Comptes Rendus
Mathematical Problems in Mechanics
Plate-like and shell-like inclusions with high rigidity
Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 697-702.

We study the problem of an elastic inclusion with high rigidity in a 3D domain. First we consider an inclusion with a plate-like geometry and then in the more general framework of curvilinear coordinates, an inclusion with a shell-like geometry. We compare our formal models to those obtained by Chapelle–Ferent and by Bessoud et al.

On étudie le problème d'une inclusion élastique de grande rigidité dans un domaine 3D. Cette inclusion est d'abord vue comme un domaine géométrique de type plaque, puis plus généralement comme un domaine géométrique de type coque. On compare les modèles obtenus formellement à ceux de Chapelle–Ferent et de Bessoud et al.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.03.002

Anne-Laure Bessoud 1, 2; Françoise Krasucki 1; Michele Serpilli 2

1 Institut de mathématiques et de modélisation de Montpellier – UMR 5149, Université Montpellier II, CC 051, place Eugène-Bataillon, 34095 Montpellier cedex 5, France
2 Laboratoire de mécanique et genie civil – UMR 5508, Université Montpellier II, CC 048, place Eugène-Bataillon, 34095 Montpellier cedex 5, France
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Anne-Laure Bessoud; Françoise Krasucki; Michele Serpilli. Plate-like and shell-like inclusions with high rigidity. Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 697-702. doi : 10.1016/j.crma.2008.03.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.03.002/

[1] K.J. Bathe; D. Chapelle The Finite Element Analysis of Shells-Fundamentals, Springer, Berlin, 2003

[2] M. Bernadou; P.G. Ciarlet Sur l'ellipticité du modèle linéaire de coques de W.T. Koiter (R. Glowinski; J.L. Lions, eds.), Computing Methods in Applied Sciences and Engineering, Lecture Notes in Economics and Mathematical Systems, vol. 134, Springer-Verlag, Heidelberg, 1976, pp. 89-136

[3] M. Bernadou; P.G. Ciarlet; B. Miara Existence theorems for two-dimensional linear shell theories, J. Elasticity, Volume 34 (1994), pp. 111-138

[4] A.L. Bessoud, F. Krasucki, G. Michaille, Multi-materials with strong interface: variational modelings, Asymptotic Anal., in press

[5] H. Brezis; L.A. Caffarelli; A. Friedman Reinforcement problems for elliptic equations and variational inequalities, Ann. Mat. Pura Appl. (4), Volume 123 (1980), pp. 219-246

[6] D. Caillerie The effect of a thin inclusion of high rigidity in an elastic body, Math. Methods Appl. Sci., Volume 2 (1980), pp. 251-270

[7] D. Chapelle; A. Ferent Modeling of the inclusion of a reinforcing sheet within a 3D medium, Math. Models Methods Appl. Sci., Volume 13 (2003), pp. 573-595

[8] P.G. Ciarlet Mathematical Elasticity, vol. III: Theory of Shells, Studies in Mathematics and its Applications, North-Holland, Amsterdam, 2000

[9] P.G. Ciarlet; V. Lods Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations, Arch. Rational Mech. Anal., Volume 136 (1996), pp. 119-161

[10] P.G. Ciarlet; E. Sanchez-Palencia An existence and uniqueness theorem for the two-dimensional linear membrane shell equations, J. Math. Pures Appl., Volume 75 (1996), pp. 51-67

[11] G. Geymonat; F. Krasucki; S. Lenci Mathematical analysis of a bonded joint with a soft thin adhesive, Math. Mech. Solids, Volume 4 (1999), pp. 201-225

[12] H. Pham Huy; E. Sanchez-Palencia Phénomène de transmission à travers des couches minces de conductivité élevée, J. Math. Anal. Appl., Volume 47 (1974), pp. 284-309

[13] J. Sanchez-Hubert; E. Sanchez-Palencia Coques élastiques minces : propriétés asymptotiques, Masson, Paris, 1997

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