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

Ciarlet, Philippe G.1 ; Mardare, Cristinel2
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, Tome 336 (2003) no. 10, pp. 873-878.

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 ∞ 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 ∞ 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 :
Publié le :
DOI : 10.1016/S1631-073X(03)00191-2
Ciarlet, Philippe G. 1 ; Mardare, Cristinel 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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Ciarlet, Philippe G.; Mardare, Cristinel. On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity. Comptes Rendus. Mathématique, Tome 336 (2003) no. 10, pp. 873-878. doi : 10.1016/S1631-073X(03)00191-2. http://www.numdam.org/articles/10.1016/S1631-073X(03)00191-2/

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