On the asymptotic behavior of transmission thin shell problems

Article type: Research Article

Authors: Merabet, I. | Nicaise, S.^; | Chacha, D.A.

Affiliations: Université de Kasdi Merbah, Ouargla, Algérie | Université Lille Nord de France, Valenciennes, France

Note: [] Corresponding author: S. Nicaise, FR CNRS 2956, Université Lille Nord de France, UVHC, 59313 Valenciennes Cedex 9, France. E-mail: snicaise@univ-valenciennes.fr

Abstract: In this paper we study the asymptotic behavior of two-dimensional transmission problems for the linear Koiter model of an elastic multi-structure composed of two thin shells with the same thickness ε<<1. Contrary to the case of membrane shells, the formal limit problem, i.e., for ε=0, fails to give a convenient approximate solution, as the limit problem is ill posed. An appropriate dilation leads to an equivalent problem, for which we prove its strong convergence towards some finite limit.

Keywords: thin shells, Koiter's model, rigid junction, elastic junction, boundary layers, sensitivity

DOI: 10.3233/ASY-121144

Journal: Asymptotic Analysis, vol. 82, no. 1-2, pp. 163-185, 2013