Steel and Composite Structures

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Postbuckling analysis of laminated composite shells under shear loads

  • Jung, Woo-Young (Department of Civil Engineering, Gangneung-Wonju National University) ;
  • Han, Sung-Cheon (Department of Civil & Railroad Engineering, Daewon University College) ;
  • Lee, Won-Hong (Department of Civil Engineering, Gyeongnam National University of Science and Technology) ;
  • Park, Weon-Tae (Division of Construction and Environmental Engineering, Kongju National University)
  • Received : 2015.02.23
  • Accepted : 2016.04.07
  • Published : 2016.06.10
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Abstract

The postbuckling behavior of laminated composite plates and shells, subjected to various shear loadings, is presented, using a modified 8-ANS method. The finite element, based on a modified first-order shear deformation theory, is further improved by the combined use of assumed natural strain method. We analyze the influence of the shell element with the various location and number of enhanced membrane and shear interpolation. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. The effects of various types of lay-ups, materials and number of layers on initial buckling and postbuckling response of the laminated composite plates and shells for various shear loading have been discussed. In addition, the effect of direction of shear load on the postbuckling behavior is studied. Numerical results and comparisons of the present results with those found in the literature for typical benchmark problems involving symmetric cross-ply laminated composites are found to be excellent and show the validity of the developed finite element model. The study is relevant to the simulation of barrels, pipes, wing surfaces, aircrafts, rockets and missile structures subjected to intense complex loading.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  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 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
  3. Bachir Bouiadjr, R., Bedia, E.A.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, 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  4. Balamurugan, V., Ganapathi, M. and Patel, B.P. (1998), "Postbuckling behavior of anisotropic laminated composite plates due to shear loading", Defense Sci. J., 48(4), 433-440. https://doi.org/10.14429/dsj.48.3970
  5. Bathe, K.J. and Dvorkin, E.N. (1986), "A formulation of general shell elements-The use of mixed interpolation of tensorial components", Int. J. Numer. Method. Eng., 22(3), 697-722. https://doi.org/10.1002/nme.1620220312
  6. Bathe, K.J., Lee, P.S. and Hiller, J.F. (2003), "Towards improving the MITC9 shell element", Comput. Struct., 81(8-11), 477-489. https://doi.org/10.1016/S0045-7949(02)00483-2
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  12. Bucalem, M.L. and Bathe, K.J. (1993), "Higher-order MITC general shell elements", Int. J. Numer. Method. Eng., 36(21), 3729-3754. https://doi.org/10.1002/nme.1620362109
  13. Chaiomphob, T., Kanok-Nukulchai, W. and Nishino, F. (1998), "An automatic arc-length control algorithm for tracing equilibrium paths of nonlinear structures", Struct. Eng. Earthq. Eng., JSCE, 5(1), 205-208.
  14. 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
  15. Gupta, A.K., Patel, B.P. and Nath, Y. (2014), "Postbuckling response of composite laminated plates with evolving damage", Int. J. Damage Mech., 23, 222-244. https://doi.org/10.1177/1056789513489322
  16. 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
  17. Han, S.C., Kim, K.D. and Kanok-Nukulchai, W. (2004), "An element-based 9-node resultant shell element for large deformation analysis of laminated composite plates and shells", Struct. Eng. Mech., Int. J., 18(6), 807-829. https://doi.org/10.12989/sem.2004.18.6.807
  18. Han, S.C., Kanok-Nukulchai, W. and Park, W.T. (2011), "A refined finite element for first-order plate and shell analysis", Struct. Eng. Mech., Int. J., 40(2), 191-213. https://doi.org/10.12989/sem.2011.40.2.191
  19. Han, S.C., Park, W.T. and Jung, W.Y. (2015), "A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface", Compos. Struct., 131, 1081-1089. https://doi.org/10.1016/j.compstruct.2015.06.025
  20. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.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, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  21. Huang, H.C. (1989), Static and Dynamic Analysis of Plates and Shells, Springer-Verlag, London, UK.
  22. Huang, H.C. and Hinton, E. (1986), "A new nine node degenerated shell element with enhanced membrane and shear interpolation", Int. J. Numer. Method Eng., 22(1), 73-92. https://doi.org/10.1002/nme.1620220107
  23. Jones, R.M. (1973), "Buckling and vibration of unsymmetrically laminated cross-ply rectangular plates", AIAA, 11, 1626-1632. https://doi.org/10.2514/3.50660
