The axisymmetric contact problem of the theory of elasticity for a half-space in the presence of body forces

We consider the axisymmetric problem of determination of the stress-strain state in an elastic half-space in the case of a circular line of separation of the boundary conditions on the boundary plane z = 0. We assume that on the entire boundary z = 0 the tangential stress _rz = 0, while inside the circle r a (z = 0) the normal displacement u_z is known and in its exterior the normal stress _z is given. In addition, we assume that body forces are acting in the half-space. The investigation of problems of similar kind presents interest in connection with the application of A. A. Il'yushin's method of elastic solutions to the problem of the indentation of punches into a nonlinear-elastic, in particular, into an elastoplastic half-space.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 110–115, July–August, 1971.The author wishes to thank M. Ya. Leonov for his valuable suggestions during the preparation of this paper.