[Une nouvelle approche de la théorie linéaire des coques et une nouvelle démonstration de l'inégalité de Korn sur une surface]
On propose une nouvelle approche pour les problèmes quadratiques de minimisation rencontrés dans la théorie linéaire de coques de Koiter. La nouveauté consiste à considérer les tenseurs linéarisés de changement de métrique et de changement de courbure comme les nouvelles inconnues, au lieu du champ de déplacement comme à l'accoutumée. Cette approche conduit aussi à une nouvelle démonstration de l'inégalité de Korn sur une surface.
We propose a new approach to the quadratic minimization problems arising in Koiter's linear shell theory. The novelty consists in considering the linearized change of metric and change of curvature tensors as the new unknowns, instead of the displacement vector field as is customary. This approach also provides a new proof of Korn's inequality on a surface.
Publié le :
@article{CRMATH_2005__340_6_471_0,
author = {Philippe G. Ciarlet and Liliana Gratie},
title = {Another approach to linear shell theory and a new proof of {Korn's} inequality on a surface},
journal = {Comptes Rendus. Math\'ematique},
pages = {471--478},
publisher = {Elsevier},
volume = {340},
number = {6},
year = {2005},
doi = {10.1016/j.crma.2005.01.021},
language = {en},
}
TY - JOUR AU - Philippe G. Ciarlet AU - Liliana Gratie TI - Another approach to linear shell theory and a new proof of Korn's inequality on a surface JO - Comptes Rendus. Mathématique PY - 2005 SP - 471 EP - 478 VL - 340 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2005.01.021 LA - en ID - CRMATH_2005__340_6_471_0 ER -
Philippe G. Ciarlet; Liliana Gratie. Another approach to linear shell theory and a new proof of Korn's inequality on a surface. Comptes Rendus. Mathématique, Volume 340 (2005) no. 6, pp. 471-478. doi : 10.1016/j.crma.2005.01.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.01.021/
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