Three-dimensional contact problem for a transversely isotropic solid

The spatial contact problem with an unknown contact domain is investigated for a transversely isotropic elastic half-space the boundary of which is perpendicular to the planes of isotropy. For a circular punch, the contact zone, as a rule, is not a circle because the stiffness of the elastic solid boundary depends on the direction. The problem is reduced to an integral equation (IE) with respect to the contact pressure the kernel of which does not include quadratures. Galanov’s numerical method which makes it possible to determine simultaneously the contact zone and the contact pressure is used to solve the IE. The simple form of the IE kernel allows regularizing it by using a parameter which depends on mesh intervals as well as on anisotropy parameters. A well-known exact solution to a punch in the form of an elliptical paraboloid is used to verify the computer program. The numerical analysis has been made for different transversely isotropic materials contacting with conical and pyramidal punches.