A bilateral asymptotic method of solving the integral equation of the contact problem of the torsion of an elastic half-space inhomogeneous in depth

An approximate semi-analytical method for solving integral equations generated by mixed problems of the theory of elasticity for inhomogeneous media is developed. An effective algorithm for constructing approximations of transforms of the kernels of integral equations by analytical expressions of a special type is proposed, and closed analytical solutions are presented. A comparative analysis of the approximation algorithms is given. The accuracy of the method is analysed using the example of the contact problem of the torsion of a medium with a non-uniform coating by a stiff circular punch. The relation between the error of the approximation of the transform of a kernel by special analytical expressions, constructed using different algorithms and the error of approximate solutions of the corresponding contact problems is investigated using a numerical experiment.