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Sensitivity phenomena for certain thin elastic shells with edges

✍ Scribed by Patrick Gerard; Evariste Sanchez-Palencia

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 165 KB
Volume: 23
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(20000310)23:4<379::aid-mma119>3.0.co;2-0

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✦ Synopsis

We consider two kinds of shells which are sensitive, i.e. they are geometrically rigid and as the thickness tends to zero the limit problem is unstable in the sense that there are very smooth loadings (belonging to the space D of test functions of distributions) such that the corresponding solutions go out of the energy space. The "rst situation occurs when there is an edge and the middle surface is elliptic on both sides of it. The second one occurs when there is an edge , the surface is respectively elliptic and hyperbolic on both sides of it and the &determination domain' in the hyperbolic region issued from intersects another edge .

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## Abstract 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 approx