DOI QR코드

DOI QR Code

A new and simple HSDT for thermal stability analysis of FG sandwich plates

  • Menasria, Abderrahmane (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • 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) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • 투고 : 2017.03.29
  • 심사 : 2017.06.28
  • 발행 : 2017.10.10

초록

The novelty of this work is the use of a new displacement field that includes undetermined integral terms for analyzing thermal buckling response of functionally graded (FG) sandwich plates. The proposed kinematic uses only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional higher shear deformation theories (HSDTs). The theory considers a trigonometric variation of transverse shear stress and verifies the traction free boundary conditions without employing the shear correction factors. Material properties of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law variation 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 assumed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is employed to derive the governing equations as an eigenvalue problem. The validation of the present work is checked by comparing the obtained results the available ones in the literature. The influences of aspect and thickness ratios, material index, loading type, and sandwich plate type on the critical buckling are all discussed.

키워드

참고문헌

  1. 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., Int. J., 22(3), 329-348. https://doi.org/10.12989/was.2016.22.3.329
  2. Abdelhak, Z., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst., Int. J., 18(2), 267-291. https://doi.org/10.12989/sss.2016.18.2.267
  3. Adda Bedia, W., Benzair, A., Semmah, A., Tounsi, A. and Mahmoud, S.R. (2015), "On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity", Brazil. J. Phys., 45(2), 225-233. https://doi.org/10.1007/s13538-015-0306-2
  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., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  5. 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
  6. 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
  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., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  8. Aizikovich, S.M., Mitrin, B.I., Seleznev, N.M., Wang, Y.C. and Volkov, S.S. (2016), "Influence of a soft FGM interlayer on contact stresses under a beam on an elastic foundation", Struct. Eng. Mech., Int. J., 58(4), 613-625. https://doi.org/10.12989/sem.2016.58.4.613
  9. Akbarov, S.D., Guliyev, H.H. and Yahnioglu, N. (2016), "Natural vibration of the three-layered solid sphere with middle layer made of FGM: Three-dimensional approach", Struct. Eng Mech., Int. J., 57(2), 239-264. https://doi.org/10.12989/sem.2016.57.2.239
  10. 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
  11. Arefi, M. (2015a), "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
  12. Arefi, M. (2015b), "Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation", Smart Struct. Syst., Int. J., 16(1), 195-211. https://doi.org/10.12989/sss.2015.16.1.195
  13. Arefi, M. and Allam, M.N.M. (2015), "Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation", Smart Struct. Syst., Int. J., 16(1), 81-100. https://doi.org/10.12989/sss.2015.16.1.081
  14. Asemi, K. and Shariyat, M. (2016), "Three-dimensional biaxial post-buckling analysis of heterogeneous auxetic rectangular plates on elastic foundations by new criteria", Comput. Methods Appl. Mech. Eng., 302, 1-26. https://doi.org/10.1016/j.cma.2015.12.026
  15. 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
  16. 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
  17. 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., Int. J., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  18. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperaturedependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., Int. J., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091
  19. 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
  20. 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., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  21. 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. https://doi.org/10.12989/scs.2015.18.4.1063
  22. 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. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  23. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., Int. J., 62(6), 695-702.
  24. Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., Int. J., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009
  25. Benbakhti, A., Bachir Bouiadjra, M., Retiel, N. and Tounsi, A. (2016), "A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates", Steel Compos. Struct., Int. J., 22(5), 975-999. https://doi.org/10.12989/scs.2016.22.5.975
  26. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., Int. J. [Accepted]
  27. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., Int. J., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  28. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder 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
  29. 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
  30. 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(6), 671-703. https://doi.org/10.1177/1099636213498888
  31. 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., Int. J., 19(6), 601-614.
  32. Birman, V., Keil, T. and Hosder, S. (2013), "Functionally Graded Materials in Engineering", In: Structural Interfaces and Attachments in Biology, (S. Thomopoulus, V. Birman, G.M. Genin Eds.), Chapter 2, Springer, New York, NY, USA.
  33. 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., Int. J., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  34. 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
  35. 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., Int. J., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  36. 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
  37. 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
  38. 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
  39. 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
  40. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "Anew 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
  41. 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
  42. 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
  43. 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
  44. Brush, D.O. and Almroth, B.O. (1975), Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, NY, USA.
