Integral equation methods in plane-strain elasticity with boundary reinforcement

Abstract

In this paper, a linear theory of elastic boundary reinforcement of an elastic solid is developed for plane–strain deformations. The reinforcement consists of a thin elastic coating bonded to part of the boundary of the solid. The elastic properties of the coating incorporate both extensibility and bending rigidity. Interior and exterior mixed–boundary problems are formulated and solved using integral equation methods. The boundary value problems are reduced to systems of singular integro–differential equations to which Noether–type theorems are shown to apply. The case corresponding to a coating which has only extensibility properties and no bending rigidity is particularly interesting from a mathematical point of view and is given special attention. Finally, existence and uniqueness results are presented for both interior and exterior reinforcement problems of plane–strain.