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Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model

  • Kettaf, Fatima Zohra (Departement de Genie Mecanique, Faculte de Technologie, Universite Sidi Bel Abbes) ;
  • Houari, Mohammed Sid Ahmed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie) ;
  • Benguediab, Mohamed (Departement de Genie Mecanique, Faculte de Technologie, Universite Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie)
  • Received : 2013.03.20
  • Accepted : 2013.07.30
  • Published : 2013.10.25

Abstract

In the present study, the thermal buckling behavior of functionally graded sandwich plates is studied using a new hyperbolic displacement model. Unlike any other theory, the theory is variationally consistent and gives four governing equations. Number of unknown functions involved in displacement field is only four, as against five in case of other shear deformation theories. This present model takes into account the parabolic distribution of transverse shear stresses and satisfies the condition of zero shear stresses on the top and bottom surfaces without using shear correction factor. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed 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 assumed as uniform, linear and non-linear temperature rises across the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates.

Keywords

new plate theory;thermal buckling;functionally graded plate;volume fraction index

References

  1. Ameur, M., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2011), "A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations", KSCE J. Civil Eng., 15(8), 1405-1414. https://doi.org/10.1007/s12205-011-1361-z
  2. Bouazza, M., Tounsi, A., Adda-Bedia, E.A. and Megueni, A. (2010), "Thermoelastic stability analysis of functionally graded plates: An analytical approach", Comput. Mater. Sci.., 49(4), 865-870. https://doi.org/10.1016/j.commatsci.2010.06.038
  3. 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
  4. 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
  5. 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
  6. Fekrar, A., El Meiche, N., Bessaim, A., Tounsi, A. and Adda Bedia, E.A. (2012), "Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory", Steel Compos. Struct. Int. J., 13(1), 91-107. https://doi.org/10.12989/scs.2012.13.1.091
  7. 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. Stresses, 34(4), 315-334. https://doi.org/10.1080/01495739.2010.550806
  8. Javaheri, R. and Eslami, M.R. (2002a), "Thermal buckling of functionally graded plates", AIAA J., 40(1), 162-169. https://doi.org/10.2514/2.1626
  9. Javaheri, R. and Eslami, M.R. (2002b), "Thermal buckling of functionally graded plates based on higher order theory", J. Therm. Stresses, 25(7), 603-625. https://doi.org/10.1080/01495730290074333
  10. Kiani, Y. and Eslami, M.R. (2012), "Thermal buckling and post-buckling response of imperfect temperature-dependent sandwich FGM plates resting on elastic foundation", Arch. Appl. Mech., 82(7), 891-905. https://doi.org/10.1007/s00419-011-0599-8
  11. Liew, K.M., Yang, J. and Kitipornchai, S. (2004), "Thermal post-buckling 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
  12. Matsunaga, H. (2005), "Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory", Compos. Struct., 68(4), 439-454. https://doi.org/10.1016/j.compstruct.2004.04.010
  13. Matsunaga, H. (2009), "Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory", Compos. Struct., 90(1), 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004
  14. Merdaci, S., Tounsi, A., Houari, M.S.A, Mechab, I., Hebali, H. and Benyoucef, S. (2011), "Two new refined shear displacement models for functionally graded sandwich plates", Arch. Appl. Mech., 81(11), 1507-1522. https://doi.org/10.1007/s00419-010-0497-5
  15. 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
  16. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  17. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods 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
  18. Sallai, B.O., Tounsi, A., Mechab, I., Bachir, B.M., Meradjah, M. and Adda Bedia E.A. (2009), "A theoretical analysis of flexional bending of Al/$Al_{2}O_{3}$ S-FGM thick beams", Computat. Mater. Sci.., 44(4), 1344-1350. https://doi.org/10.1016/j.commatsci.2008.09.001
  19. Samsam Shariat, B.A. and Eslami, M.R. (2005), "Buckling of functionally graded plates under in-plane compressive loading based on the first order plate theory", Proceeding of the Fifth International Conference on Composite Science and Technology, Sharjah, UAE, February.
  20. Samsam Shariat, B.A. and Eslami, M.R. (2007), "Buckling of thick functionally graded plates under mechanical and thermal loads", Compos. Struct., 78(3), 433-439. https://doi.org/10.1016/j.compstruct.2005.11.001
  21. Simsek, M. (2009), "Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method", Int. J. Eng. Appl. Sci., 1(3), 1-11.
  22. Wu, L. (2004), "Thermal buckling of a simply supported moderately thick rectangular FGM plate", Compos. Struct., 64(2), 211-218. https://doi.org/10.1016/j.compstruct.2003.08.004
  23. 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
  24. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 1 - deflection and stresses, Part 2 - buckling and free vibration", Int. J. Solids Struct., 42(18-19), 5224-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  25. Zenkour, A.M. and Sobhy, M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos. Struct., 93(1), 93-102. https://doi.org/10.1016/j.compstruct.2010.06.012

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