  45. Bui, T.Q., Khosravifard, A. Zhang, Ch., Hematiyan, M.R. and Golub, M.V. (2013), "Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method", Eng. Struct., 47, 90-104. https://doi.org/10.1016/j.engstruct.2012.03.041
  46. Bui, T.Q., Do, T.V., Ton, L.H.T., Doan, D.H., Tanaka, S., Pham, D.T., Nguyen-Van, T.A., Yu, T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. Part B, 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048
  47. Celebi, K., Yarimpabuc, D. and Keles, I. (2016), "A unified method for stresses in FGM sphere with exponentially-varying properties", Struct. Eng. Mech., Int. J., 57(5), 823-835. https://doi.org/10.12989/sem.2016.57.5.823
  48. Cheng, Z.Q. and Batra, R.C. (2000), "Three-dimensional thermoelastic deformations of a functionally graded elliptic plate", Compos. Pt. B-Eng., 31(2), 97-106.
  49. 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
  50. 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., Int. J., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  51. Darabi, A. and Vosoughi, A.R. (2016), "Hybrid inverse method for small scale parameter estimation of FG nanobeams", Steel Compos. Struct., Int. J., 20(5), 1119-1131. https://doi.org/10.12989/scs.2016.20.5.1119
  52. 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., Int. J., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  53. Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., Int. J., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343
  54. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen\'s nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., Int. J., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  55. 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., Int. J., 63(5), 585-595.
  56. 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., Int. J., 10(3), 357-386. https://doi.org/10.12989/gae.2016.10.3.357
  57. 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., Int. J. [In press]
  58. Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810. https://doi.org/10.1007/s11012-013-9827-3
  59. Feldman, E. and Aboudi, J. (1997), "Buckling analysis of functionally graded plates subjected to uniaxial loading", Compos. Struct., 38, 29-36. https://doi.org/10.1016/S0263-8223(97)00038-X
  60. Ganapathi, M. and Prakash, T. (2006), "Thermal buckling of simply supported functionally graded skew plates", Compos. Struct., 74(2), 247-250. https://doi.org/10.1016/j.compstruct.2005.04.004
  61. Ghorbanpour Arani, A., Cheraghbak, A. and Kolahchi, R. (2016), "Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 60(3), 489-505. https://doi.org/10.12989/sem.2016.60.3.489
  62. 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
  63. 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
  64. 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(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  65. Hebali, H., Bakora, A., Tounsi, A. and Kaci, A. (2016), "A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates", Steel Compos. Struct., Int. J., 22(3), 473-495. https://doi.org/10.12989/scs.2016.22.3.473
  66. 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., Int. J., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  67. Kar, V.R. and Panda, S.K. (2015a), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., Int. J., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661
  68. Kar, V.R. and Panda, S.K. (2015b), "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
  69. 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., Int. J. [In press]
  70. 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., Int. J. [In press]
  71. 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., Int. J., 20(4), 889-911. https://doi.org/10.12989/scs.2016.20.4.889
  72. 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
  73. Lee, Y.Y., Zhao, X. and Reddy, J.N. (2010), "Postbuckling analysis of functionally graded plates subject to compressive and thermal loads", Comput. Methods Appl. Mech. Eng., 199(25), 1645-1653. https://doi.org/10.1016/j.cma.2010.01.008
  74. Lee, Y.-H., Bae, S.-I. and Kim, J.-H. (2016), "Thermal buckling behavior of functionally graded plates based on neutral surface", Compos. Struct., 137, 208-214. https://doi.org/10.1016/j.compstruct.2015.11.023
  75. Liew, K.M., Yang, J. and Kitipornchai, S. (2003), "Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading", Int. J. Solids Struct., 40(15), 3869-3892. https://doi.org/10.1016/S0020-7683(03)00096-9
  76. Liu, S., Yu, T., Bui, T.Q., Yin, S., Thai, D.K. and Tanaka, S. (2017), "Analysis of functionally graded plates by simple locking-free quasi-3D hyperbolic plate isogeometric method", Compos. Part B: Eng., 120, 182-196. https://doi.org/10.1016/j.compositesb.2017.03.061
  77. Ma, L.S. and Wang, T.J. (2003), "Nonlinear bending and postbuckling of a functionally graded circular plate under mechanical and thermal loadings", Int. J. Solids Struct., 40(13), 3311-3330. https://doi.org/10.1016/S0020-7683(03)00118-5
  78. 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
  79. Mahmoud, S.R., Abd-Alla, A.M., Tounsi, A. and Marin, M. (2015), "The problem of wave propagation in magneto-rotating orthotropic non-homogeneous medium", J. Vib. Control, 21(16), 3281-3291. https://doi.org/10.1177/1077546314521443
  80. Matsunaga, H. (1997), "Buckling instabilities of thick elastic plates subjected to in-plane stresses", Comput. Struct., 62(1), 205-214. https://doi.org/10.1016/S0045-7949(96)00239-8
  81. Matsunaga, H. (2005), "Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higherorder deformation theory", Compos. Struct., 68(4), 439-454. https://doi.org/10.1016/j.compstruct.2004.04.010
  82. 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., Int. J., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  83. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 1099636217698443. https://doi.org/10.1177/1099636217698443
  84. 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
  85. 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
  86. Merdaci, S., Tounsi, A. and Bakora, A. (2016), "A novel four variable refined plate theory for laminated composite plates", Steel Compos. Struct., Int. J., 22(4), 713-732. https://doi.org/10.12989/scs.2016.22.4.713
  87. 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
  88. Mouaici, F., Benyoucef, S., Ait Atmane, H. and Tounsi, A. (2016), "Effect of porosity on vibrational characteristics of nonhomogeneous plates using hyperbolic shear deformation theory", Wind Struct., Int. J., 22(4), 429-454. https://doi.org/10.12989/was.2016.22.4.429
