Asymptotic Analysis of Shell-like Inclusions with High Rigidity

We study the problem of an elastic shell-like inclusion with high rigidity in a three-dimensional domain by means of the asymptotic expansion method. The analysis is carried out in a general framework of curvilinear coordinates. After defining a small real adimensional parameter ε, we characterize the limit problems when the rigidity of the inclusion has order of magnitude 1/ε and 1/ε^3 with respect to the rigidities of the surrounding bodies. Moreover, we prove the strong convergence of the solution of the initial three-dimensional problem towards the solution of the simplified limit problem.