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
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.
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.
M. Bernadou, Méthodes d'Éléments Finis pour les Problèmes de Coques Minces (Masson, Paris, 1994).
F. Brezzi, K. Bathe and M. Fortin, Mixed-interpolated elements for Reissner-Mindlin plates, Internat. J. Numer. Methods Engrg. 28 (1989) 1787–1801.
F. Brezzi and M. Fortin, Numerical approximation of Mindlin-Reissner plates, Math. Comp. 47 (1986) 151–158.
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer, New York, 1991).
P. Clement, Approximation by finite element functions using local regularization, RAIRO Anal. Numér. 9 (1975) 33–76.
R. Duran and E. Liberman, On mixed finite element methods for the Reissner-Mindlin plate model, Math. Comp. 58 (1992) 561–573.
A. Kirmse, Bending-dominated deformation of spherical shells: analysis and finite-element approximation, SIAM J. Numer. Anal. 30 (1993) 1015–1040.
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.
P.M. Naghdi, The theory of shells and plates, in: Handbuch der Physik, Vol. VI a-2 (Springer, Berlin, 1972) pp. 425–640.
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.
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.
J. Pitkäranta, Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates, Numer. Math. 53 (1988) 237–254.
J. Pitkäranta, The problem of membrane locking in finite element analysis of cylindrical shells, Numer. Math. 61 (1992) 523–542.
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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