On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity

Philippe G. Ciarlet; Cristinel Mardare

doi:10.1016/S1631-073X(03)00191-2

Mathematical Problems in Mechanics

On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity
[Déplacements rigides et leur relation au lemme du déplacement rigide infinitésimal en élasticité tri-dimensionnelle]

Présenté par : 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. 10, pp. 873-878.

Résumé
Abstract

Soit $Ω$ un ouvert connexe de $ℝ^{3}$ et $Θ$ une immersion de $Ω$ dans $ℝ^{3}$ . On établit que l'ensemble formé par les déplacements rigides de l'ouvert $Θ (Ω)$ 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 du même ouvert $Θ (Ω)$ engendrent le plan tangent à l'origine à cette sous-variété.

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

Accepté le : 2003-04-04
Publié le : 2003-05-15

DOI : 10.1016/S1631-073X(03)00191-2

Affiliations des auteurs :

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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     language = {en},
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Philippe G. Ciarlet; Cristinel Mardare. On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity. Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 873-878. doi : 10.1016/S1631-073X(03)00191-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00191-2/

Bibliographie
Cité par

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Philippe G. Ciarlet; Cristinel Mardare On rigid and infinitesimal rigid displacements in shell theory., Journal de Mathématiques Pures et Appliquées. Neuvième Série, Volume 83 (2004) no. 1, pp. 1-15 | DOI:10.1016/j.matpur.2003.09.004 | Zbl:1050.74030
Philippe G. Ciarlet; Cristinel Mardare On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory., Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 336 (2003) no. 11, pp. 959-966 | DOI:10.1016/s1631-073x(03)00205-x | Zbl:1084.74029
Philippe G. Ciarlet; Cristinel Mardare On rigid and infinitesimal rigid displacements in three-dimensional elasticity., M $^{3}$ AS. Mathematical Models Methods in Applied Sciences, Volume 13 (2003) no. 11, pp. 1589-1598 | DOI:10.1142/s0218202503003045 | Zbl:1055.74006

Cité par 3 documents. Sources : zbMATH

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