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Serendipity and bubble plus hierarchic finite elements for thin to thick plates

  • Published : 2000.05.25
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Abstract

In this paper we deal with the numerical solution of the Reissner-Mindlin plate problem with the use of high order finite elements. In previous papers we have solved the problem using approximation spaces of Serendipity type, in order to minimize the number of internal degrees of freedom. Since further numerical experiences have evidenced that the addition of bubble functions improved the quality of the results we have modified the previous family of hierarchic finite elements, adding internal degrees of freedom, to make a systematic analysis of their performance. Of course, more degrees of freedom are introduced. Nonetheless the numerical results indicate that the reduction of the error outnumbers the increase of degrees of freedom and therefore bubble plus elements are preferable.

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References

  1. Babuska, I. (1988), "The p and h-p versions of the finite element method. The state of the art", Finite Elements: Theory and Application, D.L. Dwoyer, M.Y. Hussaini, R.G. Voigt (eds), Springer-Verlag, New York, 199-239.
  2. Babuska, I., Elman, H.C. (1993), "Performance of the h-p version of the finite element method with various elements", International J. Numerical Methods in Engineering, 36, 2503-2523. https://doi.org/10.1002/nme.1620361502
  3. Babuska, I., Scapolla, T. (1989), "Benchmark computation and performance evaluation for a rhombic plate bending problem", International J. Numerical Methods in Engineering, 28, 155-179. https://doi.org/10.1002/nme.1620280112
  4. Bathe, K.-J. (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, New Jersey
  5. Brezzi, F., Fortin, M. (1991), Mixed and Hybrid Finite Element Methods, Springer Verlag, New York.
  6. Ciarlet, P.G. (1978), The Finite Element Method Jor Elliptic Problems, North Holland, Amsterdam.
  7. Della Croce, L., Scapolla, T. (1992), "High order finite elements for thin to moderately thick plates", Computational Mechanics, 10, 263-279.
  8. Della Croce, L., Scapolla, T. (1992), "Hierarchic finite elements with selective and uniform reduced integration for Reissner-Mindlin plates", Computational Mechanics, 10, 121-131. https://doi.org/10.1007/BF00369856
  9. Della Croce, L., Scapolla, T. (1993), "Transverse shear strain approximation for Reissner-Mindlin plate with high order hierarchic finite elements", Mechanics Research Communications, 20, 1-7. https://doi.org/10.1016/0093-6413(93)90071-U
  10. Della Croce, L., Scapolla, T. (1992), "On the robustness of hierarchic finite elements for Reissner-Mindlin plates", Computer Methods in Applied Mechanics and Engineering, 101, 43-60. https://doi.org/10.1016/0045-7825(92)90014-B
  11. Della Croce, L., Scapolla, T. (1995), "Hierarchic and mixed interpolated finite elements for Reissner-Mindlin plates", Communications in Numerical Methods in Engineering, 11 , 549-562. https://doi.org/10.1002/cnm.1640110702
  12. Della Croce, L., Scapolla, T. (1999a), "Effect of mesh distortion on Serendipity and mixed finite elements solution of thin shells", International Journal of Applied Science and Computations, 5, 220-237.
  13. Della Croce, L., Scapolla, T. (1999b), "Solving cylindrical shell problems with a non-standard finite element", Mathematics in Computers and Simulation, in press, 50, 153-164. https://doi.org/10.1016/S0378-4754(99)00068-3
  14. Hughes, T.J.R. (1987), The Finite Element Method, Prentice-Hall, Englewood Cliffs, New Jersey.
  15. Perugia, I., Scapolla, T. (1997), "Optimal rectangular MITC finite elements for Reissner-Mindlin plates", Numerical Methods for Partial Differential Equations, 13, 575-585. https://doi.org/10.1002/(SICI)1098-2426(199709)13:5<575::AID-NUM8>3.0.CO;2-G
  16. Pinsky, P.M., Jasti, R.V (1989), "A mixed finite element formulation for Reissner-Mindlin plates based on the use of bubble functions", International J. Numerical Methods in Engineering, 28,1677-1702. https://doi.org/10.1002/nme.1620280715
  17. Szabo, B., Babuska, I. (1991), Finite Element Analysis, John Wiley & Sons, New York.
  18. Timoshenko, S., Woinowski-Krieger, S. (1970), Theory of Plates and Shells, McGraw-Hill, Singapore.
  19. Zienkiewicz, O.C., Taylor, R.L. (1989), The Finite Element Method, McGraw-Hill, London, I.
  20. Zienkiewicz, O.C., Taylor, R.L. (1991), The Finite Element Method, McGraw-Hill, London, II.

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  1. Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum vol.19, pp.5, 2002, https://doi.org/10.1108/02644400210435843