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Error analysis of mixed finite elements for cylindrical shells

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Abstract

In this paper, based on the Naghdi shell model, we analyze the uniform convergence of mixed finite element methods for cylindrical shell problems using macroelement techniques. We show that Taylor–Hood elements p 2-P 1 and P 1 iso P 2 are locking free elements for the model problems. Optimal error estimates are presented with these elements.

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References

  1. D.N. Arnold and F. Brezzi, Locking free finite elements for shells, Research Report AM 127, Pennsylvania State University, University Park, PA (1993); also: Math. Comp., to appear.

    Google Scholar 

  2. D.N. Arnold and R.S. Falk, A uniformly accurate finite element method for Reissner-Mindlin plate, SIAM J. Numer. Anal. 26 (1989) 1276–1290.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Bernadou, Méthodes d'Éléments Finis pour les Problèmes de Coques Minces (Masson, Paris, 1994).

    Google Scholar 

  4. F. Brezzi, K. Bathe and M. Fortin, Mixed-interpolated elements for Reissner-Mindlin plates, Internat. J. Numer. Methods Engrg. 28 (1989) 1787–1801.

    Article  MATH  MathSciNet  Google Scholar 

  5. F. Brezzi and M. Fortin, Numerical approximation of Mindlin-Reissner plates, Math. Comp. 47 (1986) 151–158.

    Article  MATH  MathSciNet  Google Scholar 

  6. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer, New York, 1991).

    Google Scholar 

  7. P. Clement, Approximation by finite element functions using local regularization, RAIRO Anal. Numér. 9 (1975) 33–76.

    MathSciNet  Google Scholar 

  8. R. Duran and E. Liberman, On mixed finite element methods for the Reissner-Mindlin plate model, Math. Comp. 58 (1992) 561–573.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Kirmse, Bending-dominated deformation of spherical shells: analysis and finite-element approximation, SIAM J. Numer. Anal. 30 (1993) 1015–1040.

    Article  MATH  MathSciNet  Google Scholar 

  10. Y. Leino and J. Pitkäranta, On the membrane locking of h-p finite element in a cylindrical shell problem, Internat. J. Numer. Methods Engrg. 37 (1994) 1057–1070.

    Article  Google Scholar 

  11. P.M. Naghdi, The theory of shells and plates, in: Handbuch der Physik, Vol. VI a-2 (Springer, Berlin, 1972) pp. 425–640.

    Google Scholar 

  12. J. Piila and J. Pitkäranta, Energy estimates relating different linear elastic models of a thin cylindrical shell I: the membrane-dominated case, SIAM J. Numer. Anal. 24 (1993) 1–22.

    MATH  Google Scholar 

  13. J. Piila and J. Pitkäranta, Energy estimates relating different linear elastic models of a thin cylindrical shell II: the case of free boundary, SIAM J. Math. Anal. 24 (1995) 820–849.

    Article  Google Scholar 

  14. J. Pitkäranta, Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates, Numer. Math. 53 (1988) 237–254.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Pitkäranta, The problem of membrane locking in finite element analysis of cylindrical shells, Numer. Math. 61 (1992) 523–542.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Centre de Recherches Mathématiques (CRM), Université de Montréal, Montréal, Canada, H3C 3J7

    Geng Yang & Michel C. Delfour

  2. Centre de Recherche en Calcul Appliqué (CERCA), 5160, boul. Décarie, suite 400, Montréal, Canada, H3X 2H9

    Geng Yang

  3. Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Canada, H3C 3J7

    Michel C. Delfour

  4. Département de Mathématiques et de Statistique, Université Laval, Québec, Canada, G1K 7P4

    Michel Fortin

Authors
  1. Geng Yang
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  2. Michel C. Delfour
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  3. Michel Fortin
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Yang, G., Delfour, M.C. & Fortin, M. Error analysis of mixed finite elements for cylindrical shells. Advances in Computational Mathematics 7, 261–277 (1997). https://doi.org/10.1023/A:1018998903567

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  • DOI: https://doi.org/10.1023/A:1018998903567

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