Integral equation methods in plane-strain elasticity with boundary reinforcement

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 integrodifferential 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.