Comptes Rendus
Numerical analysis
A mixed DG method for folded Naghdi's shell in Cartesian coordinates
Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 653-658.

In this Note, a mixed formulation is proposed to solve Naghdi's equations for a thin linearly elastic shell. The unknowns of the problem are the displacement of the points of the middle surface, the rotation field of the normal vector to the middle surface of the shell and a Lagrange multiplier that is introduced in order to enforce the tangency requirement on the rotation. We prove the well posedness of the continuous and the discrete problems.

Dans cette Note, nous proposons une méthode mixte pour résoudre les équations du modèle de Naghdi de coques linéairement élastiques. Les inconnues du problème sont le déplacement des points de la surface moyenne, le vecteur de rotation de la normale à la surface moyenne et un multiplicateur de Lagrange introduit pour forcer le caractère tangentiel de la rotation. Nous démontrons le caractère bien posé du problème continu et du problème discret.

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Published online:
DOI: 10.1016/j.crma.2015.04.016
Serge Nicaise 1; Ismail Merabet 2

1 LAMAV, Université de Valenciennes, France
2 LAMA, Université Kasdi-Merbah, Ouargla, Algeria
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Serge Nicaise; Ismail Merabet. A mixed DG method for folded Naghdi's shell in Cartesian coordinates. Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 653-658. doi : 10.1016/j.crma.2015.04.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.04.016/

[1] C. Bernardi; A. Blouza; F. Hecht; H. Le Dret A posteriori analysis of finite element discretizations of a Naghdi shell model, IMA J. Numer. Anal., Volume 33 (2013), pp. 190-211

[2] A. Blouza Existence et unicité pour le modèle du Naghdi pour une coque peu régulière, C. R. Acad. Sci. Paris, Ser. I, Volume 324 (1997), pp. 839-844

[3] A. Blouza; H. Le Dret Nagdhi's shell model: existence, uniqueness and continuous dependence on the middle surface, J. Elasticity, Volume 64 (2001), pp. 199-216

[4] A. Blouza; F. Hecht; H. Le Dret Two finite element approximations of Naghdi's shell model in Cartesian coordinates, SIAM J. Numer. Anal., Volume 44 (2006), pp. 636-654

[5] P.G. Ciarlet Mathematical Elasticity, Volume III: Theory of Shells, Elsevier, Amsterdam, 2005

[6] V. Girault; P.-A. Raviart Finite Element Methods for Navier–Stokes Equations, Theory and Algorithms, Springer Series in Computational Mathematics, Springer-Verlag, Berlin, 1986

[7] P.M. Naghdi Foundations of elastic shell theory, Progress in Solid Mechanics, vol. IV, North-Holland, Amsterdam, 1963, pp. 1-90

[8] S. Nicaise; I. Merabet Error analysis of a mixed DG method for folded Naghdi's shell in Cartesian coordinates, C. R. Acad. Sci. Paris, Ser. I, Volume 353 (2015)

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