On the asymptotic behavior of transmission thin shell problems

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.