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Propagation of singularities on thin shells with hyperbolic regions

In: Numerical Mathematics and Advanced Applications

Author

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  • H. Hakula

    (Helsinki University of Technology, Institute of Mathematics)

Abstract

Summary Thin shell problems, although part of linear elasticity and thus elliptic, can exhibit hyperbolic properties such as the propagation of singularities along the characteristics if the geometry of the surface is hyperbolic. Indeed, if the thickness of a hyperbolic shell is taken to be zero the problem ceases to be elliptic. Tricomi has identified two kinds of characteristics — the 1st kind, or those normal to, and the 2nd kind, or those tangential to the geometric transition region. An example of Tricomi characteristics of the 1st kind, the so-called pinched cylinder problem, is studied in [1]. Here we demonstrate that, within hyperbolic regions of thin shells, singularities can be propagated along both kinds of characteristics. Our analysis is qualitative only.

Suggested Citation

  • H. Hakula, 2003. "Propagation of singularities on thin shells with hyperbolic regions," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 357-363, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_33
    DOI: 10.1007/978-88-470-2089-4_33
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