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Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case

Philippe KaramianJacqueline Sanchez-HubertÉvariste Sanchez Palencia — 2002

International Journal of Applied Mathematics and Computer Science

We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution.

A model problem for boundary layers of thin elastic shells

Philippe KaramianJacqueline Sanchez-HubertÉvarisite Sanchez Palencia — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a model problem (with constant coefficients and simplified geometry) for the boundary layer phenomena which appear in thin shell theory as the relative thickness ε of the shell tends to zero. For ε = 0 our problem is parabolic, then it is a model of developpable surfaces. Boundary layers along and across the characteristic have very different structure. It also appears internal layers associated with propagations of singularities along the characteristics. The special structure of...

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