Sensitivity phenomena for certain thin elastic shells with edges
Patrick Gérard, É. Sanchez-Palencia · Mathematical Methods in the Applied Sciences · 2000
We consider two kinds of shells which are sensitive, i.e. they are geometrically rigid and as the thickness ϵ 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 first 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 Γ0, the surface is respectively elliptic and hyperbolic on both sides of it and the ‘determination domain’ in the hyperbolic region issued from Γ0 intersects another edge Γ1. Copyright © 2000 John Wiley & Sons, Ltd.