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Pseudo‐reflection phenomena for singularities in thin elastic shells
Author(s) -
KaramianSurville P.,
SanchezHubert J.,
Sanchez Palencia E.
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.421
Subject(s) - gravitational singularity , singularity , mathematics , mathematical analysis , boundary (topology) , statics , reflection (computer programming) , boundary value problem , surface (topology) , geometry , classical mechanics , physics , computer science , programming language
We consider problems of statics of thin elastic shells with hyperbolic middle surface subjected to boundary conditions ensuring the geometric rigidity of the surface. The asymptotic behaviour of the solutions when the relative thickness tends to zero is then given by the membrane approximation. It is a hyperbolic problem propagating singularities along the characteristics. We address here the reflection phenomena when the propagated singularities arrive to a boundary. As the boundary conditions are not the classical ones for a hyperbolic system, there are various cases of reflection. Roughly speaking, singularities provoked elsewhere are not reflected at all at a free boundary, whereas at a fixed (or clamped) boundary the reflected singularity is less singular than the incident one. Reflection of singularities provoked along a non‐characteristic curve C are also considered. Copyright © 2003 John Wiley & Sons, Ltd.