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Another approach to linear shell theory and a new proof of Korn’s inequality on a surface. (English. Abridged French version) Zbl 1329.74176

Summary: 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.

MSC:

74K25 Shells
74G65 Energy minimization in equilibrium problems in solid mechanics
49Q10 Optimization of shapes other than minimal surfaces
53A05 Surfaces in Euclidean and related spaces
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[1] Amrouche, C.; Girault, V., Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czech. Math. J., 44, 109-140 (1994) · Zbl 0823.35140
[2] Bernadou, M.; Ciarlet, P. G., Sur l’ellipticité du modèle linéaire de coques de W.T. Koiter, (Glowinski, R.; Lions, J. L., Computing Methods in Applied Sciences and Engineering (1976), Springer-Verlag), 89-136 · Zbl 0356.73066
[3] Bernadou, M.; Ciarlet, P. G.; Miara, B., Existence theorems for two-dimensional linear shell theories, J. Elasticity, 34, 111-138 (1994) · Zbl 0808.73045
[4] Ciarlet, P. G., Mathematical Elasticity, Volume III: Theory of Shells (2000), North-Holland
[5] Ciarlet, P. G.; Ciarlet, P., Another approach to linearized elasticity and a new proof of Korn’s inequality, Math. Models Methods Appl. Sci., 15, 259-271 (2005) · Zbl 1084.74006
[6] P.G. Ciarlet, L. Gratie, A new approach to linear shell theory, Math. Models Methods Appl. Sci., in press; P.G. Ciarlet, L. Gratie, A new approach to linear shell theory, Math. Models Methods Appl. Sci., in press · Zbl 1135.74027
[7] Ciarlet, P. G.; Mardare, S., On Korn’s inequalities in curvilinear coordinates, Math. Models Methods Appl. Sci., 11, 1379-1391 (2001) · Zbl 1036.74036
[8] Duvaut, G.; Lions, J. L., Inequalities in Mechanics and Physics (1976), Springer-Verlag, English translation · Zbl 0331.35002
[9] Koiter, W. T., On the foundations of the linear theory of thin elastic shells, Proc. Kon. Ned. Akad. Wetensch B, 73, 169-195 (1970) · Zbl 0213.27002
[10] Opoka, S.; Pietraszkiewicz, W., Intrinsic equations for non-linear deformation and stability of thin elastic shells, Int. J. Solids Struct., 41, 3275-3292 (2004) · Zbl 1119.74474
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