Structural Engineering and Mechanics

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Large deflection analysis of laminated composite plates using layerwise displacement model

  • Cetkovic, M. (Faculty of Civil Engineering, University of Belgrade) ;
  • Vuksanovic, Dj. (Faculty of Civil Engineering, University of Belgrade)
  • Received : 2010.12.20
  • Accepted : 2011.08.18
  • Published : 2011.10.25
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Abstract

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

Keywords

References

  1. Argyris, J. and Tanek, L. (1994), "Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method", Comput. Meth. Appl. Mech. Eng., 113, 207-251. https://doi.org/10.1016/0045-7825(94)90047-7
  2. Altenbach, H., Altenbach, J. and Kissing, W. (2004), Mechanics of Composite Structural Elements, Springer Verlag, Berlin Heidelberg New York.
  3. Arciniega, R.A. and Reddy, J.N. (2007), "Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures", Comput. Meth. Appl. Mech. Eng., 196(4-6), 1048-1073. https://doi.org/10.1016/j.cma.2006.08.014
  4. Arciniega, R.A. and Reddy, J.N. (2007), "Large deformation analysis of functionally graded shells", Int. J. Solids Struct., 44(6), 2036-2052. https://doi.org/10.1016/j.ijsolstr.2006.08.035
  5. Barbero, E.J. and Reddy, J.N. (1990), "Nonlinear analysis of composite laminates using a generalized laminated plate theory", AIAA J., 28(11), 1987-1994. https://doi.org/10.2514/3.10509
  6. Bathe, K.J. (1996), Finite Element Procedures in Engineering Analysis, Prentice Hall.
  7. Hinton, E., Vuksanovic, Dj. and Huang, H. (1988), Finite Element Free Vibrations and Buckling Analysis of Initially Stressed Mindlin Plates, In: Hinton E. editors. Numerical Methods and Software for Dynamic Analysis of Plates and Shells, Swansea, Pineridge Press, UK, 93-167.
  8. Hughes, T.J.R. (1987), The Finite Element Method, Prentice Hall.
  9. Cetkovic, M. (2005), Application of Finite Element Method on Generalized Laminated Plate Theory, Master Thesis, in serbian, Faculty of Civil Engineering in Belgrade, Serbia.
  10. Cetkovic, M. and Vuksanovi , Dj. (2009), "Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model", Compos. Struct., 88(2), 219-227. https://doi.org/10.1016/j.compstruct.2008.03.039
  11. Kuppusamy, T., Nanda, A. and Reddy, J.N. (1984), "Materially nonlinear analysis of laminated composite plates", Compos. Struct., 2(4), 315-328. https://doi.org/10.1016/0263-8223(84)90003-5
  12. Kuppusamy, T. and Reddy, J.N. (1984), "A three-dimensional nonlinear analysis of cross-ply rectangular composite plates", Comput. Struct., 18(2), 263-272. https://doi.org/10.1016/0045-7949(84)90124-X
  13. Lee, S.J., Reddy, J.N. and Rostam-Abadi, F. (2006), "Nonlinear finite element analysis of laminated composite shells with actuating layers", Finite Elem. Analy. Des., 43(1), 1-21. https://doi.org/10.1016/j.finel.2006.04.008
  14. Laulusa, A. and Reddy, J.N. (2004), "On shear and extensional locking in nonlinear composite beams", Eng. Struct., 26(2), 151-170. https://doi.org/10.1016/S0141-0296(03)00175-5
  15. Malvern, L.E. (1969), Introduction to the Mechanics of a Continuous Medium, Prentice Hall.
  16. Naserian-Nik, A.M. and Tahani, M. (2010), "Free vibration analysis of moderately thick rectangular laminated composite plates with arbitrary boundary conditions", Struct. Eng. Mech., 35(2), 217-240. https://doi.org/10.12989/sem.2010.35.2.217
  17. Ochoa, O.O. and Reddy, J.N. (1992) Finite Element Analysis of Composite Laminates, Kluwer Academic Publishers.