  24. Jung, W.Y. and Han, S.C. (2013), "An 8-node shell element for non-linear analysis of shells using the refined combination of membrane and shear interpolation functions", Math. Problem. Eng., 2013, 1-16.
  25. Jung, W.Y. and Han, S.C. (2014), "Shear buckling responses of laminated composite shells using a modified 8-node ANS shell element", Compos. Struct., 109, 119-129. https://doi.org/10.1016/j.compstruct.2013.10.055
  26. Kanok-Nukulchai, W. (1979), "A simple and efficient finite element for general shell analysis", Int. J. Numer. Method Eng., 14(2), 179-200. https://doi.org/10.1002/nme.1620140204
  27. Kanok-Nukulchai, W., Taylor, R.L. and Hughes, T.J.R. (1981), "A large deformation formulation for shell analysis by finite element method", Comput. Struct., 13(1-3), 19-27. https://doi.org/10.1016/0045-7949(81)90105-X
  28. Kim, K.D. and Park, T.H. (2002), "An 8-node assumed strain element with explicit integration for isotropic and laminated composite shells", Struct. Eng. Mech., Int. J., 13(4), 1-18. https://doi.org/10.12989/sem.2002.13.1.001
  29. Kim, K.D., Lomboy, G.R. and Han, S.C. (2003), "A co-rotational 8-node assumed strain shell element for postbuckling analysis of laminated composite plates and shells", Computat. Mech., 30(4), 330-342. https://doi.org/10.1007/s00466-003-0415-6
  30. Kosteletos, S. (1992), "Shear buckling response of laminated plates", Compos. Struct., 20, 147-154. https://doi.org/10.1016/0263-8223(92)90021-4
  31. Kudva, N.J. (1979), "Postbuckling studies of curved laminated composite panels", Ph.D. Thesis; Virginia Polytechnic Institute and State University, VA, USA.
  32. Kumar, D. and Singh, S.B. (2010), "Postbuckling strengths of composite laminate with various shaped cutouts under in-plane shear", Compos. Struct., 92(12), 2966-2978. https://doi.org/10.1016/j.compstruct.2010.05.008
  33. Lakshminarayana, H.V. and Kailash, K. (1989), "A shear deformable curved shell element of quadrilateral shape", Comput. Struct., 33(4), 987-1001. https://doi.org/10.1016/0045-7949(89)90434-3
  34. Lee, S.J. and Kanok-Nukulchai, W. (1998), "A nine-node assumed strain finite element for largedeformation analysis of laminated shells", Int. J. Numer. Method Eng., 42(5), 777-798. https://doi.org/10.1002/(SICI)1097-0207(19980715)42:5<777::AID-NME365>3.0.CO;2-P
  35. Ma, H. and Kanok-Nukulchai, W. (1989), "On the application of assumed strained methods", Proceedings of the Second East Asia-Pacific Conference on Structural Engineering and Construction, Chiang Mai, Thailand, January.
  36. MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Finite Elem. Anal. Des., 1(1), 3-20. https://doi.org/10.1016/0168-874X(85)90003-4
  37. MacNeal, R.H. and Harder, R.L. (1992), "Eight nodes or nine?", Int. J. Numer. Method. Eng., 33(5), 1049-1058. https://doi.org/10.1002/nme.1620330510
  38. 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, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  39. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", J. Appl. Mech., ASME, 51, 745-752. https://doi.org/10.1115/1.3167719
  40. Tanov, R. and Tabiei, A. (2000), "Simple correction to the first-order shear deformation shell finite element formulations", Finite Elem. Anal. Des., 35, 189-197. https://doi.org/10.1016/S0168-874X(99)00069-4
  41. 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, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  42. Vinson, J.R. and Chou, T.W. (1975), Composite Materials and their Use in Structures, Applied Science Publishers Ltd., London, UK.
  43. Whitney, J.M. (1969a), "Bending-extensional coupling in laminated plates under transverse loading", J. Compos. Mater., 3, 20-28. https://doi.org/10.1177/002199836900300102
  44. Whitney, J.M. (1969b), "The effect of transverse shear deformation on the bending of laminated plates", J. Compos. Mater., 3, 534-547. https://doi.org/10.1177/002199836900300316
  45. Wilkins, D.J. and Olson, F. (1974), "Shear buckling of advanced composite curved panels", J. Experim. Mech., 14(8), 326-330.
  46. Zhang, Y. and Matthews, F.L. (1983a), "Initial buckling of curved panels of generally layered composite materials", Compos. Struct., 1, 3-30. https://doi.org/10.1016/0263-8223(83)90014-4
  47. Zhang, Y. and Matthews, F.L. (1983b), "Postbuckling behaviour of curved panels of generally layered composite materials", Compos. Struct., 1, 115-135. https://doi.org/10.1016/0263-8223(83)90008-9
  48. Zhang, Y. and Matthews, F.L. (1985), "Large deflection behavior of simply supported laminated panels under in-plane loading", J. Appl. Mech., ASME, 52(3), 553-558. https://doi.org/10.1115/1.3169100
  49. 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
  50. Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method, Butterworth-Heinemann, London, UK.

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