Complete asymptotics for shallow shells

Article type: Research Article

Authors: Andreoiu, Georgiana^; | Faou, Erwan

Affiliations: Mathematics Department, EPFL, 1015 Lausanne, Switzerland E‐mail: [email protected] | IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France E‐mail: Erwan.Faou@univ‐rennes1.fr

Note: [] Corresponding author.

Abstract: In this paper we study the asymptotics of the three‐dimensional displacement field for clamped and free linear elastic shallow shells as the thickness tends to zero. As in the case of plates, the asymptotics contains regular terms and boundary layers. The two‐dimensional generators of the regular parts are solutions of two‐dimensional problems governed by an elliptic system in the sense of S. Agmon, A. Douglis and L. Nirenberg. This asymptotics is justified by optimal error estimates and improves the results obtained by S. Busse, P.G. Ciarlet and B. Miara.

Keywords: mechanics of solids, shallow shells, linear elasticity, boundary layers

Journal: Asymptotic Analysis, vol. 25, no. 3-4, pp. 239-270, 2001