Passage à la limite de l'élasticité tridimensionnelle à la théorie asymptotique des coques minces

We perform an asymptotic expansion of the two-scale kind analogous to that of homogenization theory involving a large scale associated with the medium surface and a small scale associated with the thickness 2e of the shell. There are two very different asymptotic schemes according to the medium surface admits whether or not «pure flexions» (i.e. «inextensional» displacements keeping invariant the first fundamental form). In the first case the limit behavior is given by a «pure flexion», and in the second, by the membrane theory. Consequently, we find again, starting from the three-dimensional elasticity, the results obtained in [1] and [2] from the Koiter theory of shells