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Comptes Rendus Mathématique
Volume 353, n° 7
pages 653-658 (juillet 2015)
Doi : 10.1016/j.crma.2015.04.016
Received : 16 December 2014 ;  accepted : 20 April 2015
A mixed DG method for folded Naghdi's shell in Cartesian coordinates
Une méthode de Galerkin discontinue mixte pour une coque de Naghdi pliée en coordonnées cartésiennes

Serge Nicaise a , Ismail Merabet b
a LAMAV, Université de Valenciennes, France 
b LAMA, Université Kasdi-Merbah, Ouargla, Algeria 


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.

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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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1  I.e., without the constraint  .

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