Multi-scale asymptotic expansion for a singular problem of a free plate with thin stiffener

Article type: Research Article

Authors: Rahmani, Leila^; | Vial, Grégory

Affiliations: Université Mouloud Mammeri de Tizi-Ouzou, Tizi Ouzou, Algérie | École Centrale de Lyon, CNRS UMR 5208, Université de Lyon, Ecully, France

Note: [] Corresponding author. E-mail: [email protected]

Abstract: In this paper, we consider a partially clamped plate which is stiffened on a portion of its free boundary. Our aim is to build an asymptotic expansion of the displacement, solution of the Kirchhoff–Love model, with respect to the thickness of the stiffener. Due to the mixed boundary conditions, singularities appear, obstructing the construction of the terms of the asymptotic expansion in the same way as if the plate was surrounded by the stiffener on its whole boundary. Using a splitting into regular and singular parts, we are able to formulate an asymptotic expansion involving profiles which allow to take into account the singularities.

Keywords: thin plate, stiffener, asymptotic expansion, elliptic partial differential equation, corner singularities

DOI: 10.3233/ASY-141236

Journal: Asymptotic Analysis, vol. 90, no. 1-2, pp. 161-187, 2014