DOI QR코드

DOI QR Code

A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation

  • Benahmed, Abdelkarim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Houari, Mohammed Sid Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benyoucef, Samir (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Belakhdar, Khalil (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)
  • 투고 : 2015.08.14
  • 심사 : 2016.09.08
  • 발행 : 2017.01.25

초록

In this work, an efficient and simple quasi-3D hyperbolic shear deformation theory is developed for bending and vibration analyses of functionally graded (FG) plates resting on two-parameter elastic foundation. The significant feature of this theory is that, in addition to including the thickness stretching effect, it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The foundation is described by the Pasternak (two-parameter) model. The material properties of the plate are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. Equations of motion for thick FG plates are obtained within the Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The numerical results are given in detail and compared with the existing works such as 3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates resting on elastic foundation.

키워드

과제정보

연구 과제 주관 기관 : Algerian National Thematic Agency of Research in Science and Technology (ATRST), university of Sidi Bel Abbes (UDL SBA) in Algeria

참고문헌

  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., Mechab, I. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6(2), 113-121. https://doi.org/10.1007/s10999-010-9110-x
  3. 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., Int. J., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  4. 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., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  5. Akavci, S.S. (2015), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676.
  6. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  7. Amini, M.H., Soleimani, M. and Rastgoo, A. (2009), "Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation", Smart Mater. Struct., 18(8), 1-9.
  8. 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
  9. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., Int. J., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659
  10. 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., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  11. 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., Int. J., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  12. Baferani, A.H., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93(7), 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020
  13. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., Int. J., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  14. Barati, M.R., Zenkour, A.M. and Shahverdi, H. (2016), "Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory", Compos. Struct., 141, 203-212. https://doi.org/10.1016/j.compstruct.2016.01.056
  15. 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
  16. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  17. 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., Int. J., 18(4), 1063-1081.
  18. 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
  19. 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
  20. 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., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  21. 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
  22. Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A., Ait Atmane, H. and Adda Bedia, E.A. (2010), "Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations", Mech. Compos. Mater., 46(4), 425-434. https://doi.org/10.1007/s11029-010-9159-5
  23. 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., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  24. 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., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  25. 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., Int. J., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  26. 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., Int. J., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679
  27. 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., Int. J., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  28. 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., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  29. 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
