Schokotova O. Plane problems of smooth and frictional contact for elastic wedge.

The object is the contact interaction of the wedge-shaped elastic body with the hard punch in conditions of plane deformation. The aim is the building of analytical solutions of plane contact problems for elastic wedge. Methods - integral Mellin and Fourier transformation, theory of residues for calculation of integrals, Wiener-Hopf method, numerical method of Newton and asymptotic method of finding the roots of transcendental equations. Using the Wiener - Hopf method the methodology of determining the two-dimensional stress-strain state of wedge-shaped elastic bodies in conditions of a smooth and frictional contact with the punch of various forms is developed. By this method for the first time the analytical solutions of a number of the contact problems of elasticity theory for a wedge with one fixed face are obtained. The stress in the contact region and on the wedge fixed face as well as the displacements of spots of the elastic wedge unfixed face are determined. The influence of friction on the contact interaction of punch with elastic wedge is investigated. Scope - machine building, instrument making, the learning process.