Streliaiev Y. The solution of quasistatic contact problems of elastic bodies' interaction with Coulomb friction taken into account

A method of approximate solution of three-dimensional quasistatic contact problems of the interaction of elastic bodies taking into account Coulomb friction, partial slip and adhesion is developed. The method is based on original hypothesis of a small perturbation of the loading conditions in quasistatic process for frictional contact problems of elasticity. Qualitatively new nonlinear boundary integral equations of the contact problem are obtained. The uniqueness of the quasistatic contact problem solution is proved for natural properties of the elastic materials of interacting bodies. The method consists in regularization of the integral equations, discretization of the regularized equations and construction of iterative process for solving the discretized equations. Approbation of the proposed method consisted in comparing obtained approximate solutions of various contact problems with some other known solutions of these problems. The method was applied to solution of quasistatic contact problems of interaction of an elastic sphere and an elastic half-space and interaction of cylindrical punches with an elastic half-space. Comparison of obtained solutions with known solutions of the contact problems confirms the validity of hypothesis of the loading conditions perturbation and the correctness of based on this hypothesis method for solving considered contact problems.