Comptes Rendus
no. 5
Mathematical Problems in Mechanics
Beltrami's solutions of general equilibrium equations in continuum mechanics
[Solutions de Beltrami des équations d'équilibre de la mécanique des milieux continus]

Présenté par : Philippe G. Ciarlet

Giuseppe Geymonat1 ; Françoise Krasucki1
1 Laboratoire de Mécanique et de Génie Civil, UMR 5508, Université Montpellier II, place Eugène-Bataillon, 34695 Montpellier cedex 5, France
Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 359-363.

M. Gurtin a montré que la représentation de Beltrami, S=rotrotA, d'un champ régulier de contraintes à divergence nulle dans un ouvert à bord régulier est vérifiée si et seulement si S est auto-équilibré. Les conditions données par Gurtin sont étendues au cas d'un ouvert à bord Lipschitzien pour un champ S∈L2(Ω;Msym3). Par application de ce résultat on trouve une extension des conditions de compatibilité de Saint Venant aux domaines non nécessairement simplement connexes.

M. Gurtin has proved that the Beltrami representation, S=rotrotA, of a smooth, divergence-free stress tensor in a smooth domain, is verified if and only if S is self-equilibrated. Here, Gurtin's conditions are extended to the case of a bounded domain with a Lipschitz-continuous boundary, for a tensor field S∈L2(Ω;Msym3). We apply this result to obtain an extension of the Saint Venant's equations of compatibility to non necessarily simply-connected domains.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.12.031

Giuseppe Geymonat 1 ; Françoise Krasucki 1

1 Laboratoire de Mécanique et de Génie Civil, UMR 5508, Université Montpellier II, place Eugène-Bataillon, 34695 Montpellier cedex 5, France 
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Giuseppe Geymonat; Françoise Krasucki. Beltrami's solutions of general equilibrium equations in continuum mechanics. Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 359-363. doi : 10.1016/j.crma.2005.12.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.031/

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