  89. Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and 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., Int. J. [In press]
  90. Morimoto, T., Tanigawa, Y. and Kawamura, R. (2006), "Thermal buckling of functionally graded rectangular plates subjected to partial heating", Int. J. Mech. Sci., 48(9), 926-937. https://doi.org/10.1016/j.ijmecsci.2006.03.015
  91. Na, K.-S. and Kim, J.-H. (2004), "Three-dimensional thermal buckling analysis of functionally graded materials", Compos., Part B, Eng., 35(5), 429-437. https://doi.org/10.1016/j.compositesb.2003.11.013
  92. 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
  93. Najafizadeh, M.M. and Eslami, M.R. (2002), "Buckling analysis of circular plates of functionally graded materials under uniform radial compression", Int. J. Mech. Sci., 44(12), 2479-2493. https://doi.org/10.1016/S0020-7403(02)00186-8
  94. Najafizadeh, M.M. and Heydari, H.R. (2008), "An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression", Int. J. Mech. Sci., 50(3), 603-612. https://doi.org/10.1016/j.ijmecsci.2007.07.010
  95. 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., Int. J., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  96. Raminnea, M., Biglari, H. and Vakili Tahami, F. (2016), "Nonlinear higher order Reddy theory for temperaturedependent vibration and instability of embedded functionally graded pipes conveying fluid-nanoparticle mixture", Struct. Eng. Mech., Int. J., 59(1), 153-186. https://doi.org/10.12989/sem.2016.59.1.153
  97. Reddy, J.N. (1984), Energy Principles and Variational Methods in Applied Mechanics, John Wiley, New York, NY, USA.
  98. Reddy, J.N. and Cheng, Z.Q. (2001), "Three-dimensional thermomechanical deformations of functionally graded rectangular plates", Eur. J. Mech. A-Solids, 20(5), 841-855.
  99. 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
  100. Shi, G. (2007), "A new simple third-order shear deformation theory of plates", Int. J. Solids Struct., 44(13), 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
  101. 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
  102. Swaminathan, K. and Naveenkumar, D.T. (2014), "Higher order refined computational models for the stability analysis of FGM plates: Analytical solutions", Eur. J. Mech. A/Solid., 47, 349-361. https://doi.org/10.1016/j.euromechsol.2014.06.003
  103. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M. and Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM plates-a state-of-the-art review", Compos. Struct., 120, 10-31. https://doi.org/10.1016/j.compstruct.2014.09.070
  104. 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
  105. 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
  106. 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
  107. Tran, L.V., Thai, C.H. and Nguyen-Xuan, H. (2013), "An isogeometric finite element formulation for thermal buckling analysis of functionally graded plates", Finite Elem. Anal. Des., 73, 65-76. https://doi.org/10.1016/j.finel.2013.05.003
  108. 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
  109. Tung, H.V. (2015), "Thermal and thermomechanical postbuckling of FGM sandwich plates resting on elastic foundations with tangential edge constraints and temperature dependent properties", Compos. Struct., 131, 1028-1039. https://doi.org/10.1016/j.compstruct.2015.06.043
  110. Turan, M., Adiyaman, G., Kahya, V. and Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Struct. Eng. Mech., Int. J., 58(3), 423-442. https://doi.org/10.12989/sem.2016.58.3.423
  111. Vel, S.S. and Batra, R.C. (2002), "Exact solution for thermoelastic deformations of functionally graded thick rectangular plates", AIAA J., 40(7), 1421-1433. https://doi.org/10.2514/2.1805
  112. Vinson, J.R. (2001), "Sandwich structures", Appl. Mech. Rev., 54(3), 201-214. https://doi.org/10.1115/1.3097295
  113. Vinson, J.R. (2005), "Sandwich Structures: Past, Present, and Future", In: Sandwich Structures 7: Advancing with Sandwich Structures and Materials, (O.T. Thomsen, E. Bozhevolnaya, A. Lyckegaard Eds.), Chapter 1, Springer, Netherlands.
  114. Vu, T.V., Nguyen, N.H., Khosravifard, A., Hematiyan, M.R., Tanaka, S. and Bui, T.Q. (2017), "A simple FSDT-based meshfree method for analysis of functionally graded plates", Eng. Anal. Bound. Elem., 79, 1-12. https://doi.org/10.1016/j.enganabound.2017.03.002
  115. 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
  116. Yaghoobi, H., Valipour, M.S., Fereidoon, A. and Khoshnevisrad, P. (2014), "Analytical study on postbuckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loading using VIM", Steel Compos. Struct., Int. J., 17(5), 753-776. https://doi.org/10.12989/scs.2014.17.5.753
  117. Yin, S., Hale, J.S., Yu, T., Bui, T.Q. and Bordas, S.P.A. (2014), "Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates", Compos. Struct., 118, 121-138. https://doi.org/10.1016/j.compstruct.2014.07.028
  118. Yin, S., Yu, T., Bui, T.Q., Zheng, X. and Tanaka, S. (2016), "Inplane material inhomogeneity of functionally graded plates: A higher-order shear deformation plate isogeometric analysis", Compos. Part B, 106, 273-284. https://doi.org/10.1016/j.compositesb.2016.09.008
  119. Yu, T., Yin, S., Bui, T.Q. and Hirose, S. (2015), "A simple FSDTbased isogeometric analysis for geometrically nonlinear analysis of functionally graded plates", Finite Elem. Anal. Des., 96, 1-10. https://doi.org/10.1016/j.finel.2014.11.003
  120. Yu, T., Bui, T.Q., Yin, S., Doan, D.H., Wu, C.T., Van Do, T. and Tanaka, S. (2016a), "On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis", Compos. Struct., 136, 684-695. https://doi.org/10.1016/j.compstruct.2015.11.002
  121. Yu, T., Yin, S., Bui, T.Q., Xia, S., Tanaka, S. and Hirose, S. (2016b), "NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method", Thin-Wall. Struct., 101, 141-156. https://doi.org/10.1016/j.tws.2015.12.008
  122. Yu, T., Yin, S., Bui, T.Q., Liu, C. and Wattanasakulpong, N. (2017), "Buckling isogeometric analysis of functionally graded plates under combined thermal and mechanical loads", Compos. Struct., 162, 54-69. https://doi.org/10.1016/j.compstruct.2016.11.084
  123. 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
  124. Zhang, L.W., Zhu, P. and Liew, K.M. (2014), "Thermal buckling of functionally graded plates using a local Kriging meshless method", Compos. Struct., 108, 472-492. https://doi.org/10.1016/j.compstruct.2013.09.043
  125. 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. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  126. 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., Int. J. [In press]

