[Nouvelles formulations de problèmes d'élasticité linéarisée, basées sur des généralisations du théorème de Donati]
Le théorème classique de Donati sert à caractériser les champs de matrices réguliers qui sont des champs de déformation linéarisés. Dans cette Note, on donne plusieurs généralisations de ce théorème, en particulier à des champs de matrices dont les composantes sont seulement dans . On montre ensuite que de telles généralisations conduisent à de nouvelles formulations des problèmes d'élasticité linéarisée tridimensionnelle, comme des problèmes de minimisation quadratique où les déformations sont les inconnues principales.
The classical Donati theorem is used for characterizing smooth matrix fields as linearized strain tensor fields. In this Note, we give several generalizations of this theorem, notably to matrix fields whose components are only in . We then show that our extensions of Donati's theorem allow to reformulate in a novel fashion linearized three-dimensional elasticity problems as quadratic minimization problems with the strains as the primary unknowns.
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@article{CRMATH_2006__342_10_785_0,
author = {Amrouche, Cherif and Ciarlet, Philippe G. and Gratie, Liliana and Kesavan, Srinivasan},
title = {New formulations of linearized elasticity problems, based on extensions of {Donati's} theorem},
journal = {Comptes Rendus. Math\'ematique},
pages = {785--789},
publisher = {Elsevier},
volume = {342},
number = {10},
year = {2006},
doi = {10.1016/j.crma.2006.03.027},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.03.027/}
}
TY - JOUR AU - Amrouche, Cherif AU - Ciarlet, Philippe G. AU - Gratie, Liliana AU - Kesavan, Srinivasan TI - New formulations of linearized elasticity problems, based on extensions of Donati's theorem JO - Comptes Rendus. Mathématique PY - 2006 SP - 785 EP - 789 VL - 342 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.03.027/ DO - 10.1016/j.crma.2006.03.027 LA - en ID - CRMATH_2006__342_10_785_0 ER -
%0 Journal Article %A Amrouche, Cherif %A Ciarlet, Philippe G. %A Gratie, Liliana %A Kesavan, Srinivasan %T New formulations of linearized elasticity problems, based on extensions of Donati's theorem %J Comptes Rendus. Mathématique %D 2006 %P 785-789 %V 342 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.03.027/ %R 10.1016/j.crma.2006.03.027 %G en %F CRMATH_2006__342_10_785_0
Amrouche, Cherif; Ciarlet, Philippe G.; Gratie, Liliana; Kesavan, Srinivasan. New formulations of linearized elasticity problems, based on extensions of Donati's theorem. Comptes Rendus. Mathématique, Tome 342 (2006) no. 10, pp. 785-789. doi : 10.1016/j.crma.2006.03.027. http://www.numdam.org/articles/10.1016/j.crma.2006.03.027/
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