Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates

  • Elmossouess, Bouchra (Laboratoire de mecanique applique, Universite des Sciences et Technologie d'ORAN Mouhamed Boudiaf) ;
  • Kebdani, Said (Laboratoire de mecanique applique, Universite des Sciences et Technologie d'ORAN Mouhamed Boudiaf) ;
  • Bouiadjra, Mohamed Bachir (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2016.09.20
  • Accepted : 2016.12.23
  • Published : 2017.05.25
⟨ Previous Next ⟩

Abstract

A new higher shear deformation theory (HSDT) is presented for the thermal buckling behavior of functionally graded (FG) sandwich plates. It uses only four unknowns, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The theory considers a hyperbolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a new displacement field which includes undetermined integral terms. Material characteristics and thermal expansion coefficient of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are supposed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is used to derive the governing equations as an eigenvalue problem. The validation of the present work is carried out with the available results in the literature. Numerical results are presented to demonstrate the influences of variations of volume fraction index, length-thickness ratio, loading type and functionally graded layers thickness on nondimensional thermal buckling loads.

Keywords

References

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical postbuckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  8. 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
  9. 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
  10. 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
  11. 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(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  12. 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
  13. 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
  14. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  15. 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
  16. 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
  17. 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
  18. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  19. 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
  20. 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
  21. Brush, D.O. and Almroth, B.O. (1975), "Buckling of bars, plates, and shells", New York: McGraw-Hill.
  22. 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
  23. 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
  24. Fuchiyama, T. and Noda, N. (1995), "Analysis of thermal stress in a plate of functionally gradient material", JSAE Rev., 16(3), 263-268. https://doi.org/10.1016/0389-4304(95)00013-W
  25. 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
  26. 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(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  27. 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
  28. Houari, M.S.A., Tounsi, A. and 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, 467-479.
  29. Houari, M.S.A, Benyoucef, S., Mechab, I., 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
  30. Kar, V.R. and Panda, S.K. (2016a), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronautics, 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007
  31. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygrothermo-mechanical loading", Steel Compos. Struct., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011
  32. Kar, V.R. and Panda, S.K. (2015a), "Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method", Compos. Struct., 129, 202-212. https://doi.org/10.1016/j.compstruct.2015.04.006
  33. Kar, V.R. and Panda, S.K. (2015b), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661
  34. Kar, V.R. and Panda, S.K. (2015c), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Solid. Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691
  35. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircraft Eng. Aero. Technol., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  36. Kar, V.R. and Panda, S.K. (2016b), "Nonlinear thermomechanical behavior of functionally graded material cylindrical/hyperbolic/elliptical shell panel with temperaturedependent and temperature-independent properties", J. Press. Vessel Technol., 138(6), 061202. https://doi.org/10.1115/1.4033701
  37. Kar, V.R. and Panda, S.K. (2016c), "Post-buckling analysis of shear deformable FG shallow spherical shell panel under uniform and non-uniform thermal environment", J. Therm. Stress., 40(1), 25-39.
  38. Kar, V.R. and Panda, S.K. (2016d), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115, 318-324.
  39. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2016), "Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247.
  40. 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
  41. Laoufi, I., Ameur, M., Zidi, M., Adda Bedia, E.A. and Bousahla, A.A. (2016), "Mechanical and hygrothermal behaviour of functionally graded plates using a hyperbolic shear deformation theory", Steel Compos. Struct., 20(4), 889-911. https://doi.org/10.12989/scs.2016.20.4.889
  42. 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
  43. Liew, K.M., Yang, J. and Kitipornchai, S. (2004), "Thermal postbuckling of laminated plates comprising functionally graded materials with temperature-dependent properties", J. Appl. Mech. Trans., ASME, 71(6), 839-850. https://doi.org/10.1115/1.1795220
  44. Ma, L.S. and Lee, D.W. (2011), "A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading", Compos. Struct., 93(2), 831-842. https://doi.org/10.1016/j.compstruct.2010.07.011
  45. Ma, L.S. and Lee, D.W. (2012), "Exact solutions for nonlinear static responses of a shear deformable FGM beam under an inplane thermal loading", Euro. J. Mech.-A/Solids, 31(1), 13-20. https://doi.org/10.1016/j.euromechsol.2011.06.016
  46. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016a), "Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment", Int. J. Struct. Stability Dyn., 16(3), 1450105. https://doi.org/10.1142/S0219455414501053
  47. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016b), "Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model", Mech. Adv. Mater. Struct., 23(11), 1343-1359. https://doi.org/10.1080/15376494.2015.1085606
  48. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016c), "Large amplitude bending behaviour of laminated composite curved panels", Eng. Comput., 33(1), 116-138. https://doi.org/10.1108/EC-05-2014-0119
