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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     author = {Philippe G. Ciarlet and Cristinel Mardare},
     title = {On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {873--878},
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     volume = {336},
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     year = {2003},
     doi = {10.1016/S1631-073X(03)00191-2},
     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/

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