Torsion problem in multiconnected reinforced structures

Article type: Research Article

Authors: Mossino, Jacqueline^; | Vanninathan, Muthusamy

Affiliations: C.M.L.A, École Normale Supérieure de Cachan, 61, avenue du Président Wilson, 94235 Cachan cedex, France E‐mail: [email protected]‐cachan.fr | IISc‐TIFR Mathematics Programme, TIFR Center, PO Box 1234, Bangalore 560012, India

Note: [] Corresponding author.

Abstract: This work considers a reinforcement of a multiconnected domain representing the cross section of a cylindrical bar. The model studied in this paper is motivated from the classical problem of elastic torsion of such a structure. The stress potential is assumed to satisfy an equation involving p‐Laplacian in the interior. Dirichlet boundary condition is imposed on the outer boundary. We seek the potential in the space of functions with trace being an unknown constant on the inner boundary. Consequently, there is an induced natural condition involving the integral of its conormal derivative on the inner boundary. We assume that the reinforcement is nonhomogeneous, periodically oscillating and has small thickness which is of the same order as the period. We describe its limiting behaviour as the period goes to zero. The limit problem has certain new features which are pointed out.

Keywords: reinforcement, boundary layer, Γ‐convergence, torsional rigidity, quasilinear elliptic problem

Journal: Asymptotic Analysis, vol. 31, no. 3-4, pp. 247-263, 2002