Justification d'un modèle linéaire bi-dimensionnel de coques « faiblement courbées » en coordonnées: Curvilignes

We consider a family of linearly elastic shells that are « shallow « in a sense specified in the article. We show that, if the applied forces are of a specific order of magnitude, the covariant components of the displacement field, once properly scaled, converge in H¹ when the thickness of the shells approaches zero. Moreover, the limits are completely determined by the solution of a two-dimensional problem that constitutes a model of « shallow » shell in curvilinear coordinates. This new model thus complements the model previously obtained in Cartesian coordinates by the last two authors.