DOI QR코드

DOI QR Code

A new hierarchic degenerated shell element for geometrically non-linear analysis of composite laminated square and skew plates

  • 투고 : 2003.03.29
  • 심사 : 2003.12.01
  • 발행 : 2004.06.25

초록

This paper extends the use of the hierarchic degenerated shell element to geometric non-linear analysis of composite laminated skew plates by the p-version of the finite element method. For the geometric non-linear analysis, the total Lagrangian formulation is adopted with moderately large displacement and small strain being accounted for in the sense of von Karman hypothesis. The present model is based on equivalent-single layer laminate theory with the first order shear deformation including a shear correction factor of 5/6. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. A wide variety of linear and non-linear results obtained by the p-version finite element model are presented for the laminated skew plates as well as laminated square plates. A numerical analysis is made to illustrate the influence of the geometric non-linear effect on the transverse deflections and the stresses with respect to width/depth ratio (a/h), skew angle (${\beta}$), and stacking sequence of layers. The present results are in good agreement with the results in literatures.

키워드

참고문헌

  1. Actis, R.L., Szabo, B.A. and Schwab, Ch. (1999), "Hierarchic models for laminated plates and shells", Comput. Meth. Appl. Mech. Engrg., 172, 79-107. https://doi.org/10.1016/S0045-7825(98)00226-6
  2. Fares, M.E. (1999), "Non-linear bending analysis of composite laminated plates using a refined first-order theory", Composite Structures, 46, 257-266. https://doi.org/10.1016/S0263-8223(99)00062-8
  3. Holzer, S. and Yosibash, Z. (1996), "The p-version of finite element methods in incremental elasto-plastic analysis", Numer. Meth. Engng, 39, 1859-1878. https://doi.org/10.1002/(SICI)1097-0207(19960615)39:11<1859::AID-NME932>3.0.CO;2-7
  4. Krause, R., Mucke, R. and Rank, E. (1995), "hp-Version finite elements for geometrically nonlinear problems", Communications in Numer. Meth. Eng., 101, 887-897.
  5. Liu, J.H. and Surana, K.S. (1995), "A p-version curved shell element based on piecewise hierarchical displacement approximation for laminated composite plates and shells", Comput. Struct., 55(3), 527-542. https://doi.org/10.1016/0045-7949(95)98878-T
  6. Liu, R.H., Xu, J.C. and Zhai, S.Z. (1997), "Large-deflection bending of symmetrically laminated rectilinearly orthotropic elliptical plates including transverse shear", Archiv. Appl. Mech., 67, 507-520. https://doi.org/10.1007/s004190050135
  7. Madenci, E. and Barut, A. (1994), "A free-formulation-based flat shell element for non-linear analysis of composite structures", Numer. Meth. Engng., 37, 3825-3842. https://doi.org/10.1002/nme.1620372206
  8. Owen, D.R.J. and Figuerias, J.A. (1983), "Anisotropic elasto-plastic finite element analysis of thick and thin plates and shells", Numer. Meth. Engng., 19, 541-566. https://doi.org/10.1002/nme.1620190407
  9. Owen, D.R.J. and Li, Z.H. (1987), "A refined analysis of laminated plates by finite element displacement methods-I. fundamentals and static analysis", Comput. Struct., 26(6), 907-914. https://doi.org/10.1016/0045-7949(87)90107-6
  10. Rank, E., Krause, R. and Preusch, K. (1998), "On the accuracy of p-version elements for the Reissner-Mindlin plate problem", Numer. Meth. Engng, 43, 51-67. https://doi.org/10.1002/(SICI)1097-0207(19980915)43:1<51::AID-NME382>3.0.CO;2-T
  11. Reddy, J.N. (1984), "Exact solution of moderately thick laminated shells", Engineering Mechanics, ASCE, 110, 794-809. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:5(794)
  12. Reddy, J.N. (1997), Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press.
  13. Schwartz, M. (1992), Composite Materials Handbook. 2nd Ed., McGraw-Hill.
  14. Szabo, B. and Babuska, I. (1991), Finite Element Analysis, John Wiley & Sons, Inc.
  15. Timoshenko, S. and Woinowsky, K.S. (1959), Theory of Plates and Shells. 2nd Ed., McGraw-Hill.
  16. Woo, K.S. (1993), "Robustness of hierarchical elements formulated by integrals of Legendre polynomials", Comput. Struct., 49, 421-426. https://doi.org/10.1016/0045-7949(93)90043-D

피인용 문헌

  1. Analysis of Cantilever Plates with Stepped Section Using p-Convergent Transition Element for Solid-to-Shell Connections vol.14, pp.6, 2011, https://doi.org/10.1260/1369-4332.14.6.1167
  2. A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates vol.52, pp.12, 2010, https://doi.org/10.1016/j.ijmecsci.2010.07.008
  3. A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells vol.101, 2015, https://doi.org/10.1016/j.finel.2015.03.004
  4. Analysis of cracked aluminum plates with one-sided patch repair using p-convergent layered model vol.46, pp.5, 2010, https://doi.org/10.1016/j.finel.2010.01.008