Thin covers from different materials are often applied in engineering to improve the functional properties of the surfaces of machines and structures components. On the other hand, thin covers with certain mechanical properties are used to model the real microstructure of surfaces, adhesion and glue bondings. The classical methods for solution of contact problems for bodies with thin covers are grounded on integral equations and are reviewed in work. Nowadays, one of the most effective numerical methods for such contact problems are methods, based on variational formulations and finite element approximations.
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