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A model problem for boundary layers of thin elastic shells

Published online by Cambridge University Press:  15 April 2002

Philippe Karamian ,
Jacqueline Sanchez-Hubert  and
Évarisite Sanchez Palencia
Philippe Karamian
Affiliation:
Laboratoire de Mécanique, Université de Caen, Boulevard Maréchal Juin, 14032 Caen Cedex, France.
Jacqueline Sanchez-Hubert
Affiliation:
Laboratoire de Modélisation en Mécanique, Université Paris VI, 4 place Jussieu, 75252 Paris Cedex 05, France Laboratoire de Mécanique, Université de Caen, Boulevard Maréchal Juin, 14032 Caen Cedex, France.Laboratoire de Modélisation en Mécanique, Université Paris VI, 4 place Jussieu, 75252 Paris Cedex 05, FranceLaboratoire de Modélisation en Mécanique, Université Paris VI, 4 place Jussieu, 75252 Paris Cedex 05, France. (sanchez@lmm.jussieu.fr)
Évarisite Sanchez Palencia
Affiliation:
Laboratoire de Mécanique, Université de Caen, Boulevard Maréchal Juin, 14032 Caen Cedex, France.Laboratoire de Modélisation en Mécanique, Université Paris VI, 4 place Jussieu, 75252 Paris Cedex 05, FranceLaboratoire de Modélisation en Mécanique, Université Paris VI, 4 place Jussieu, 75252 Paris Cedex 05, France. (sanchez@lmm.jussieu.fr)
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Abstract

We consider a model problem (with constant coefficients and simplified geometry) for the boundary layer phenomena which appear in thin shell theoryas the relative thickness ε of the shell tends tozero. For ε = 0 our problem is parabolic, then it is amodel of developpable surfaces. Boundary layers along and across the characteristichave very different structure. It also appears internal layers associatedwith propagations of singularities along the characteristics. The specialstructure of the limit problem often implies solutions which exhibitdistributional singularities along the characteristics. The correspondinglayers for small ε have a very large intensity. Layers alongthe characteristics have a special structure involving subspaces; thecorresponding Lagrange multipliers are exhibited. Numerical experimentsshow the advantage of adaptive meshes in these problems.

Keywords

Shellsboundary layerssingular perturbation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 1 , January 2000 , pp. 1 - 30
Copyright
© EDP Sciences, SMAI, 2000

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