Another approach to linear shell theory and a new proof of Korn's inequality on a surface

Philippe G. Ciarlet; Liliana Gratie

doi:10.1016/j.crma.2005.01.021

Mathematical Problems in Mechanics

Another approach to linear shell theory and a new proof of Korn's inequality on a surface

Presented by: Robert Dautray

Philippe G. Ciarlet ¹; Liliana Gratie ²

¹ Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong
² Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong

Comptes Rendus. Mathématique, Volume 340 (2005) no. 6, pp. 471-478.

Abstract
Résumé

We propose a new approach to the quadratic minimization problems arising in Koiter's linear shell theory. The novelty consists in considering the linearized change of metric and change of curvature tensors as the new unknowns, instead of the displacement vector field as is customary. This approach also provides a new proof of Korn's inequality on a surface.

On propose une nouvelle approche pour les problèmes quadratiques de minimisation rencontrés dans la théorie linéaire de coques de Koiter. La nouveauté consiste à considérer les tenseurs linéarisés de changement de métrique et de changement de courbure comme les nouvelles inconnues, au lieu du champ de déplacement comme à l'accoutumée. Cette approche conduit aussi à une nouvelle démonstration de l'inégalité de Korn sur une surface.

Received: 2005-01-22
Published online: 2005-02-24

DOI: 10.1016/j.crma.2005.01.021

Author's affiliations:

Philippe G. Ciarlet ¹; Liliana Gratie ²

¹ Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong
² Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong

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     author = {Philippe G. Ciarlet and Liliana Gratie},
     title = {Another approach to linear shell theory and a new proof of {Korn's} inequality on a surface},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {471--478},
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Philippe G. Ciarlet; Liliana Gratie. Another approach to linear shell theory and a new proof of Korn's inequality on a surface. Comptes Rendus. Mathématique, Volume 340 (2005) no. 6, pp. 471-478. doi : 10.1016/j.crma.2005.01.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.01.021/

References
Cited by

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