Structural Engineering and Mechanics

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Variable-node axisymmetric solid element and its application to adaptive mesh refinement

  • Published : 2001.04.25
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Abstract

This paper presents an effective application of a variable-node axisymmetric solid element designated as AQV (Axisymmetric Quadrilateral Variable-node element). The variable-node element with physical midside nodes helps to overcome some problems in connecting the different layer patterns on a quadrilateral mesh in the adaptive h-refinement. This element alleviates the necessity of imposing displacement constraints on irregular (hanging) nodes in order to enforce the inter-element compatibility. Therefore, the elements with variable mid-side nodes can be used effectively in the local mesh refinement for the axisymmetric structures which have stress concentrations. A modified Gaussian quadrature should be adopted to evaluate the stiffness matrices of the variable-node elements mainly because of the slope discontinuity of assumed displacement within the elements. Some numerical examples show the usefulness of variable-node axisymmetric elements in the practical application.

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References

  1. Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey.
  2. Hughes, T.J.R. (1987), The Finite Element Method - Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, New Jersey.
  3. Choi, C.K., and Park Y.M. (1989), "Nonconforming transition plate bending elements with variable mid-side nodes", Comput. and Struct., An Int. J., 32(2), 295-304. https://doi.org/10.1016/0045-7949(89)90041-2
  4. Choi, C.K., and Park, Y.M. (1992), "Transition plate bending elements for compatible mesh gradation", J. Eng. Mech. ASCE, 118(3), 462-480. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:3(462)
  5. Choi, C.K., and Kim, S.H. (1992), "Improvement of quadratic finite element for mindlin plate bending", Int. J. Numer Meth. Eng., 34(1), 197-208. https://doi.org/10.1002/nme.1620340112
  6. Choi, C.K., and Lee, N.H. (1993), "Three dimensional transition solid elements for adaptive mesh gradation", Struct. Eng. and Mech. An Int. J., 1(1), 61-74. https://doi.org/10.12989/sem.1993.1.1.061
  7. Zhu, J.Z., Zienkiewicz, O.C., and Wu, J. (1991), "A new approach to the development of automatic quadrilateral mesh generation", Int. J. Numer. Methods Eng., 32, 849-866. https://doi.org/10.1002/nme.1620320411
  8. Yunus, S.M., Pawlak, T.P., and Wheeler, M.J. (1990), "Application of the Zienkiewicz-Zhu error estimator for plate and shell analysis", Int. J. Numer. Meth. Eng., 29, 1281-1298. https://doi.org/10.1002/nme.1620290612
  9. Evans, A., Marchant, M.J., Szmelterm J., and Weatherill, N.P. (1991), "Adaptivity for compressible flow computations using point embedding on 2-D structured multiblock meshes", Int. J. Numer. Meth. Eng., 32, 895-919. https://doi.org/10.1002/nme.1620320413
  10. Abel, J.F., and Shephard, M.S. (1979), "An algorithm for multipoint constrains in the finite element analysis", Int. J. Numer. Methods Eng., 14, 464-467. https://doi.org/10.1002/nme.1620140312
  11. Cook, R.D. (1981), Concepts and Applications of Finite Element Analysis, 2nd edn., John Wiley & Sons, New York.
  12. Choi, C.K., and Lee, W.H. (1996), "Versatile variable-node flat-shell element", J. Eng. Mech., ASCE, 122(5), 432-441. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:5(432)
  13. Choi, C.K., and Lee, W.H. (1995), "Transition membrane elements with drilling freedom for local mesh refinements", Struct. Eng. and Mech. An Int. J., 3(1), 75-89. https://doi.org/10.12989/sem.1995.3.1.075
  14. Gupta, A.K. (1978), "A finite element for transition from a fine to a coarse grid", Int. J. Numer. Meth. Eng., 12, 35-45. https://doi.org/10.1002/nme.1620120104
  15. 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, 337-357. https://doi.org/10.1002/nme.1620240206
  16. Zienkiewicz, O.C., and Zhu, J.Z. (1989), "Error estimates and adaptive refinement for plate bending problems", Int. J. Numer. Meth. Eng., 28, 879-891. https://doi.org/10.1002/nme.1620280411
  17. Zienkiewicz, O.C., and Zhu, J.Z. (1992), "The superconvergent patch recovery and A posteriori error estimates. Part 1: The recovery technique", Int. J. Numer. Meth. Eng., 33, 1331-1364. https://doi.org/10.1002/nme.1620330702
  18. MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Finite Elements Anal. Des., 1, 1-20. https://doi.org/10.1016/0168-874X(85)90002-2
  19. Wanji, Chen, and Cheung, Y.K. (1996), "The nonconforming element method and refined hybrid element method for axisymmetric solid", Int. J. Numer. Meth. Eng., 39, 2509-2529. https://doi.org/10.1002/(SICI)1097-0207(19960815)39:15<2509::AID-NME963>3.0.CO;2-8

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