  30. 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., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  31. 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., Int. J., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  32. 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. Computat. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  33. 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., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  34. Buczkowski, R. and Torbacki, W. (2001), "Finite element modeling of thick plates on two-parameter elastic foundation", Int. J. Numer. Anal. Method. Geomech., 25(14), 1409-1427. https://doi.org/10.1002/nag.187
  35. 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., Int. J., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617
  36. Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., Int. J., 18(2), 395-408. https://doi.org/10.12989/scs.2015.18.2.395
  37. 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., Int. J., 17(1), 69-81. https://doi.org/10.12989/scs.2014.17.1.069
  38. Ebrahimi, F. and Dashti, S. (2015), "Free vibration analysis of a rotating non-uniform functionally graded beam", Steel Compos. Struct., Int. J., 19(5), 1279-1298. https://doi.org/10.12989/scs.2015.19.5.1279
  39. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., Int. J., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  40. Ebrahimi, F. and Salari, E. (2016), "Thermal loading effects on electro-mechanical vibration behavior of piezoelectrically actuated inhomogeneous size-dependent Timoshenko nanobeams", Adv. Nano Res., Int. J., 4(3), 197-228.
  41. El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. 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
  42. Fallah, A., Aghdam, M.M. and Kargarnovin, M.H. (2013), "Free vibration analysis of moderately thick functionally graded plates on elastic foundation using the extended Kantorovich method", Arch. Appl. Mech., 83(2), 177-191. https://doi.org/10.1007/s00419-012-0645-1
  43. Hadji, L. and Adda Bedia, E.A. (2015a), "Influence of the porosities on the free vibration of FGM beams", Wind Struct., Int. J., 21(3), 273-287. https://doi.org/10.12989/was.2015.21.3.273
  44. Hadji, L. and Adda Bedia, E.A. (2015b), "Analyse of the behavior of functionally graded beams based on neutral surface position", Struct. Eng. Mech., Int. J., 55(4), 703-717. https://doi.org/10.12989/sem.2015.55.4.703
  45. 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.-Engl. Ed., 32(7), 925-942. https://doi.org/10.1007/s10483-011-1470-9
  46. 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., Int. J., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507
  47. 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., Int. J., 57(2), 315-325. https://doi.org/10.12989/sem.2016.57.2.315
  48. 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., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  49. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  50. Huang, Z.Y., Lu, C.F. and Chen, W.Q. (2008), "Benchmark solutions for functionally graded thick plates resting on Winkler-Pasternak elastic foundations", Compos. Struct., 85(2), 95-104. https://doi.org/10.1016/j.compstruct.2007.10.010
  51. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  52. 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. Computat. Methods, 11(5), 135007.
  53. Kitipornchai, S., Yang, J. and Liew, K.M. (2006), "Random vibration of the functionally graded laminates in thermal environments", Comput. Method. Appl. Mech. Eng., 195(9-12), 1075-1095. https://doi.org/10.1016/j.cma.2005.01.016
  54. Kobayashi, H. and Sonoda, K. (1989), "Rectangular Mindlin plates on elastic foundations", Int. J. Mech. Sci., 31(9), 679-692. https://doi.org/10.1016/S0020-7403(89)80003-7
  55. Lam, K.Y., Wang, C.M. and He, X.Q. (2000), "Canonical exact solutions for Levy-plates on two parameter foundation using Green's functions", Eng. Struct., 22(4), 364-378. https://doi.org/10.1016/S0141-0296(98)00116-3
  56. 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., Int. J., 20(4), 889-912. https://doi.org/10.12989/scs.2016.20.4.889
  57. 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., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  58. 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(8), 576-584. https://doi.org/10.1080/15376490903138888
  59. 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
  60. Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89(3), 367-373. https://doi.org/10.1016/j.compstruct.2008.08.007
  61. Matsunaga, H. (2000), "Vibration and stability of thick plates on elastic foundations", J. Eng. Mech. (ASCE), 126(1), 27-34. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(27)
  62. 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., Int. J., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  63. Merazi, M., Hadji, L., Daouadji, T.H., Tounsi, A. and Adda Bedia, E.A. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., Int. J., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305
  64. Moradi-Dastjerdi, R. (2016), "Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube", Struct. Eng. Mech., Int. J., 57(3), 441-456. https://doi.org/10.12989/sem.2016.57.3.441
