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Boundary layers in thin elastic shells with developable middle surface. (English) Zbl 1006.74064
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.

MSC:
74K25 Shells
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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