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A hybrid formulation for Naghdi’s shell model. (Une formulation hybride du modèle de coque de Naghdi.) (French. Abridged English version) Zbl 1410.74043

Summary: We present a new version of the Naghdi model for shells with curvature discontinuities. The unknowns - the displacement and the rotation of the normal to the shell midsurface - are described respectively in Cartesian and local covariant or contravariant basis. Our purpose here is to consider a constraint-free formulation instead of the one introduced by A. Blouza et al. [SIAM J. Numer. Anal. 44, No. 2, 636–654 (2006; Zbl 1109.74048)], where the tangency character of the rotation is enforced by penalization or by duality. This new version enables us, in particular, to approximate by conforming finite elements the solution with less degrees of freedom compared to the method of Blouza et al. [loc. cit.].

MSC:

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

Citations:

Zbl 1109.74048
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References:

[1] Bernadou, M.; Ciarlet, P. G.; Miara, B., Existence theorem for two-dimensional linear shell theories, J. Elast., 34, 111-138 (1994) · Zbl 0808.73045
[2] Bernardi, C.; Blouza, A.; Hecht, F.; Le Dret, H., A posteriori analysis of finite element discretizations of a Naghdi shell model, IMA J. Numer. Anal. (2012)
[3] Blouza, A., Existence et unicité pour le modèle de Naghdi pour une coque peu régulière, C. R. Acad. Sci. Paris, Ser. I, 324, 839-844 (1997) · Zbl 0878.73037
[4] Blouza, A.; Le Dret, H., Existence and uniqueness for the linear Koiter model for shells with little regularity, Q. Appl. Math., LVII, 2, 317-337 (1999) · Zbl 1025.74020
[5] Blouza, A.; Le Dret, H., Nagdhiʼs shell model: Existence, uniqueness and continuous dependence on the midsurface, J. Elast., 64, 199-216 (2001) · Zbl 1034.74037
[6] Blouza, A.; Hecht, F.; Le Dret, H., Two finite element approximation of Naghdiʼs shell model in Cartesian coordinates, SIAM J. Numer. Anal., 44, 2, 636-654 (2006) · Zbl 1109.74048
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