We discuss a linear theory of elastic boundary reinforcement for plane deformations of elastic solids. The reinforcement consists of a thin elastic coating bonded to part of the boundary of the elastic solid. The elastic properties of the coating incorporate both extensibility and bending rigidity. Interior and exterior mixed boundary value problems are formulated and solved using integral equation methods. The boundary-value problems are reduced to systems of singular integro-differential equations on the coating. Finally, analytical solutions of the boundary value problems are obtained in the form of integral potentials.
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