DOI QR코드

DOI QR Code

Examination of non-homogeneity and lamination scheme effects on deflections and stresses of laminated composite plates

  • Received : 2015.06.07
  • Accepted : 2015.12.31
  • Published : 2016.02.25

Abstract

In this study, a convenient formulation for the bending of laminated composite plates that hold non-homogeneous properties is examined. The constitutive equations of first order shear deformation plate theory are obtained using Hamilton Principle. The effect of non-homogeneity, lamination schemes and aspect ratio on the deflections and stresses is analysed. It is understood from the study that economical and optimum designs for laminated composite plates can be achieved by changing lamination scheme and by considering non-homogeneity response of composite plate.

Keywords

References

  1. Aydogdu, M. (2009), "A new shear deformation theory for laminated composite plates", Compos. Struct., 89(1), 94-101. https://doi.org/10.1016/j.compstruct.2008.07.008
  2. Beena, K. and Parvathy, U. (2014), "Linear static analysis of functionally graded plate using spline finite strip method", Compos. Struct., 117, 309-315. https://doi.org/10.1016/j.compstruct.2014.07.002
  3. Delale, F. and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. Appl. Mech., 50(3), 609-614. https://doi.org/10.1115/1.3167098
  4. Erdogan, F., Kaya, A. C. and Joseph, P. F. (1991), "The crack problem in bonded nonhomogeneous materials", J. Appl. Mech., 58(2), 410-418. https://doi.org/10.1115/1.2897201
  5. Fares, M. (1999), "Non-linear bending analysis of composite laminated plates using a refined first-order theory", Compos. Struct., 46(3), 257-266. https://doi.org/10.1016/S0263-8223(99)00062-8
  6. Fares, M. and Zenkour, A. (1999), "Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories", Compos. Struct., 44(4), 279-287. https://doi.org/10.1016/S0263-8223(98)00135-4
  7. Goswami, S. (2006), "A C0 plate bending element with refined shear deformation theory for composite structures", Compos. Struct., 72(3), 375-382. https://doi.org/10.1016/j.compstruct.2005.01.007
  8. Gupta, U., Lal, R. and Sharma, S. (2006), "Vibration analysis of non-homogeneous circular plate of nonlinear thickness variation by differential quadrature method", J. Sound Vib., 298(4), 892-906. https://doi.org/10.1016/j.jsv.2006.05.030
  9. Hashin, Z. and Shtrikman, S. (1962), "On some variational principles in anisotropic and nonhomogeneous elasticity", J. Mech. Phys. Solid., 10(4), 335-342. https://doi.org/10.1016/0022-5096(62)90004-2
  10. He, W.M., Chen, W.Q. and Qiao, H. (2013), "In-plane vibration of rectangular plates with periodic inhomogeneity: natural frequencies and their adjustment", Compos. Struct., 105, 134-140. https://doi.org/10.1016/j.compstruct.2013.05.013
  11. He, W.M., Qiao, H. and Chen, W.Q. (2012), "Analytical solutions of heterogeneous rectangular plates with transverse small periodicity", Compos. Part B: Eng., 43(3), 1056-1062. https://doi.org/10.1016/j.compositesb.2011.09.010
  12. Kant, T. and Swaminathan, K. (2002), "Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56(4), 329-344. https://doi.org/10.1016/S0263-8223(02)00017-X
  13. Khoroshun, L., Kozlov, S., Ivanov, Y.A. and Koshevoi, I. (1988), The Generalized Theory of Plates and Shells Non-Homogeneous in Thickness Direction.
  14. Kolpakov, A. (1999), "Variational principles for stiffnesses of a non-homogeneous plate", J. Mech. Phys. Solid., 47(10), 2075-2092. https://doi.org/10.1016/S0022-5096(99)00010-1
  15. Lal, R. (2007), "Transverse vibrations of non-homogeneous orthotropic rectangular plates of variable thickness: a spline technique", J. Sound Vib., 306(1), 203-214. https://doi.org/10.1016/j.jsv.2007.05.014
  16. Leknitskii, S.G. and Fern, P. (1963), Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day.
  17. Lomakin, V. (1976), The Elasticity Theory of Non-Homogeneous Materials, Nauka, Moscow.
  18. Pagano, N. (1970), "Exact solutions for rectangular bidirectional composites and sandwich plates", J. Compos. Mater., 4(1), 20-34. https://doi.org/10.1177/002199837000400102
  19. Pagano, N. and Hatfield, H.J. (1972), "Elastic behavior of multilayered bidirectional composites", AIAA J., 10(7), 931-933. https://doi.org/10.2514/3.50249
  20. Patel, S.N. (2014), "Nonlinear bending analysis of laminated composite stiffened plates", Steel Compos. Struct., 17(6), 867-890. https://doi.org/10.12989/scs.2014.17.6.867
  21. Phan, N. and Reddy, J. (1985), "Analysis of laminated composite plates using a higher order shear deformation theory", Int. J. Numer. Meth. Eng., 21(12), 2201-2219. https://doi.org/10.1002/nme.1620211207
  22. 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
  23. Reddy, J. N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
  24. Reissner, E. (1975), "On transverse bending of plates, including the effect of transverse shear deformation", Int. J. Solid. Struct., 11(5), 569-573. https://doi.org/10.1016/0020-7683(75)90030-X
  25. Sadoune, M., Tounsi, A., Houari, M.S.A. and Bedia, E.L.A.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., 17(3), 321-338. https://doi.org/10.12989/scs.2014.17.3.321
  26. Schmitz, A. and Horst, P. (2014), "A finite element unit-cell method for homogenised mechanical properties of heterogeneous plates", Compos. Part A: Appl. Sci. Manuf., 61, 23-32. https://doi.org/10.1016/j.compositesa.2014.01.014
  27. Sofiyev, A. and Kuruoglu, N. (2014), "Combined influences of shear deformation, rotary inertia and heterogeneity on the frequencies of cross-ply laminated orthotropic cylindrical shells", Compos. Part B: Eng., 66, 500-510. https://doi.org/10.1016/j.compositesb.2014.06.015
  28. Sofiyev, A., Zerin, Z. and Korkmaz, A. (2008), "The stability of a thin three-layered composite truncated conical shell containing an fgm layer subjected to non-uniform lateral pressure", Compos. Struct., 85(2), 105-115. https://doi.org/10.1016/j.compstruct.2007.10.022
  29. Sturzenbecher, R. and Hofstetter, K. (2011), "Bending of cross-ply laminated composites: an accurate and efficient plate theory based upon models of Lekhnitskii and Ren", Compos. Struct., 93(3), 1078-1088. https://doi.org/10.1016/j.compstruct.2010.09.020
  30. Thai, H.T. and Choi, D.H. (2013a), "A simple first-order shear deformation theory for laminated composite plates", Compos. Struct., 106, 754-763. https://doi.org/10.1016/j.compstruct.2013.06.013
  31. Thai, H.T. and Choi, D.H. (2013b), "A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates", Compos. Struct., 101, 332-340. https://doi.org/10.1016/j.compstruct.2013.02.019
  32. Yin, S., Hale, J.S., Yu, T., Bui, T.Q. and Bordas, S.P. (2014), "Sogeometric 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
  33. Zenkour, A. and Fares, M. (1999), "Non-homogeneous response of cross-ply laminated elastic plates using a higher-order theory", Compos. Struct., 44(4), 297-305. https://doi.org/10.1016/S0263-8223(99)00006-9

Cited by

  1. Curvilinear free-edge form effect on stability of perforated laminated composite plates vol.61, pp.2, 2016, https://doi.org/10.12989/sem.2017.61.2.255