  65. Mouaici, F., Benyoucef, S., Ait Atmane, H. and Tounsi, A. (2016), "Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory", Wind Struct., Int. J., 22(4), 429-454. https://doi.org/10.12989/was.2016.22.4.429
  66. 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), 641-650. https://doi.org/10.1007/s11029-013-9380-0
  67. 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., Int. J., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  68. 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(4), 421-433. https://doi.org/10.1080/15397734.2013.763713
  69. Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, 1, Moscow: USSR, 1-56. [In Russian]
  70. Pradhan, K.K. and Chakraverty, S. (2015), "Free vibration of functionally graded thin elliptic plates with various edge supports", Struct. Eng. Mech., Int. J., 53(2), 337-354. https://doi.org/10.12989/sem.2015.53.2.337
  71. Qian, L.F. and Batra, R.C. (2005), "Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin Method", Computat. Mech., 35(3), 214-226. https://doi.org/10.1007/s00466-004-0617-6
  72. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. 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
  73. 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 Vib., 98, 157-170. https://doi.org/10.1016/0022-460X(85)90383-9
  74. Saidi, H., Tounsi, A. and Bousahla, A.A. (2016), "A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations", Geomech. Eng., Int. J., 11(2), 289-307. https://doi.org/10.12989/gae.2016.11.2.289
  75. 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., Int. J., 19(4), 829-841. https://doi.org/10.12989/scs.2015.19.4.829
  76. Sheikholeslami, S.A. and Saidi, A.R. (2013), "Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory", Compos. Struct., 106, 350-361. https://doi.org/10.1016/j.compstruct.2013.06.016
  77. Shimpi, R.P., Arya, H. and Naik, N.K. (2003), "A higher order displacement model for the plate analysis", J. Reinf. Plast. Compos., 22(22), 1667-1688. https://doi.org/10.1177/073168403027618
  78. 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
  79. Srinivas S., Joga, C.V. and Rao, A.K. (1970a), "Bending, vibration and buckling of simply supported thick orthotropic rectangular plate and laminates", Int. J. Solid. Struct., 6(11), 1463-1481. https://doi.org/10.1016/0020-7683(70)90076-4
  80. Srinivas, S., Joga Rao, C.V. and Rao, A.K. (1970b), "An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates", J. Sound Vib., 12(2), 187-199. https://doi.org/10.1016/0022-460X(70)90089-1
  81. 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., Int. J., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259
  82. 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., Int. J., 18(2), 443-465. https://doi.org/10.12989/scs.2015.18.2.443
  83. Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci. Technol., 71(16), 1850-1858. https://doi.org/10.1016/j.compscitech.2011.08.016
  84. 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
  85. 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., Int. J., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  86. Trinh, T.H., Nguyen, D.K., Gan, B.S. and Alexandrov, S. (2016), "Post-buckling responses of elastoplastic FGM beams on nonlinear elastic foundation", Struct. Eng. Mech., Int. J., 58(3), 515-532. https://doi.org/10.12989/sem.2016.58.3.515
  87. Whitney, J.M. and Pagano, N.J. (1970), "Shear deformation in heterogeneous anisotropic plates", J. Appl. Mech., 37(4), 1031-1036. https://doi.org/10.1115/1.3408654
  88. Winkler, E. (1867), "Die Lehre von der Elasticitaet und Festigkeit", Prag Dominicus.
  89. 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(8), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0
  90. Yang, J., Liew, K.M. and Kitipornchai, S. (2005), "Stochastic analysis of compositionally graded plates with system randomness under static loading", Int. J. Mech. Sci., 47(10), 1519-1541. https://doi.org/10.1016/j.ijmecsci.2005.06.006
  91. 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., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  92. Zenkour, A.M. and Sobhy, M. (2012), "Elastic foundation analysis of uniformly loaded functionally graded viscoelastic sandwich plates", J. Mech., 28(3), 439452. https://doi.org/10.1017/jmech.2012.53
  93. Zenkour, A.M. and Sobhy, M. (2013), "Dynamic bending response of thermoelastic functionally graded plates resting on elastic foundations", Aerosp. Sci. Technol., 29(1), 7-17. https://doi.org/10.1016/j.ast.2013.01.003
  94. Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004), "Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation", Int. J. Numer. Meth. Eng., 59(10), 1313-1334. https://doi.org/10.1002/nme.915
  95. 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

