Let be an open connected subset of and let be an immersion from into . It is established that the set formed by all rigid displacements of the open set is a submanifold of dimension 6 and of class of the space . It is also shown that the infinitesimal rigid displacements of the same set span the tangent space at the origin to this submanifold.
Soit un ouvert connexe de et une immersion de dans . On établit que l'ensemble formé par les déplacements rigides de l'ouvert est une sous-variété de dimension 6 et de classe de l'espace . On montre aussi que les déplacements rigides infinitésimaux du même ouvert engendrent le plan tangent à l'origine à cette sous-variété.
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Philippe G. Ciarlet 1; Cristinel Mardare 2
@article{CRMATH_2003__336_10_873_0, 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}, publisher = {Elsevier}, volume = {336}, number = {10}, year = {2003}, doi = {10.1016/S1631-073X(03)00191-2}, language = {en}, }
TY - JOUR AU - Philippe G. Ciarlet AU - Cristinel Mardare TI - On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity JO - Comptes Rendus. Mathématique PY - 2003 SP - 873 EP - 878 VL - 336 IS - 10 PB - Elsevier DO - 10.1016/S1631-073X(03)00191-2 LA - en ID - CRMATH_2003__336_10_873_0 ER -
%0 Journal Article %A Philippe G. Ciarlet %A Cristinel Mardare %T On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity %J Comptes Rendus. Mathématique %D 2003 %P 873-878 %V 336 %N 10 %I Elsevier %R 10.1016/S1631-073X(03)00191-2 %G en %F CRMATH_2003__336_10_873_0
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/
[1] Manifolds, Tensor Analysis, and Applications, Springer-Verlag, New York, 1988
[2] Mathematical Elasticity, Volume III: Theory of Shells, North-Holland, Amsterdam, 2000
[3] On the recovery of a surface with prescribed first and second fundamental forms, J. Math. Pures Appl., Volume 81 (2002), pp. 167-185
[4] P.G. Ciarlet, C. Mardare, On rigid and infinitesimal rigid displacements in three-dimensional elasticity, Math. Models Methods Appl. Sci., to appear
[5] P.G. Ciarlet, C. Mardare, On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory, C. R. Acad. Sci. Paris, Sér. I, to appear
[6] A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity, Comm. Pure Appl. Math., Volume 55 (2002), pp. 1461-1506
[7] Liouville's theory on conformal mappings under minimal regularity assumptions, Siberian Math. J., Volume 8 (1967), pp. 69-85
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