Steel and Composite Structures

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Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory

  • Fekrar, A. (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • El Meiche, N. (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • Bessaim, A. (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • Tounsi, A. (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • Adda Bedia, E.A. (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes)
  • Received : 2012.02.26
  • Accepted : 2012.05.01
  • Published : 2012.07.25
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Abstract

In this research, mechanical buckling of hybrid functionally graded plates is considered using a new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. The effectiveness of the theories is brought out through illustrative examples.

Keywords

References

  1. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Composites Part B: Engineering, 39(1), 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026
  2. Bodaghi, M., Saidi, A. (2010), "Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory", Appl. Math. Model., 34(11), 3659-3673. https://doi.org/10.1016/j.apm.2010.03.016
  3. Bouazza, M., Tounsi, A., Adda-Bedia, E.A., 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
  4. Chehel Amirani, M., Khalili, S.M.R., Nemati, N. (2009), "Free vibration analysis of sandwich beam with FG core using the element free Galerkin method" Compos. Struct., 90(3), 373-379. https://doi.org/10.1016/j.compstruct.2009.03.023
  5. Chi, S., Chung, Y. (2006a), "Mechanical behavior of functionally graded material plates under transverse load - Part I: Analysis." Int. J. Sol. Struc, 43(13), 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011
  6. Chi, S., Chung, Y. (2006b), "Mechanical behavior of functionally graded material plates under transverse load - Part II: Numerical results", Int. J. Sol. Struc, 43(13), 3675-3691. https://doi.org/10.1016/j.ijsolstr.2005.04.010
  7. Delale, F., Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. of Appl. Mech, 50, 609-614. https://doi.org/10.1115/1.3167098
  8. Feldman, E., Aboudi, J. (1997), "Buckling analysis of functionally graded plates subjected to uniaxial loading", Compos. Struct., 38(1-4), 29-36. https://doi.org/10.1016/S0263-8223(97)00038-X
  9. Gibson, LJ, Ashby, MF, Karam, GN., Wegst, U., Shercliff, HR. (1995), "Mechanical properties of natural materials. II. Microstructures for mechanical efficiency", Proc Roy Soc Lond A, 450(1938), 141-162. https://doi.org/10.1098/rspa.1995.0076
  10. Hill, R. (1965), "A self-consistent mechanics of composite materials", J Mech Phys Solids, 13(4), 213-222. https://doi.org/10.1016/0022-5096(65)90010-4
  11. Javaheri, R., Eslami, M. (2002), "Buckling of functionally graded plates under in-plane compressive loading", J. Appl. Math. Mech., 82(4), 277-283.
  12. Levinson, M. (1980), "An accurate simple theory of the statics and dynamics of elastic plates", Mech Res Commun, 7(6), 343-350. https://doi.org/10.1016/0093-6413(80)90049-X
  13. Mahdavian, M. (2009), "Buckling analysis of simply-supported functionally graded rectangular plates under non-uniform In-plane compressive loading", J. Solid Mech., 1(3), 213-225.
  14. Mindlin, RD. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech, 18(1), 31-38.
  15. Mohammadi, M., Saidi, A.R., Jomehzadeh, E. (2010a), "Levy solution for buckling analysis of functionally graded rectangular plates", Appl. Compos. Mater., 17(2), 81-93. https://doi.org/10.1007/s10443-009-9100-z
  16. Mohammadi, M., Saidi, A.R., Jomehzadeh, E. (2010b), "A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges", Proc. Inst. Mech. Engrs. Part C J. Mech. Eng. Sci., 224(9), 1831-1841. https://doi.org/10.1243/09544062JMES1804
  17. Mori, T., Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall, 2, 1571-1574.
  18. Narita, Y. (2000), "Combinations for the free vibration behaviors of anisotropic rectangular plates under general edge conditions", J. Appl. Mech, 67(3), 568-573. https://doi.org/10.1115/1.1311959
  19. Reddy, J. (2004), "Mechanics of laminated composite plates and shells: theory and analysis", CRC.
  20. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", J. Appl. Mech, 51, 745-752. https://doi.org/10.1115/1.3167719
  21. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J Appl Mech-T ASME, 12(2), 69-77.
  22. Shariat, B., Eslami, M. (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; American University of Sharjah, United Arab Emirates.
  23. Yang, J., Liew, K., Kitipornchai, S. (2005), "Second-order statistics of the elastic buckling of functionally graded rectangular plates", Compos. Sci. Technol., 65(7-8), 1165-1175. https://doi.org/10.1016/j.compscitech.2004.11.012
  24. Zhao, X., Lee, Y.Y., 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

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