Axially symmetric contact problem for half spaces with geometrically perturbed surface

We consider an axially symmetric problem of frictionless contact of two semiinfinite bodies. The surface of one of these bodies has a geometric inhomogeneity in the form of a depression of small depth. The corresponding mixed boundary-value problem is formulated and solved by the method of coupled integral equations. We determine the geometric characteristics of the gap and the distribution of contact pressure depending on the mechanical characteristics of the materials and the loading mode. Franko L'viv State University, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 6, pp. 22–26, November–December, 1999.     

Shear of Two Half Planes Pressed to Each Other and Containing a Surface Groove. Part 1. Full Contact

We consider a plane problem of shear of two half planes preliminarily pressed to each other. One of these planes contains a shallow surface groove. By using the Kolosov-Muskhelishvili complex-valued potentials, the problem is reduced to a singular integral equation. This equation is analytically solved for a special form of the groove. We discovered three ranges of external tangential loads in which the contact couple exhibits qualitatively different types of behavior: perfect adhesion of the bodies, local sliding of points of the surface, and global sliding of the bodies relative to each other. The behavior of the system under the conditions of local sliding is analyzed in detail. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 2, pp. 39–44, March–April, 2005.     

Problem of Contact of Two Half Spaces with a Ring-Shaped Groove in One of Them. Part 2. Numerical Method and Results

A numerical algorithm is proposed for the solution of a singular integral equation of the axisymmetric elastic problem of contact of two half spaces one of which contains a ring-shaped groove. By the methods of orthogonal polynomials and collocations, the singular integral equation is reduced to a system of nonlinear algebraic equations for the geometric parameters of the gap and the coefficients of Fourier expansion of the required function in Chebyshev polynomials of the first kind. A numerical solution of the posed problem is constructed and used for the analysis of contact parameters regarded as functions of the radii of the ring-shaped groove of fixed width.     

Contact of Two Half Spaces One of Which Contains a Ring-Shaped Pit. Part 1. Singular Integral Equation

We consider an axisymmetric problem of elastic contact of two half spaces one of which contains a ring-shaped pit. A method proposed for the solution of this problem is based on the construction of a special integral representation of the components of the vector of displacements and stress tensor via the height of the gap with subsequent reduction of the original problem to the solution of a singular integral equation with leading singularity of the Cauchy type relative to the derivative of the height of the gap.     

Thermoelastic State of a Semiinfinite Body with Plane Surface Crack under the Action of Heat Sources

We study the influence of stationary heat sources on the stressed state of a semiinfinite body with a surface crack (in the form of a circular segment) perpendicular to its boundary by the method of boundary integral equations. The load-free boundary is maintained at zero temperature; the crack is not loaded and is either thermoisolated or maintained at a certain specified temperature. The dependences of the stress intensity factor on the angular coordinate of a point on the contour of the crack are constructed for various distances of a heat source from the boundary of the half-space and depths of the crack.