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Variable-node non-conforming membrane elements

  • Choi, Chang-Koon (Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology) ;
  • Lee, Tae-Yeol (Department of Civil and Environmental Engineering, University of California)
  • Received : 2003.01.24
  • Accepted : 2003.07.15
  • Published : 2003.10.25

Abstract

Non-conforming membrane elements which have variable number of mid-side nodes with drilling degrees of freedom and which is designated as NMDx have been presented in this paper. The non-conforming elements with variable number of mid-side nodes can be efficiently used in the local mesh refinement for the in-plane structures. To guarantee the developed elements always pass the patch test, the direct modification method is incorporated into the element formulation. Detailed numerical tests in this study show the validity of the variable node NC elements developed in this study and a wide applicability of these elements to practical problems.

Keywords

References

  1. Argyris, J.H., Hease, M. and Mlejnek, H.P. (1980), "On an unconventional but natural formulation of a stiffness matrix", Comp. Meth. Appl. Mech. Eng., 22, 1-22. https://doi.org/10.1016/0045-7825(80)90048-1
  2. Bathe, K.J. and Dvorkin, E.N. (1986), "A formulation of general shell elements - the use of mixed interpolation of tensorial components", Int. J. Num. Meth. Eng., 22, 697-722. https://doi.org/10.1002/nme.1620220312
  3. Chen, W. and Cheung, Y.K. (1997), "Refined non-conforming quadrilateral thin plate bending element", Int. J. Num. Meth. Eng., 40, 3919-3935. https://doi.org/10.1002/(SICI)1097-0207(19971115)40:21<3919::AID-NME243>3.0.CO;2-A
  4. Cheung, Y.K. and Chen, W. (1995), "Refined nine-parameter triangular thin plate bending element by using refined direct stiffness methods", Int. J. Num. Meth. Eng., 38, 283-298. https://doi.org/10.1002/nme.1620380208
  5. Choi, C.K. and Park, Y.M. (1989), "Nonconforming transition plate bending elements with variable midside nodes", Comput. Struct., 32, 295-304. https://doi.org/10.1016/0045-7949(89)90041-2
  6. Choi, C.K., Chung, K.Y. and Lee, T.Y. (2001), "A direct modification method for strains due to non-conforming modes", Struct. Eng. Mech., 11(3), 325-340. https://doi.org/10.12989/sem.2001.11.3.325
  7. Choi, C.K. and Lee, T.Y. (2002a), "Non-conforming modes for improvement of finite element performance", Struct. Eng. Mech., 14(5), 595-610. https://doi.org/10.12989/sem.2002.14.5.595
  8. Choi, C.K. and Lee, T.Y. (2002b), "Directly modified non-conforming modes for Mindlin plate-bending elements" J. Eng. Mech. ASCE, submitted.
  9. Choi, C.K., Lee, T.Y. and Chung, K.Y. (2002c), "Direct modification for non-conforming elements with drilling DOF", Int. J. Num. Meth. Eng., 55, 1463-1476. https://doi.org/10.1002/nme.550
  10. Choi, C.K. and Lee, T.Y. (2003), "Efficient remedy for membrane locking of 4-node flat shell elements by nonconforming modes", Comp. Meth. Appl. Mech. Eng., 192, 1961-1971. https://doi.org/10.1016/S0045-7825(03)00203-2
  11. Choi, C.K. and Lee, W.H. (1995), "Transition membrane elements with drilling freedom for local mesh refinements", Struct. Eng. Mech., 3(1), 75-89. https://doi.org/10.12989/sem.1995.3.1.075
  12. Choi, C.K. and Lee, W.H. (1996), "Versatile variable-node flat shell element", J. Eng. Mech. ASCE, 122, 432-441. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:5(432)
  13. Choi, C.K. and Paik, J.G. (1994), "An efficient four node degenerated shell element based on the assumed covariant strain", Struct. Eng. Mech., 2(1), 17-34. https://doi.org/10.12989/sem.1994.2.1.017
  14. Choi, C.K. and Schnobrich, W.C. (1975), "Nonconforming finite element analysis of shells", J. Eng. Mech. Div. ASCE, 101, 447-464.
  15. Fellipa, C.A. and Bergan, P.G.. (1987), "A triangular bending element based on energy-orthogonal free formulation", Comp. Meth. Appl. Mech. Eng., 61, 129-160. https://doi.org/10.1016/0045-7825(87)90001-6
  16. Iura, M. and Atluri, S.N. (1992), "Formulation of a membrane finite element with drilling degrees of freedom", Comput. Mech., 9, 417-428. https://doi.org/10.1007/BF00364007
  17. Kim, S.H. and Choi, C.K. (1992), "Improvement of quadratic finite-element for Mindlin plate bending", Int. J. Num. Meth. Eng., 34(1), 197-208. https://doi.org/10.1002/nme.1620340112
  18. Lee, T.Y. and Choi, C.K. (2002), "A new quadrilateral 5-node non-conforming membrane element with drilling DOF", Struct. Eng. Mech., 14(6), 699-712. https://doi.org/10.12989/sem.2002.14.6.699
  19. MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Finite Elem. Anal. Des., 1, 3-20. https://doi.org/10.1016/0168-874X(85)90003-4
  20. Park, Y.M. and Choi, C.K. (1997), "The patch tests and convergence for nonconforming Mindlin plate bending elements", Struct. Eng. Mech., 5(4), 471-490. https://doi.org/10.12989/sem.1997.5.4.471
  21. Taylor, R.L., Beresford, P.L. and Wilson, E.L. (1976), "A non-conforming element for stress analysis", Int. J. Num. Meth. Eng., 10, 1211-1219. https://doi.org/10.1002/nme.1620100602
  22. Wilson, E.L. and Ibrahimbegovic, A. (1990), "Use of incompatible displacement modes for the calculation of element stiffnesses or stresses", Finite Elem. Anal. Des., 31, 229-241.
  23. Wilson, E.L., Taylor, R.L., Doherty, W.P. and Ghaboussi, J. (1973), "Incompatible displacement models", in Numerical and Computer Models in Structural Mechanics, eds. S.J. Fenves, N. Perrone, A.R. Robinson, and W.C. Schnobrich, Academic Press, New York, 43-57.