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

Busse, Stéphane; Ciarlet, Philippe G.; Miara, Bernadette

C. R. Acad. Sci., Paris, Sér. I 322, No. 11, 1093-1098 (1996).

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.

MSC:

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

Keywords:

H(1)-convergence; covariant components of displacement field; linearly elastic shells; two-dimensional problem