피인용 문헌

  1. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation vol.72, 2018, https://doi.org/10.1016/j.ast.2017.11.004
  2. A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.047
  3. Fracture problems, vibration, buckling, and bending analyses of functionally graded materials: A state-of-the-art review including smart FGMS pp.1548-0046, 2018, https://doi.org/10.1080/02726351.2017.1410265
  4. Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media vol.29, pp.11, 2018, https://doi.org/10.1177/1045389X18770856
  5. 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
  6. Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading vol.20, pp.2, 2017, https://doi.org/10.12989/cac.2017.20.2.229
  7. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2017, https://doi.org/10.12989/sem.2017.63.5.585
  8. An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities vol.13, pp.3, 2017, https://doi.org/10.12989/eas.2017.13.3.255
  9. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2017, https://doi.org/10.12989/gae.2017.13.3.385
  10. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2017, https://doi.org/10.12989/sss.2017.20.3.369
  11. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2017, https://doi.org/10.12989/scs.2017.25.2.157
  12. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2017, https://doi.org/10.12989/sem.2017.64.2.145
  13. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  14. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2017, https://doi.org/10.12989/scs.2017.25.3.257
  15. 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
  16. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2017, https://doi.org/10.12989/sem.2017.64.6.737
  17. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2017, https://doi.org/10.12989/scs.2017.25.6.693
  18. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2017, https://doi.org/10.12989/scs.2017.25.6.735
  19. The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams vol.68, pp.1, 2018, https://doi.org/10.12989/sem.2018.68.1.053
  20. Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles vol.27, pp.2, 2017, https://doi.org/10.12989/scs.2018.27.2.201
  21. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2017, https://doi.org/10.12989/gae.2018.14.6.519
  22. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2017, https://doi.org/10.12989/gae.2018.15.1.711
  23. A new plate model for vibration response of advanced composite plates in thermal environment vol.67, pp.4, 2017, https://doi.org/10.12989/sem.2018.67.4.369
  24. An efficient and simple refined theory for free vibration of functionally graded plates under various boundary conditions vol.16, pp.1, 2017, https://doi.org/10.12989/gae.2018.16.1.001
  25. A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations vol.30, pp.1, 2017, https://doi.org/10.12989/scs.2019.30.1.013
  26. Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT vol.69, pp.5, 2017, https://doi.org/10.12989/sem.2019.69.5.511
  27. Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT vol.7, pp.2, 2017, https://doi.org/10.12989/anr.2019.7.2.089
  28. Vibration analysis of different material distributions of functionally graded microbeam vol.69, pp.6, 2017, https://doi.org/10.12989/sem.2019.69.6.637
  29. 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
  30. 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
  31. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT vol.7, pp.3, 2017, https://doi.org/10.12989/anr.2019.7.3.191
  32. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2017, https://doi.org/10.12989/gae.2019.18.2.161
  33. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2017, https://doi.org/10.12989/scs.2019.31.5.503
  34. Face stability analysis of rock tunnels under water table using Hoek-Brown failure criterion vol.18, pp.3, 2017, https://doi.org/10.12989/gae.2019.18.3.235
  35. 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
  36. 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
  37. Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory vol.17, pp.5, 2017, https://doi.org/10.12989/eas.2019.17.5.447
  38. 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
  39. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2017, https://doi.org/10.12989/was.2019.29.6.371
  40. Size-dependent buckling behaviour of FG annular/circular thick nanoplates with porosities resting on Kerr foundation based on new hyperbolic shear deformation theory vol.73, pp.3, 2020, https://doi.org/10.12989/sem.2020.73.3.225
  41. Buckling and vibration analysis of FG-CNT-reinforced composite rectangular thick nanoplates resting on Kerr foundation based on nonlocal strain gradient theory vol.26, pp.5, 2017, https://doi.org/10.1177/1077546319878976
  42. 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
  43. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2017, https://doi.org/10.12989/sss.2020.25.4.409
  44. Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT vol.36, pp.3, 2017, https://doi.org/10.1007/s00366-019-00732-1
  45. Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect vol.234, pp.9, 2017, https://doi.org/10.1177/1464420720928378
  46. Quasi-3D Hyperbolic Shear Deformation Theory for the Free Vibration Study of Honeycomb Microplates with Graphene Nanoplatelets-Reinforced Epoxy Skins vol.25, pp.21, 2017, https://doi.org/10.3390/molecules25215085
  47. Mindlin’s strain gradient theory for vibration analysis of FG-CNT-reinforced composite nanoplates resting on Kerr foundation in thermal environment vol.34, pp.1, 2017, https://doi.org/10.1177/0892705719843175
  48. Forced vibration of a functionally graded porous beam resting on viscoelastic foundation vol.24, pp.1, 2017, https://doi.org/10.12989/gae.2021.24.1.091
  49. Theoretical and Numerical Solution for the Bending and Frequency Response of Graphene Reinforced Nanocomposite Rectangular Plates vol.11, pp.14, 2017, https://doi.org/10.3390/app11146331