Mathematical Problems in Mechanics
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.

Let ω be an open connected subset of 2 and let θ be an immersion from ω into 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 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 2 et θ une immersion de ω dans 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 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.

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DOI: 10.1016/S1631-073X(03)00205-X
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 shell theory. Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 959-966. doi : 10.1016/S1631-073X(03)00205-X. http://www.numdam.org/articles/10.1016/S1631-073X(03)00205-X/

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