[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 = {Ciarlet, Philippe G. and Gratie, Liliana},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.01.021/}
}
TY - JOUR AU - Ciarlet, Philippe G. AU - Gratie, Liliana 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2005.01.021/ DO - 10.1016/j.crma.2005.01.021 LA - en ID - CRMATH_2005__340_6_471_0 ER -
%0 Journal Article %A Ciarlet, Philippe G. %A Gratie, Liliana %T Another approach to linear shell theory and a new proof of Korn's inequality on a surface %J Comptes Rendus. Mathématique %D 2005 %P 471-478 %V 340 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.01.021/ %R 10.1016/j.crma.2005.01.021 %G en %F CRMATH_2005__340_6_471_0
Ciarlet, Philippe G.; Gratie, Liliana. Another approach to linear shell theory and a new proof of Korn's inequality on a surface. Comptes Rendus. Mathématique, Tome 340 (2005) no. 6, pp. 471-478. doi : 10.1016/j.crma.2005.01.021. http://www.numdam.org/articles/10.1016/j.crma.2005.01.021/
[1] Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czech. Math. J., Volume 44 (1994), pp. 109-140
[2] Sur l'ellipticité du modèle linéaire de coques de W.T. Koiter (Glowinski, R.; Lions, J.L., eds.), Computing Methods in Applied Sciences and Engineering, Springer-Verlag, 1976, pp. 89-136
[3] Existence theorems for two-dimensional linear shell theories, J. Elasticity, Volume 34 (1994), pp. 111-138
[4] Mathematical Elasticity, Volume III: Theory of Shells, North-Holland, 2000
[5] Another approach to linearized elasticity and a new proof of Korn's inequality, Math. Models Methods Appl. Sci., Volume 15 (2005), pp. 259-271
[6] P.G. Ciarlet, L. Gratie, A new approach to linear shell theory, Math. Models Methods Appl. Sci., in press
[7] On Korn's inequalities in curvilinear coordinates, Math. Models Methods Appl. Sci., Volume 11 (2001), pp. 1379-1391
[8] Les Inéquations en Mécanique et en Physique, Inequalities in Mechanics and Physics, Dunod, 1972 (English translation, 1976, Springer-Verlag)
[9] On the foundations of the linear theory of thin elastic shells, Proc. Kon. Ned. Akad. Wetensch B, Volume 73 (1970), pp. 169-195
[10] Intrinsic equations for non-linear deformation and stability of thin elastic shells, Int. J. Solids Struct., Volume 41 (2004), pp. 3275-3292
Cité par Sources :
