an:01797011
Zbl 1006.74064
Karamian, P.; Sanchez-Hubert, J.
Boundary layers in thin elastic shells with developable middle surface
EN
Eur. J. Mech., A, Solids 21, No. 1, 13-47 (2002).
00081549
2002
j
74K25 74G10
boundary layer; thin shell theory; developable middle surface; internal layers; propagation of singularities; characteristics; limit problem; Lagrange multipliers; adaptive anisotropic meshes
Summary: We consider boundary layer phenomena which appear in thin shell theory as the relative thickness \(\varepsilon\) tends to zero. We deal with a developable middle surface. Boundary layers along and across the generators (which are characteristics of the underlying system) have very different structure. We also observe the appearance of internal layers associated with propagation of singularities along the characteristics. The special structure of the limit problem often generates solutions which exhibit distributed singularities along the characteristics. The corresponding layers for small \(\varepsilon\) have a very large intensity. Layers along the characteristics have a special structure involving subspaces, and the corresponding Lagrange multipliers are exhibited. Numerical experiments show the advantage of adaptive anisotropic meshes in these problems.