A NEW KIND OF SINGULAR STIFF PROBLEMS AND APPLICATION TO THIN ELASTIC SHELLS

Abstract

We consider the asymptotic behavior of the solution of a class of problems involving a small parameter ε and ε2. This generalizes the “singular stiff” problems arising in classical thin shell theory. The new problems appear in theory of composite shells, when the local structure implies coupling between membrane stresses and flexions. According to specific hypotheses, this kind of problems contains singular perturbations and penalty problems where the limit solution belongs to a subspace G1 of the general configuration space V. In addition to the coercive problem, spectral properties are considered in the small and medium frequency ranges, including spectral families in the case without compactness.