ELASTIC THIN SHELLS - ASYMPTOTIC THEORY IN THE ANISOTROPIC AND HETEROGENEOUS CASES

Asymptotic (two-scale) methods are used to derive thin shell theory fr om three-dimensional elasticity. The asymptotic process is done direct ly for the variational formulations, and existence and uniqueness theo rems are given for the shell problem. The asymptotic behavior is the s ame as that recently derived by the authors using classical hypotheses of shell theory. The role of the subspace G of pure bendings (inexten sional motions) appears in a natural way. The asymptotic is basically described by a leading older term contained in G and a lower order ter m contained in the orthogonal to G. As in anisotropic heterogeneous pl ates, which exhibit a coupling between flexion and traction, in hetero geneous shells there is coupling between the terms in G and in its ort hogonal.