Comptes Rendus
no. 11-12
Mathematical problems in mechanics
Intrinsic formulation of the displacement-traction problem in linear shell theory
[Formulation intrinsèque du problème en déplacement-traction en théorie linéaire des coques]

Présenté par : Philippe G. Ciarlet

Philippe G. Ciarlet1 ; Cristinel Mardare2
1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2 Sorbonne Université, CNRS, Laboratoire Jacques-Louis-Lions (LJLL), 75005 Paris, France
Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1243-1250.

On reformule les conditions aux limites de Dirichlet satisfaites par le champ de déplacements de la surface moyenne d'une coque linéairement élastique comme des conditions aux limites satisfaites par les champs de tenseurs linéarisés de changement de métrique et de coubure correspondants. Ceci permet ensuite de donner une formulation intrinsèque du modèle linéaire de coques de W.T. Koiter avec ces deux champs de tenseurs comme seules inconnues.

We recast the Dirichlet boundary conditions satisfied by the displacement field of the middle surface of a linearly elastic shell as boundary conditions satisfied by the corresponding linearized change of metric and of curvature tensor fields. This in turn allows us to give an intrinsic formulation of the linear shell model of W.T. Koiter with these two tensor fields as the sole unknowns.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.09.007
Philippe G. Ciarlet 1 ; Cristinel Mardare 2

1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2 Sorbonne Université, CNRS, Laboratoire Jacques-Louis-Lions (LJLL), 75005 Paris, France 
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Philippe G. Ciarlet; Cristinel Mardare. Intrinsic formulation of the displacement-traction problem in linear shell theory. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1243-1250. doi : 10.1016/j.crma.2018.09.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.09.007/

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[5] P.G. Ciarlet; C. Mardare An intrinsic formulation of the Kirchhoff–Love theory of linearly elastic plates, Anal. Appl., Volume 16 (2018), pp. 565-584

[6] P.G. Ciarlet; C. Mardare The intrinsic theory of linearly elastic plates, Math. Mech. Solids (2018) (in press) | DOI

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