Plane problems of multiple interactions of rigid punches and bodies with complex multilayer coatings

The article deals with the most general formulation of the problem of the interaction of a system of rigid punches and a viscoelastic aging foundation covered by several different nonuniform thin layers of variable thickness. It is shown that the mathematical model of such a problem is a system of mixed integral equations with additional integral conditions. On the basis of a special approach described in present article, an analytical solution is obtained in series for various versions of the problem statement. It is indicated that the obtained solution representation is effective even in the case when the properties of the coating layers and the shape of the contacting surfaces are described by complex functions.

Automated summary

The article discusses the interaction between a system of rigid punches and a viscoelastic aging foundation covered by nonuniform thin layers of variable thickness. It proposes a mathematical model consisting of mixed integral equations with additional integral conditions. By using a special approach, the article presents an analytical solution in series for different versions of the problem statement. It demonstrates the effectiveness of the solution representation even when the coating layers' properties and contacting surfaces' shape are described by complex functions.