Mathematical modeling of the contact interaction of two elastic transversely isotropic half-spaces, one of which contains a near-surface groove of an elliptical section

On the basis of a mathematical model, problem compression two elastic transversely isotropic half-spaces, one which contains shallow near-surface groove an elliptical section, is considered. The solution to obtained using Elliott representation for body in terms harmonic functions, classical potentials and reducing boundary value considering integro-differential equation with unknown domain integration. As special case, analytical expressions yield basic parameters contact half-spaces presence axisymmetric them, as well interaction cross-section groove. Numerical results are obtained, influence properties geometrical loading on closing gap between bodies studied.