Structural Engineering and Mechanics

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A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate

  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Houari, Mohammed Sid Ahmed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Bessaim, Aicha (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2016.05.29
  • Accepted : 2016.07.19
  • Published : 2016.11.25
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Abstract

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.

Keywords

References

  1. Abdelaziz, H.H., Ait Atmane, H., Boumia, L., Tounsi, A. and Adda Bedia, E.A. (2011), "Static analysis of functionally graded sandwich plates using an efficient and simple refined theory", Chin. J. Aeronaut., 24(4), 434-448. https://doi.org/10.1016/S1000-9361(11)60051-4
  2. Abdelbari, S., Fekrar, A., Heireche, H., Saidi, H., Tounsi, A. and Adda Bedia, E.A. (2016), "An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations", Wind Struct., 22(3), 329-348. https://doi.org/10.12989/was.2016.22.3.329
  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 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
  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 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
  7. 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
  8. Akvaci, S.S. (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
  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. Anderson, T.A. (2003), "A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere", Compos. Struct., 60, 265-274. https://doi.org/10.1016/S0263-8223(03)00013-8
  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. Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  13. 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
  14. 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
  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(6), 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. Benselama, K., El Meiche, N., Adda Bedia, E.A. and Tounsi, A. (2015), "Buckling analysis in hybrid crossply composite laminates on elastic foundation using the two variable refined plate theory", Struct. Eng. Mech., 55(1), 47-64. https://doi.org/10.12989/sem.2015.55.1.047
  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. 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
  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. and Houari, M.S.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. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  29. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2016), "Thermomechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617
  30. 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
  31. 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
  32. 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
  33. El Meiche, N., Tounsi, A., Ziane, N. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  34. Etemadi, E., Khatibi, A.A. and Takaffoli, M. (2009), "3D finite element simulation of sandwich panels with a functionally graded core subjected to low velocity impact", Compos Struct, 89, 28-34. https://doi.org/10.1016/j.compstruct.2008.06.013
  35. Hadji, L., Ait Atmane, H., Tounsi, A. and Adda Bedia, E.A. (2011), "Free vibration of functionally graded sandwich plates using four-variable refined plate theory", Appl. Math. Mech., 32(7), 925-942. https://doi.org/10.1007/s10483-011-1470-9
  36. Hadji, L., Hassaine Daouadji, T., Tounsi, A. and Adda Bedia, A. (2015), "A n-order refined theory for bending and free vibration of functionally graded beams", Struct. Eng. Mech., 54(5), 923-936. https://doi.org/10.12989/sem.2015.54.5.923
  37. 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
  38. 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., ASCE, 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  39. Houari, A.M.S., Benyoucef, S., Tounsi, A. and Adda Bedia, E.A. (2011), "Two-variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates", J. Therm. Stress., 34(4), 315-334. https://doi.org/10.1080/01495739.2010.550806
  40. 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
  41. Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., 15(4), 399-423. https://doi.org/10.12989/scs.2013.15.4.399
  42. Koizumi, M. (1993), "The concept of FGM", Ceram. Tran. Function. Grad. Mater., 34, 3-10.
  43. 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
  44. Li, Q., Iu, V.P., and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311, 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
  45. 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
  46. Majumdar, A. and Das, D. (2016), "A study on thermal buckling load of clamped functionally graded beams under linear and nonlinear thermal gradient across thickness", J Mater. Des. Appl., doi:10.1177/1464420716649213.
  47. 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
  48. Natarajan, S. and Ganapathi, M. (2012), "Bending and vibration of functionally graded material sandwich plates using an accurate theory", Finite Elem. Anal. Des., 57, 32-42. https://doi.org/10.1016/j.finel.2012.03.006
  49. Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 629-640. https://doi.org/10.1007/s11029-013-9379-6
  50. 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
  51. 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. Base. Des. Struct. Mach., 41(4), 421-433. https://doi.org/10.1080/15397734.2013.763713
  52. 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
  53. Reddy, J. (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
  54. Reddy, J.N. (1984), "A simple higher order shear deformation theory for laminated composite plates", J. Appl. Mech., 51, 754-752.
  55. 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
  56. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018
  57. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech, 94, 195-220. https://doi.org/10.1007/BF01176650
  58. 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
  59. 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", Aero. Sci. Technol., 24 (1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  60. 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
  61. Xiang, S., Kang, G.W., Yang, M.S. and Zhao, Y. (2013), "Natural frequencies of sandwich plate with functionally graded face and homogeneous core", Compos. Struct., 96, 226-231. https://doi.org/10.1016/j.compstruct.2012.09.003