피인용 문헌

  1. A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment pp.1539-7742, 2019, https://doi.org/10.1080/15397734.2018.1557529
  2. Impulsive Response of Rectangular Metal Sandwich Plate with a Graded Foam Core vol.10, pp.6, 2017, https://doi.org/10.1142/s1758825118500643
  3. Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations vol.25, pp.9, 2019, https://doi.org/10.1177/1077546319825671
  4. Nonlinear bending of functionally graded porous nanobeam subjected to multiple physical load based on nonlocal strain gradient theory vol.31, pp.5, 2019, https://doi.org/10.12989/scs.2019.31.5.469
  5. 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
  6. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2017, https://doi.org/10.12989/scs.2019.33.5.699
  7. 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
  8. 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
  9. Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method vol.26, pp.1, 2020, https://doi.org/10.1177/1077546319876389
  10. Free Vibration and Static Bending Analysis of Piezoelectric Functionally Graded Material Plates Resting on One Area of Two-Parameter Elastic Foundation vol.2020, pp.None, 2017, https://doi.org/10.1155/2020/9236538
  11. Numerical analysis of thermal post-buckling strength of laminated skew sandwich composite shell panel structure including stretching effect vol.34, pp.2, 2017, https://doi.org/10.12989/scs.2020.34.2.279
  12. Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method vol.34, pp.3, 2020, https://doi.org/10.12989/scs.2020.34.3.361
  13. Buckling response of smart plates reinforced by nanoparticles utilizing analytical method vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.001
  14. Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.147
  15. Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories vol.74, pp.2, 2020, https://doi.org/10.12989/sem.2020.74.2.175
  16. Effect of boundary conditions on thermal buckling of laminated composite shallow shell vol.42, pp.p5, 2021, https://doi.org/10.1016/j.matpr.2020.12.501
  17. A New Sinusoidal Shear Deformation Theory for Static Bending Analysis of Functionally Graded Plates Resting on Winkler-Pasternak Foundations vol.2021, pp.None, 2017, https://doi.org/10.1155/2021/6645211