  18. Polat, C. and Ulucan, Z. (2007), "Geometrically non-linear analysis of axisymmetric plates and shells", Int. J. Sc. Technol., 2(1), 33-40.
  19. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermo elastic analysis of functionally graded ceramic-metal plates", Solids Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  20. Putcha, N.S. and Reddy, J.N. (1986), "A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates", Comput. Struct., 22(4), 529-538. https://doi.org/10.1016/0045-7949(86)90002-7
  21. Reddy, J.N., Barbero, E.J. and Teply, J.L. (1989), "A plate bending element based on a generalized laminated plate theory", Int. J. Numer. Meth. Eng., 28, 2275-2292. https://doi.org/10.1002/nme.1620281006
  22. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates-theory and Analysis, CRC press.
  23. Reddy, J.N. (2008), An Introduction to Continuum Mechanics, Cambridge University Press.
  24. Reddy, J.N. and Chao, W.C. (1981), "Non-linear bending of thick rectangular, laminated composite plates", Int. J. Nonlin. Mech., 16(3/4), 291-301. https://doi.org/10.1016/0020-7462(81)90042-1
  25. Reddy, J.N. and Haung, C.L. (1981), "Nonlinear axisymmetric bending of annular plates with varying thickness", Int. J. Solids Struct., 17(8), 811-825. https://doi.org/10.1016/0020-7683(81)90090-1
  26. Reddy, J.N. and Chao, W.C. (1983), "Nonlinear bending of bimodular-material plates", Int. J. Solids Struct., 19(3), 229-237. https://doi.org/10.1016/0020-7683(83)90059-8
  27. Reddy, Y.S.N., Dakshina Moorthy, C.M. and Reddy, J.N. (1995), "Non-linear progressive failure analysis of laminated composite plates", Int. J. Nonlin. Mech., 30(5), 629-649. https://doi.org/10.1016/0020-7462(94)00041-8
  28. Reddy, J.N. (1984), "A refined nonlinear theory of plates with transverse shear deformation", Int. J. Solids Struct., 20(9-10), 881-896. https://doi.org/10.1016/0020-7683(84)90056-8
  29. Tanriover, H. and Senocak, E. (2004), "Large deflection analysis of unsymmetrically laminated composite plates: analytical-numerical type approach", Int. J. Nonlin. Mech., 39, 1385-1392. https://doi.org/10.1016/j.ijnonlinmec.2004.01.001
  30. Thankam, V.S., Singh, G., Rao, G.V. and Rath, A.K. (2003), "Shear flexible element based on coupled displacement field for large deflection analysis of laminated plates", Comput. Struct., 81, 309-320. https://doi.org/10.1016/S0045-7949(02)00450-9
  31. Thankam, V.S., Singh, G., Rao, G.V. and Rath, A.K. (2003), "Shear flexible element based on coupled displacement field for large deflection analysis of laminated plates", Comput. Struct., 81, 309-320. https://doi.org/10.1016/S0045-7949(02)00450-9
  32. Vuksanovi, Dj. (2000), "Linear analysis of laminated composite plates using single layer higher-order discrete models", Compos. Struct., 48, 205-211. https://doi.org/10.1016/S0263-8223(99)00096-3
  33. Zhang, Y., Wang, S. and Petersson, B. (2003), "Large deflection analysis of composite laminates", J. Mater. Pro. Technol., 138, 34-40. https://doi.org/10.1016/S0924-0136(03)00045-1
  34. Zhang, Y.X. and Kim, K.S. (2006), "Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements", Compos. Struct., 72, 301-310. https://doi.org/10.1016/j.compstruct.2005.01.001
  35. Zhang, Y.X. and Kim, K.S. (2005), "A simple displacement-based 3-node triangular element for linear and geometrically nonlinear analysis of laminated composite plates", Comput. Meth. Appl. Mech. Eng., 194, 4607- 4632. https://doi.org/10.1016/j.cma.2004.11.011

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