“Shallow” shells in curvilinear coordinates. (Coques ”faiblement courbées” en coordonnées curvilignes.) (French) Zbl 0862.73036

Summary: We consider a family of linearly elastic shells that are “shallow” in a sense specified in the note. 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 \(H^1\) when the thickness of the shell approaches zero. Moreover, the limits are completely determined by the solution of a two-dimensional problem that constitutes a model of “shallow” shells in curvilinear coordinates. This new model complements the model previously obtained in Cartesian coordinates by the last two authors.


74K15 Membranes
35Q72 Other PDE from mechanics (MSC2000)