Justification d'un modéle bi-dimensionnel non linèaire de coque analogue à celui de W.T. Koiter

A two-dimensional nonlinear shell model "of Koiter's type" has recently been proposed by the first author. We show here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the "small" parameter, satisfies either the two-dimensional equations of a nonlinearly elastic "membrane" shell or those of a nonlinearly elastic "flexural" shell. These conclusions being identical to those recently drawn by V. Lods and B. Miara for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the tickness as the "small" parameter, the nonlinear shell model of Koiter's type considered here is thus justified, at least formally. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.