Structural Engineering and Mechanics

  • 제39권3호
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  • Pages.339-360
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  • 2011
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

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New slave-node constraints and element for adaptive analysis of C0 plates

  • Sze, K.Y. (Department of Mechanical Engineering, The University of Hong Kong) ;
  • Wu, D. (Department of Mechanical Engineering, The University of Hong Kong)
  • 투고 : 2010.06.18
  • 심사 : 2011.04.08
  • 발행 : 2011.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

In the h-type adaptive analysis, when an element is refined or subdivided, new nodes are added. Among them are the transition nodes which are the corner nodes of the new elements formed by subdivision and, simultaneously, the mid-side nodes of the adjacent non-subdivided elements. To secure displacement compatibility, the slave-node approach in which the DOFs of a transition node are constrained by those of the adjacent nodes had been used. Alternatively, transition elements which possess the transition nodes as active mid-side/-face nodes can be used. For C0 plate analyses, the conventional slave-node constraints and the previously derived ANS transition elements are implemented. In both implementations, the four-node element is the ANS element. With reference to the predictions of the transition elements, the slave-node approach not only delivers erroneous results but also fails the patch test. In this paper, the patch test failure is resolved by developing a set of new constraints with which the slave-node approach surpasses the transition-element approach. The accuracy of the slave-node approach is further improved by developing a hybrid four-node element in which the assumed moment and shear force modes are in strict equilibrium.

