The three-dimensional contact problem for a wedge-shaped valve

The three-dimensional contact problem for an elastic wedge-shaped valve, situated in a wedge-shaped cavity in an elastic space, is investigated. A regular asymptotic method is used to solve the integral equation of this problem. The method is effective for a contact area relatively far from the edge of the wedge-shaped cavity. Calculations are carried out. The solutions of the three-dimensional auxiliary problems on the equilibrium of an elastic wedge-shaped cavity and an elastic wedge are based on well-known Green's functions, constructed using Fourier and Kontorovich–Lebedev integral transformations.