  62. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: An analytical approach", Meccanica, 48, 2019-2035. https://doi.org/10.1007/s11012-013-9720-0
  63. 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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  42. A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.317
  43. Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams vol.6, pp.1, 2016, https://doi.org/10.12989/amr.2017.6.1.013
  44. Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities vol.6, pp.1, 2017, https://doi.org/10.12989/amr.2017.6.1.045
  45. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT vol.19, pp.3, 2016, https://doi.org/10.12989/sss.2017.19.3.289
  46. Wave propagation in functionally graded beams using various higher-order shear deformation beams theories vol.62, pp.2, 2016, https://doi.org/10.12989/sem.2017.62.2.143
  47. A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates vol.62, pp.4, 2017, https://doi.org/10.12989/sem.2017.62.4.401
  48. A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams vol.62, pp.6, 2017, https://doi.org/10.12989/sem.2017.62.6.695
  49. Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory vol.19, pp.6, 2016, https://doi.org/10.12989/sss.2017.19.6.601
  50. A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.569
  51. Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading vol.20, pp.2, 2016, https://doi.org/10.12989/cac.2017.20.2.229
  52. An original single variable shear deformation theory for buckling analysis of thick isotropic plates vol.63, pp.4, 2017, https://doi.org/10.12989/sem.2017.63.4.439
  53. Rotating effects on hygro-mechanical vibration analysis of FG beams based on Euler-Bernoulli beam theory vol.63, pp.4, 2016, https://doi.org/10.12989/sem.2017.63.4.471
  54. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2016, https://doi.org/10.12989/sem.2017.63.5.585
  55. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  56. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.369
  57. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  58. Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment vol.64, pp.1, 2016, https://doi.org/10.12989/sem.2017.64.1.121
  59. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  60. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  61. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  62. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates vol.64, pp.4, 2016, https://doi.org/10.12989/sem.2017.64.4.391
  63. Vibration analysis of micro composite thin beam based on modified couple stress vol.64, pp.4, 2017, https://doi.org/10.12989/sem.2017.64.4.403
  64. Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments vol.65, pp.6, 2018, https://doi.org/10.12989/sem.2018.65.6.645
  65. Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility vol.66, pp.1, 2018, https://doi.org/10.12989/sem.2018.66.1.085
  66. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory vol.21, pp.4, 2016, https://doi.org/10.12989/sss.2018.21.4.397
  67. Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models vol.66, pp.3, 2018, https://doi.org/10.12989/sem.2018.66.3.317
  68. A unified formulation for modeling of inhomogeneous nonlocal beams vol.66, pp.3, 2016, https://doi.org/10.12989/sem.2018.66.3.369
  69. Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter vol.28, pp.1, 2016, https://doi.org/10.12989/scs.2018.28.1.013
  70. The critical buckling load of reinforced nanocomposite porous plates vol.67, pp.2, 2016, https://doi.org/10.12989/sem.2018.67.2.115
  71. A novel shear and normal deformation theory for hygrothermal bending response of FGM sandwich plates on Pasternak elastic foundation vol.67, pp.3, 2016, https://doi.org/10.12989/sem.2018.67.3.219
  72. A new plate model for vibration response of advanced composite plates in thermal environment vol.67, pp.4, 2016, https://doi.org/10.12989/sem.2018.67.4.369
  73. An integrated framework of exact modeling, isogeometric analysis and optimization for variable-stiffness composite panels vol.339, pp.None, 2016, https://doi.org/10.1016/j.cma.2018.04.046
  74. Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix vol.67, pp.5, 2016, https://doi.org/10.12989/sem.2018.67.5.517
  75. A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.269
  76. A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations vol.30, pp.1, 2016, https://doi.org/10.12989/scs.2019.30.1.013
  77. 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
  78. 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
  79. 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
  80. Forced vibration analysis of functionally graded sandwich deep beams vol.8, pp.3, 2016, https://doi.org/10.12989/csm.2019.8.3.259
  81. A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations vol.21, pp.6, 2016, https://doi.org/10.1177/1099636217727577
  82. Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory vol.69, pp.4, 2016, https://doi.org/10.2478/scjme-2019-0039
  83. Flexoelectric effects on dynamic response characteristics of nonlocal piezoelectric material beam vol.8, pp.4, 2016, https://doi.org/10.12989/amr.2019.8.4.259
  84. 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
  85. A comprehensive review on the modeling of smart piezoelectric nanostructures vol.74, pp.5, 2016, https://doi.org/10.12989/sem.2020.74.5.611
  86. On scale-dependent stability analysis of functionally graded magneto-electro-thermo-elastic cylindrical nanoshells vol.75, pp.6, 2016, https://doi.org/10.12989/sem.2020.75.6.659
  87. 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
  88. Thermal frequency analysis of FG sandwich structure under variable temperature loading vol.77, pp.1, 2016, https://doi.org/10.12989/sem.2021.77.1.057
  89. Bending and free vibration analysis of functionally graded sandwich plates: An assessment of the Refined Zigzag Theory vol.23, pp.3, 2021, https://doi.org/10.1177/1099636219843970
  90. On the buckling of advanced composite sandwich rectangular plates vol.23, pp.7, 2016, https://doi.org/10.1177/1099636220925084
  91. Bending analysis of functionally graded porous nanocomposite beams based on a non-local strain gradient theory vol.27, pp.1, 2022, https://doi.org/10.1177/10812865211011759