키워드

참고문헌

  1. Ayad, R., Dhatt, G. and Batoz, J.L. (1998), "A new hybrid-mixed variational approach for Reissner-Mindlin plates. The MiSP model", Int. J. Numer. Meth. Eng., 42(7), 1149-1179. https://doi.org/10.1002/(SICI)1097-0207(19980815)42:7<1149::AID-NME391>3.0.CO;2-2
  2. Bathe, K.J. and Dvorkin, E.N. (1985), "A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation", Int. J. Numer. Meth. Eng., 21(2), 367-383. https://doi.org/10.1002/nme.1620210213
  3. Batoz, J.L. (1982), "Explicit formulation for an efficient triangular plate-bending element", Int. J. Numer. Meth. Eng., 18(7), 1077-1089. https://doi.org/10.1002/nme.1620180711
  4. Batoz, J.L. and Tahar, M.B. (1982), "Evaluation of a new quadrilateral thin plate bending element", Int. J. Numer. Meth. Eng., 18(11), 1655-1677. https://doi.org/10.1002/nme.1620181106
  5. Choi, C.K. and Lee, E.J. (2004), "Nonconforming variable-node axisymmetric solid element", J. Eng. Mech., 130(5), 578-588. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:5(578)
  6. Choi, C.K. and Park, Y.M. (1992), "Transition plate-bending elements for compatible mesh gradation", J. Eng. Mech., 118(3), 462-480. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:3(462)
  7. Choi, C.K. and Park, Y.M. (1997), "Conforming and nonconforming transition plate bending elements for an adaptive h-refinement", Thin Wall. Struct., 28(1), 1-20. https://doi.org/10.1016/S0263-8231(97)00007-4
  8. Devloo, P., Oden, J.T. and Strouboulis, T. (1987), "Implementation of an adaptive refinement technique for the SUPG algorithm", Comput. Meth. Appl. Mech. Eng., 61(3), 339-358. https://doi.org/10.1016/0045-7825(87)90099-5
  9. Donea, J. and Lamain, L.G. (1987), "A modified representation of transverse shear in $C^{0}$ quadrilateral plate elements", Comput. Meth. Appl. Mech. Eng. 63(2), 183-207. https://doi.org/10.1016/0045-7825(87)90171-X
  10. Dvorkin, E.N. and Bathe, K.J. (1984), "A continuum mechanics based four-node shell element for general nonlinear analysis", Eng. Comput. (Swansea, Wales), 1(1), 77-88. https://doi.org/10.1108/eb023562
  11. Gupta, A.K. (1978), "A finite element for transition from a fine to a coarse grid", Int. J. Numer. Meth. Eng., 12(1), 35-45. https://doi.org/10.1002/nme.1620120104
  12. Huang, H.C. and Hinton, E. (1986), "A new nine node degenerated shell element with enhanced membrane and shear interpolation", Int. J. Numer. Meth. Eng., 22(1), 73-92. https://doi.org/10.1002/nme.1620220107
  13. Hughes, J.R. (1987), "The finite element method : linear static and dynamic finite element analysis", Englewood Cliffs, Prentice-Hall.
  14. Lee, C.K. and Lo, S.H. (1999), "A full 3D finite element analysis using adaptive refinement and PCG solver with back interpolation", Comput. Meth. Appl. Mech. Eng., 170, 39-64. https://doi.org/10.1016/S0045-7825(98)00188-1
  15. Lee, S.W. and Pain, T.H.H. (1978), "Improvement of plate and shell finite elements by mixed formulations", AIAA J., 16(1), 29-34. https://doi.org/10.2514/3.60853
  16. Lee, S.W., Wong, S.C. and Rhiu, J.J. (1985), "Study of the nine-node mixed formulation finite element for thin plates and shells", Comput. Struct., 21(6), 1325-1334. https://doi.org/10.1016/0045-7949(85)90186-5
  17. Lo, S.H., Wan, K.H. and Sze, K.Y. (2006), "Adaptive refinement analysis using hybrid-stress transition elements", Comput. Struct., 84, 2212-2230. https://doi.org/10.1016/j.compstruc.2006.08.013
  18. MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Finite Elem. Analy. Des., 1(1), 3-20. https://doi.org/10.1016/0168-874X(85)90003-4
  19. Park, K.C. and Stanley, G.M. (1986), "A curved $C^{0}$ shell element based on assumed natural coordinate strains", J. Appl. Mech-T. ASME, 53(2), 278-290. https://doi.org/10.1115/1.3171752
  20. Saleeb, A.F. and Chang, T.Y. (1987), "An efficient quadrilateral element for plate bending analysis", Int. J. Numer. Meth. Eng., 24(6), 1123-1155. https://doi.org/10.1002/nme.1620240607
  21. Simo, J.C. and Rifai, M.S. (1990), "Class of mixed assumed strain methods and the method of incompatible modes", Int. J. Numer. Meth. Eng., 29(8), 1595-1638. https://doi.org/10.1002/nme.1620290802
  22. Somervaille, I.J. (1973), "A technique for mesh grading applied to conforming plate bending finite elements", Int. J. Numer. Meth. Eng., 6(2), 310-312.
  23. Sze, K.Y. (1994a), "An explicit hybrid-stabilized 9-node Lagrangian shell element", Comput. Meth. Appl. Mech. Eng., 117(3-4), 361-379. https://doi.org/10.1016/0045-7825(94)90123-6
  24. Sze, K.Y. (1994b), "Minimal assumed moments and optimal local coordinates for plate elements based upon the complementary energy functional", Comput. Mech., 14(6), 586-595. https://doi.org/10.1007/BF00350838
  25. Sze, K.Y. and Chow, C.L. (1991a), "Incompatible element for axisymmetric structure and its modification by hybrid method", Int. J. Numer. Meth. Eng., 31(2), 385-405. https://doi.org/10.1002/nme.1620310211
  26. Sze, K.Y. and Chow, C.L. (1991b), "Efficient hybrid quadrilateral Kirchhoff plate bending element", Int. J. Numer. Meth. Eng., 32(1), 149-169. https://doi.org/10.1002/nme.1620320109
  27. Sze, K.Y. and Zhu, D. (1998), "Quadratic assumed natural strain triangular element for plate bending analysis", Commun. Numer. Meth. Eng., 14(11), 1013-1025. https://doi.org/10.1002/(SICI)1099-0887(199811)14:11<1013::AID-CNM204>3.0.CO;2-V
  28. Taylor, R.L., Beresford, P.J. and Wilson, E.L. (1976), "A non-conforming element for stress analysis", Int. J. Numer. Meth. Eng., 10(6), 1211-1219. https://doi.org/10.1002/nme.1620100602
  29. Wan, K.H. (2004), "Transition finite elements for mesh refinement in plane and plate bending analysis", M.Ph. Thesis, Department of Mechanical Engineering, The University of Hong Kong.
  30. Weissman, S.L. and Taylor, R.L. (1990), "Resultant fields for mixed plate bending elements", Comput. Meth. Appl. Mech. Eng., 79(3), 321-355. https://doi.org/10.1016/0045-7825(90)90067-V
  31. Yuan, K.Y., Huang, Y.S. and Pian, T.H.H. (1993), "New strategy for assumed stresses for 4-node hybrid stress membrane element", Int. J. Numer. Meth. Eng., 36(10), 1747-1763. https://doi.org/10.1002/nme.1620361009
  32. Zienkiewicz, O.C. and Zhu, J.Z. (1987), "A simple error estimator and adaptive procedure for practical engineering analysis", Int. J. Numer. Meth. Eng., 24(2), 337-357. https://doi.org/10.1002/nme.1620240206
  33. Zienkiewicz, O.C. and Zhu, J.Z. (1992a), "Superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique", Int. J. Numer. Meth. Eng., 33(7), 1331-1364. https://doi.org/10.1002/nme.1620330702
  34. Zienkiewicz, O.C. and Zhu, J.Z. (1992b), "Superconvergent patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity", Int. J. Numer. Meth. Eng., 33(7), 1365-1382. https://doi.org/10.1002/nme.1620330703