On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory

Philippe G. Ciarlet; Cristinel Mardare

doi:10.1016/S1631-073X(03)00205-X

Mathematical Problems in Mechanics

On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory

Presented by: Robert Dautray

Philippe G. Ciarlet ¹; Cristinel Mardare ²

¹ Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong
² Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France

Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 959-966.

Abstract (OV)
Résumé

Let ω be an open connected subset of $ℝ^{2}$ and let $θ$ be an immersion from ω into $ℝ^{3}$ . It is established that the set formed by all rigid displacements of the surface $θ (ω)$ is a submanifold of dimension 6 and of class $𝒞^{\infty}$ of the space $𝐇^{1} (ω)$ . It is shown that the infinitesimal rigid displacements of the same surface $θ (ω)$ span the tangent space at the origin to this submanifold.

Soit ω un ouvert connexe de $ℝ^{2}$ et $θ$ une immersion de ω dans $ℝ^{3}$ . On établit que l'ensemble formé par les déplacements rigides de la surface $θ (ω)$ est une sous-variété de dimension 6 et de classe $𝒞^{\infty}$ de l'espace $𝐇^{1} (ω)$ . On montre aussi que les déplacements rigides infinitésimaux de la même surface $θ (ω)$ engendrent le plan tangent à l'origine à cette sous-variété.

Received: 2003-04-16
Accepted: 2003-04-16
Published online: 2003-06-01

DOI: 10.1016/S1631-073X(03)00205-X

Author's affiliations:

Philippe G. Ciarlet ¹; Cristinel Mardare ²

¹ Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong
² Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France

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     title = {On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory},
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Philippe G. Ciarlet; Cristinel Mardare. On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory. Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 959-966. doi : 10.1016/S1631-073X(03)00205-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00205-X/

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