Ostrik V. The Elaboration of Mathematical Methods and Research of Contact Interaction of Elastic Bodies in the Presence of Friction

Thesis for a doctor degree in physics and mathematics by speciality 01.02.04 - Mechanics of Deformable Solids. - Dnipropetrovsk National University, Dnipropetrovsk, 2004. On the basis of Wiener-Hopf method the calculation united mathematical approach to the solution for some classis for boundary problems for contact mehanics for elastic bodies in the presence of friction. Wiener-Hopf method for his using to the solution for mixed problems for theory of elasticity for wedge and cone was developed, exactly: the method to the receipt for asymptotic estimations of infinite products arising in the course of factorization of meromorphic functions was offered; the method to the receipt for asymptotic forms of roots for complicated transcendental equations was developed; the Wiener-Hopf method applied to the integral equation on finite interval with the difference kernel. The exact solutions of the plain contact problems of the theory of elasticity for wedge and axisymmetric contact problems for cones with smooth and frictional contact were obtained. The contact of elastic and rigid wedges and two elastic wedges in their contact by common vertex; a press in rigid tip in an elastic wedge; analogous problems for cones; contact of elastic cone with rigid clasp is studied. On the basis of the Spense theory of eigenvalues the frictional interaction of indentor of various geometry with elastic half-plane in the precence of adhesion and slipping zones in contact domain was investigated. A solution of problem of bounded steady rotation of two pressed elastic and rigid disks with leading rigid disk was obtained. The exact solutions of problems for elastic part-homogeneous environment with interface crack in conditions of contact of shores crack according to the Comninou models of smooth and frictional contact were obtained. A influence of friction at the stressed-straired state of bodies in contact.