  49. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016d), "Nonlinear flexural analysis of laminated composite panel under hygrothermo-mechanical loading: A micromechanical approach", Int. J. Comput. Meth., 13(3), 1650015. https://doi.org/10.1142/S0219876216500158
  50. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016e), "Geometrically nonlinear flexural analysis of hygro-thermoelastic laminated composite doubly curved shell panel", Int. J. Mech. Mater. Des., 12(2), 153-171. https://doi.org/10.1007/s10999-015-9299-9
  51. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016f), "Nonlinear free vibration analysis of laminated composite doubly curved shell panel in hygrothermal environment", J. Sandw. Struct. Mater., 17(5), 511-545. https://doi.org/10.1177/1099636215577363
  52. Mahapatra, T.R. and Panda, S.K. (2015), "Thermoelastic vibration analysis of laminated doubly curved shallow panels using nonlinear FEM", J. Therm. Stress., 38(1), 39-68. https://doi.org/10.1080/01495739.2014.976125
  53. Mahapatra, T.R. and Panda, S.K. (2016), "Nonlinear free vibration analysis of laminated composite spherical shell panel under elevated hygrothermal environment: A micromechanical approach", Aerosp. Sci. Technol., 49, 276-288. https://doi.org/10.1016/j.ast.2015.12.018
  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, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  55. Matsunaga, H. (2009), "Thermal buckling of functionally graded plates according to a 2 D higher-order deformation theory", Compos. Struct., 90(1), 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004
  56. Mehar, K. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038
  57. Mehar, K. and Panda, S.K. (2016b), "Thermoelastic analysis of FG-CNT reinforced shear deformable composite plate under various loadings", Int. J. Comput. Method., 1750019.
  58. 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., 18(2), 151-173. https://doi.org/10.1177/1099636215613324
  59. Mehar, K. and Panda, S.K. (2017), "Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads", Compos. Struct., 161, 287-298. https://doi.org/10.1016/j.compstruct.2016.10.135
  60. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  61. 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
  62. Meyers, C.A. and Hyer, M.W. (1991), "Thermal buckling and postbuckling of symmetrically laminated composite plates", J. Therm. Stress., 14(4), 519-540. https://doi.org/10.1080/01495739108927083
  63. Na, K.S. and Kim, J.H. (2006), "Three-dimensional thermomechanical buckling analysis for functionally graded composite plates", Compos. Struct., 73(4), 413-422. https://doi.org/10.1016/j.compstruct.2005.02.012
  64. Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higherorder shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  65. Panda, S.K. and Singh, B.N. (2009), "Thermal post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method", Compos. Struct., 91(3), 366-374. https://doi.org/10.1016/j.compstruct.2009.06.004
  66. Panda, S.K. and Singh, B.N. (2013a), "Post-buckling analysis of laminated composite doubly curved panel embedded with SMA fibers subjected to thermal environment", Mech. Adv. Mater. Struct., 20(10), 842-853. https://doi.org/10.1080/15376494.2012.677097
  67. Panda, S.K. and Singh, B.N. (2013b), "Thermal postbuckling behavior of laminated composite spherical shell panel using NFEM", Mech. Based Des. Struct. Machines, 41(4), 468-488. https://doi.org/10.1080/15397734.2013.797330
  68. Panda, S.K. and Singh, B.N. (2013c), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29(1), 47-57. https://doi.org/10.1016/j.ast.2013.01.007
  69. Panda, S.K. and Singh, B.N. (2013d), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers", Nonlinear Dyn., 74(1), 395-418. https://doi.org/10.1007/s11071-013-0978-5
  70. Panda, S.K. and Singh, B.N. (2011), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM", Finite Element. Anal. Des, 47(4), 378-386. https://doi.org/10.1016/j.finel.2010.12.008
  71. Panda, S.K. and Singh, B.N. (2010a), "Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method", Proceeding of the IMechE Part C: Journal of Mechanical Engineering and Science, 224(4), 757-769. https://doi.org/10.1243/09544062JMES1809
  72. Panda, S.K. and Singh, B.N. (2010b), "Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel", Int. J. Mech. Mater. Des., 6(2), 175-188. https://doi.org/10.1007/s10999-010-9127-1
  73. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermomechanical loading", Int. J. Appl. Comput. Math., 1(3), 475-490. https://doi.org/10.1007/s40819-015-0035-9
  74. Piovan, M.T. and Machado, S.P. (2011), "Thermoelastic dynamic stability of thin-walled beams with graded material properties", Thin Wall. Struct., 49(3), 437-447. https://doi.org/10.1016/j.tws.2010.11.002
  75. Reddy, J.N. (1984), Energy principles and variational methods in applied mechanics, New York: John Wiley.
  76. Singh, V.K. and Panda, S.K. (2015), "Large amplitude free vibration analysis of laminated composite spherical shells embedded with piezoelectric layers", Smart Struct. Syst., 16(5), 853-872. https://doi.org/10.12989/sss.2015.16.5.853
  77. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  78. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  79. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005
  80. 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

Cited by

  1. A high-order gradient model for wave propagation analysis of porous FG nanoplates vol.29, pp.1, 2018, https://doi.org/10.12989/scs.2018.29.1.053
  2. Quasi-3D static analysis of two-directional functionally graded circular plates vol.27, pp.6, 2017, https://doi.org/10.12989/scs.2018.27.6.789
  3. Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations vol.66, pp.6, 2017, https://doi.org/10.12989/sem.2018.66.6.729
  4. Analytical, numerical and experimental investigation of low velocity impact response of laminated composite sandwich plates using extended high order sandwich panel theory vol.68, pp.3, 2018, https://doi.org/10.12989/sem.2018.68.3.325
  5. Vibration of sandwich plates considering elastic foundation, temperature change and FGM faces vol.70, pp.5, 2017, https://doi.org/10.12989/sem.2019.70.5.601
  6. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2017, https://doi.org/10.12989/cac.2019.24.4.347
  7. Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory vol.69, pp.4, 2017, https://doi.org/10.2478/scjme-2019-0039
  8. 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