Abstract
The method employed in [1] is used to solve the first fundamental three-dimensional problem of the theory of elasticity for a wedge. This consists of reducing it, using a complex Fourier-Kontorovich-Lebedev integral, to a generalized Hilbert boundary-value problem, as generalized by Vekua. Formulae are given which enable one to calculate the displacement vector and the stress tensor completely in a three-dimensional elastic wedge, one face of which is stress-free, while a normal and shear load (perpendicular to the edge) act on the other. Using the solution obtained, the contact problem of the motion of a punch on the face of an elastic wedge in a direction perpendicular to the wedge edge us considered (in the quasi-static formulation). The punch is considerably elongated along the edge of an elliptic paraboloid, and hence it can be assumed approximately that the friction forces are collinear with the direction of motion. The effect of the Coulomb friction coefficient on the relation between the impressing force and the settlement of the punch for different wedge angles is investigated. The effective stress on the axis of symmetry of the contact region is calculated for different wedge angles and as a function of the distance of the punch from the wedge edge and also as a function of the direction and value of the friction forces.
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