Boundary layers in thin elastic shells with developable middle surface

We consider the boundary layer phenomena which appear in thin shell theory as the relative thickness ε tends to zero. We deal with a developable middle surface. Boundary layers along and across the generators (which are the characteristics of the underlying system) have very different structure. It also appear internal layers associated with propagation of singularities along the characteristics. The special structure of the limit problem often implies solutions which exhibit distributional singularities along the characteristics. The corresponding layers for small ε have a very large intensity. Layers along the characteristics have a special structure involving subspaces, the corresponding Lagrange multipliers are exhibited. Numerical experiments show the advantage of adaptive anisotropic meshes in these problems.