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Approximation technics for an unsteady dynamic Koiter shell. (English) Zbl 1140.74022

Summary: We propose a mixed formulation in dynamical elasticity of shells which allows a locking-free finite element approximation for bending-dominated Koiter shells.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
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References:

[1] D. Chapelle and R. Stenberg, “Stabilized finite element formulations for shells in a bending dominated state,” SIAM Journal on Numerical Analysis, vol. 36, no. 1, pp. 32-73, 1999. · Zbl 0940.74059 · doi:10.1137/S0036142996302918
[2] D. Chapelle, “Etude du verrouillage numérique de quelques méthodes d/éléments finis pour les coques,” Tech. Rep. 2740, INRIA, Le Chesnay Cedex, France, 1995.
[3] D. N. Arnold and F. Brezzi, “Locking-free finite element methods for shells,” Mathematics of Computation, vol. 66, no. 217, pp. 1-14, 1997. · Zbl 0854.65095 · doi:10.1090/S0025-5718-97-00785-0
[4] F. Brezzi, “Towards shell elements avoiding locking in the general case,” in Shells, Mathematical Modelling and Scientific Computing, M. Bernadou, P. G. Ciarlet, and J. M. Viano, Eds., vol. 105 of Courses and Conferences of the University of Santiago de Compostela, pp. 45-48, Universidade de Santiago de Compostela, Santiago de Compostela, Chile, 1997. · Zbl 1052.74582
[5] J. H. Bramble and T. Sun, “A locking-free finite element method for Naghdi shells,” Journal of Computational and Applied Mathematics, vol. 89, no. 1, pp. 119-133, 1998. · Zbl 0913.73065 · doi:10.1016/S0377-0427(97)00234-3
[6] G. Yang, M. C. Delfour, and M. Fortin, “Error analysis of mixed finite elements for cylindrical shells,” in Plates and Shells (Québec, QC, 1996), vol. 21 of CRM Proc. Lecture Notes, pp. 267-280, American Mathematical Society, Providence, RI, USA, 1999. · Zbl 0958.74075
[7] M. Bernadou, Méthodes d/éléments finis pour les problèmes de coques minces, Masson, Paris, France, 1994.
[8] A. Blouza and H. Le Dret, “Existence et unicité pour le modèle de Koiter pour une coque peu régulière,” Comptes Rendus de l/Académie des Sciences, vol. 319, no. 10, pp. 1127-1132, 1994. · Zbl 0813.73039
[9] M. Bernadou and P. G. Ciarlet, “Sur l/ellipticité du modèle linéaire de coques de W. T. Koiter,” in Computing Methods in Applied Sciences and Engineering (Second Internat. Sympos., Versailles, 1975)-Part 1, vol. 134 of Lecture Notes in Econom. and Math. Systems, pp. 89-136, Springer, Berlin, Germany, 1976. · Zbl 0356.73066
[10] P. G. Ciarlet, Introduction to Linear Shell Theory, vol. 1 of Series in Applied Mathematics (Paris), Gauthier-Villars, Paris, France; North-Holland, Amsterdam, The Netherlands, 1998. · Zbl 0912.73001
[11] A. Blouza, F. Brezzi, and C. Lovadina, “Sur la classification des coques linéairement élastiques,” Comptes Rendus de l/Académie des Sciences, vol. 328, no. 9, pp. 831-836, 1999. · Zbl 0943.74036 · doi:10.1016/S0764-4442(99)80281-X
[12] L. Xiao, “Asymptotic analysis of dynamic problems for linearly elastic shells-justification of equations for dynamic Koiter shells,” Chinese Annals of Mathematics, vol. 22, no. 3, pp. 267-274, 2001. · Zbl 0986.35022 · doi:10.1142/S0252959901000279
[13] J.-L. Lions, “Quelques méthodes de résolution des problèmes aux limites non linéaires,” Dunod, Paris, France, 1969. · Zbl 0189.40603
[14] X. Zhang, “Two-level Schwarz methods for the biharmonic problem discretized conforming C1 elements,” SIAM Journal on Numerical Analysis, vol. 33, no. 2, pp. 555-570, 1996. · Zbl 0856.65133 · doi:10.1137/0733029
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