989/EAS.2017.13.3.255
  23. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., 65(1), 19-31. https://doi.org/10.12989/SEM.2018.65.1.019
  24. 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
  25. 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
  26. 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
  27. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with nano-fiber reinforced polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053
  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. 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
  30. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich gkplates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  31. 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
  32. 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
  33. 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
  34. 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", Comput. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  35. 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
  36. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B Eng., 42(2), 123-133.
  37. 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
  38. 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
  39. 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
  40. 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., 13(3), 385-410. https://doi.org/10.12989/GAE.2017.13.3.385
  41. 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
  42. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, A., Tounsi, A. and Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., 25(6), 717-726. https://doi.org/10.12989/SCS.2017.25.6.717
  43. Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E. (2015), "A refined exponential shear deformation theory for free vibration of FGM beam with porosities", Geomech. Eng., 9(3), 361 - 372. https://doi.org/10.12989/gae.2015.9.3.361
  44. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally gradedcarbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., In Press.
  45. 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
  46. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  47. 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
  48. Jha, D.K., Kant, T. and Singh, R.K. (2012), "Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates", Nucl. Eng. Des., 250, 8-13. https://doi.org/10.1016/j.nucengdes.2012.05.001
  49. 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., 64(4), 391-402. https://doi.org/10.12989/SEM.2017.64.4.391
  50. 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
  51. Kolahchi, R. and Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8
  52. 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
  53. Mahapatra, T.R., Kar, V.R. and Panda, V.R. (2016), "Large amplitude bending behaviour of laminated composite curved panels", Eng. Comput. Int. J. Comput.-Aid. Eng. Softw., 33(1), 116-138.
  54. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  55. Malekzadeh, P. and Monajjemzadeh, S.M. (2013), "Dynamic response of functionally graded plates in thermal environment under moving load", Compos. Part B: Eng., 45(1), 1521-1533. https://doi.org/10.1016/j.compositesb.2012.09.022
  56. 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(6), 1991-2000. https://doi.org/10.1016/j.compstruct.2012.01.005
  57. Mantari, J.L. and Granados, E.V. (2015), "Dynamic analysis of functionally graded plates using a novel FSDT", Compos. Part B, 75, 148-155. https://doi.org/10.1016/j.compositesb.2015.01.028
  58. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 1099636217698443.
  59. 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
  60. 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
  61. Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A., 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
  62. Mousavi, S.M. and Tahani, M. (2012), "Analytical solution for bending of moderately thick radially functionally graded sector plates with general boundary conditions using multi-term extended Kantorovich method", Compos. Part B: Eng., 43(3), 1405-1416. https://doi.org/10.1016/j.compositesb.2011.11.068
  63. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C.. Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B Eng., 43, 711-725.
  64. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity", J. Sol. Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  65. 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
  66. Krishna Murty, A.V. (1987), "Flexure of composite plates", Compos. Struct., 7(3), 161-177. https://doi.org/10.1016/0263-8223(87)90027-4
  67. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "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
  68. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9
  69. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
  70. Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  71. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017a), "Wave propagation of embedded viscoelastic FGCNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039
  72. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017b), "Visco-nonlocal-refined zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-bolotin methods", Thin-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  73. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017c), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using grey wolf algorithm", J. Sandw. Struct. Mater., In Press.
  74. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using bolotin method", Nonlin. Dyn., 90(1), 479-492. https://doi.org/10.1007/s11071-017-3676-x
  75. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016
  76. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  77. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higherorder finite element formulation", J. Sound Vibr., 318(1-2), 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  78. Reddy, J.N. and Phan, N.D. (1985), "Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory", J. Sound Vibr., 98.
  79. Reddy, J.N. (2000), "Analysis of functionally graded plates", J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  80. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017a), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., 64(6), 737-749. https://doi.org/10.12989/SEM.2017.64.6.737
  81. Sekkal, M., Fahsi, B., Tounsi, A., Mahmoud, S.R. (2017b), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., 25(4), 389-401. https://doi.org/10.12989/SCS.2017.25.4.389
  82. Senthilnathan, N.R., Chow, S.T., Lee, K.H. and Lim, S.P. (1987), "Buckling of shear-deformable plates", AIAA J., 25(9), 1268-1271. https://doi.org/10.2514/3.48742
  83. Shahrjerdi, A., Mustapha, F., Bayat, M., Sapuan, S.M., Zahari, R. and Shahzamanian, M.M. (2011), "Natural frequency of F.G. rectangular plate by shear deformation theory", Mater. Sci. Eng., 17.
  84. Shimpi, R.P., Arya, H. and Naik, N.K. (2003), "A higher order displacement model for the plate analysis", J. Reinf. Plast. Comp., 18(22), 1667-1688.
  85. Shokravi, M. (2017a), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM", Geomech. Eng., 12(2), 327-346. https://doi.org/10.12989/gae.2017.12.2.327
  86. Shokravi, M. (2017b), "Vibration analysis of silica nanoparticlesreinforced concrete beams considering agglomeration effects", Comput. Concrete, 19(3), 333-338. https://doi.org/10.12989/cac.2017.19.3.333
  87. Shokravi, M. (2017c), "Dynamic pull-in and pull-out analysis of viscoelastic nanoplates under electrostatic and casimir forces via sinusoidal shear deformation theory", Microelectr. Reliab., 71, 17-28. https://doi.org/10.1016/j.microrel.2017.02.006
  88. Shokravi, M. (2017d), "Buckling of sandwich plates with FGCNT-reinforced layers resting on orthotropic elastic medium using Reddy plate theory", Steel Compos. Struct., 23(6), 623-631. https://doi.org/10.12989/SCS.2017.23.6.623
  89. Srinivas, S., Joga, C.V. and Rao, A.K. (1970a), "Bending, vibration and buckling of simply supported thick orthotropic rectangular plate and laminates", J. Sol. Struct., 6, 1463-1481. https://doi.org/10.1016/0020-7683(70)90076-4
  90. Srinivas, S., Joga, C.V. and Rao, A.K. (1970b), "Exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates", J. Sound Vibr., 12, 187-199. https://doi.org/10.1016/0022-460X(70)90089-1
  91. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3), 195-220. https://doi.org/10.1007/BF01176650
  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. Thai, H.T. and Kim, S.E. (2013), "A size-dependent functionally graded Reddy plate model based on a modified couple stress theory", Compos. Part B: Eng., 45(1), 1636-1645. https://doi.org/10.1016/j.compositesb.2012.09.065
  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, 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(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  96. Whitney, J.M. and Pagano, N.J. (1970), "Shear deformation in heterogeneous anisotropic plates", J. Appl. Mech., 37, 1031-1036. https://doi.org/10.1115/1.3408654
  97. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with $SiO_2$ nano-particles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043
  98. Zarei, M.S., Kolahchi, R., Hajmohammad, M.H. and Maleki, M. (2017), "Seismic response of underwater fluid-conveying concrete pipes reinforced with $SiO_{2}$ nanoparticles and fiber reinforced polymer (FRP) layer", Soil Dyn. Earthq. Eng., 103, 76-85. https://doi.org/10.1016/j.soildyn.2017.09.009
  99. 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
  100. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  101. 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
  102. 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., 64(2), 145-153.
  103. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/SCS.2018.26.2.125

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