On internal and boundary layers with unbounded energy in thin shell theory. Parabolic characteristic and non-characteristic cases

Article type: Research Article

Authors: Caillerie, D. | Raoult, A. | Sanchez-Palencia, E.^;

Affiliations: Laboratoire des Sols, Solides et Structures, INPG, Domaine Universitaire, B.P. 53, 38041 Grenoble, France E-mail: [email protected] | LMC-IMAG, Université de Grenoble, B.P. 53X, 38041 Grenoble, France E-mail: [email protected] | Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris, France E-mail: [email protected]

Note: [] Corresponding author.

Abstract: We consider the system of equations of Koiter shell theory in a slightly simplified form, in the case when the limit (for small thickness) problem is parabolic, i.e., the directions of the principal curvatures of the middle surface coincide everywhere. Under loadings not belonging to the dual of the energy space of the limit problem, the energy of the solutions grows without limit as the thickness tends to zero and concentrates on internal or boundary layers. Two cases are considered, when the singular loadings are applied either along a non-characteristic or a characteristic curve. In both cases we define and prove the convergence to the leading order in the layers.

Journal: Asymptotic Analysis, vol. 46, no. 3-4, pp. 221-249, 2006