[Reconstruction d'un champ de déplacements à partir de son tenseur des déformations linéarisées en coordonnées curvilignes]
Nous montrons que, si un champ de matrices symétriques défini sur un ouvert simplement connexe vérifie les équations de Saint Venant en coordonnées curvilignes, alors c'est le tenseur des déformations linéarisées associé à un champ de déplacements. Notre démonstration fournit un algorithme explicite de reconstruction d'un tel champ de déplacements, qui peut être considéré comme la version linéarisée de la reconstruction d'une immersion à partir d'une métrique riemannienne plate.
We establish that, if a symmetric matrix field defined over a simply-connected open set satisfies the Saint Venant equations in curvilinear coordinates, then its coefficients are the linearized strains associated with a displacement field. Our proof provides an explicit algorithm for recovering such a displacement field, which may be viewed as the linear counterpart of the reconstruction of an immersion from a given flat Riemannian metric.
Publié le :
@article{CRMATH_2007__344_8_535_0,
author = {Ciarlet, Philippe G. and Mardare, Cristinel and Shen, Ming},
title = {Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates},
journal = {Comptes Rendus. Math\'ematique},
pages = {535--540},
publisher = {Elsevier},
volume = {344},
number = {8},
year = {2007},
doi = {10.1016/j.crma.2007.03.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.03.012/}
}
TY - JOUR AU - Ciarlet, Philippe G. AU - Mardare, Cristinel AU - Shen, Ming TI - Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates JO - Comptes Rendus. Mathématique PY - 2007 SP - 535 EP - 540 VL - 344 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.03.012/ DO - 10.1016/j.crma.2007.03.012 LA - en ID - CRMATH_2007__344_8_535_0 ER -
%0 Journal Article %A Ciarlet, Philippe G. %A Mardare, Cristinel %A Shen, Ming %T Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates %J Comptes Rendus. Mathématique %D 2007 %P 535-540 %V 344 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.03.012/ %R 10.1016/j.crma.2007.03.012 %G en %F CRMATH_2007__344_8_535_0
Ciarlet, Philippe G.; Mardare, Cristinel; Shen, Ming. Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates. Comptes Rendus. Mathématique, Tome 344 (2007) no. 8, pp. 535-540. doi : 10.1016/j.crma.2007.03.012. http://www.numdam.org/articles/10.1016/j.crma.2007.03.012/
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