Instabilities Produced by Edges in Thin Shells

  • J. L. Lions
  • E. Sanchez-Palencia
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)


It is known that thin shells of elliptic type (i.e. having everywhere principal curvatures of the same sign) which are fixed by a part of the boundary and free by another part of it are sensitive. This means that the limit behaviour as the thickness tends to zero is highly unstable, in the sense that very small and smooth (= belonging to the space D of test functions for distributions) given forces produces very large perturbations going even out of the distribution space and of the energy space. This instability desappears when the shell is fixed by its whole boundary. We prove here that shells fixed by the whole boundary but having an edge are sensitive.


Interface Condition Principal Curvature Elliptic System Thin Shell Parameter Plane 
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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • J. L. Lions
    • 1
  • E. Sanchez-Palencia
    • 2
  1. 1.Collège de FranceParis Cedex 05France
  2. 2.Laboratoire de Modélisation en MécaniqueUniversité Pierre et Marie CurieParis Cedex 05France

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