The three-dimensional Galin’s type contact problem for a two-layered elastic base (a layer completely attached to a half-space from another material) is investigated when an extra loading (concentrated force) is applied outside the contact area. The contact zone is supposed to be unknown. The punch foot form is an elliptic paraboloid. The problem is reduced to an integral equation with respect to the unknown contact pressure distributed in the unknown contact zone. Galanov’s method of nonlinear boundary integral equations is used to determine the contact pressure and the contact zone simultaneously. Calculations made for various values of elastic and geometric parameters allow estimating an extra force input to the dependence between the punch settlement and the force applied to the punch. The problem is important for the strength analysis of coated surfaces of various elastic solids subjected to contact and extra loadings. The solution can be also useful in the frame of the discrete contact theory for bodies with rough surfaces.
theory of elasticity, contact problems, two-layered elastic base, nonlinear boundary integral equations, Galanov’s method
Introduction. Bodies with coverings represent a widespread class of materials, so their study has the great theoretical and practical significance. L. A. Galin was probably the first who has considered the contact problem for a half-space with an additional concentrated force applied outside the contact area [1]. A similar contact problem for a two-layered elastic base was investigated earlier [2] without additional force. The Galanov’s method used below to take the additional concentrated force into account allows us to estimate the influence of the extra force onto the contact pressure as well as onto the force applied of the punch. This problem is of interest for the contact mechanics of the bodies with coverings.
1. Argatov, A. A., Dmitriev, N. N. Osnovy teorii uprugogo diskretnogo kontakta / A. A. Argatov, N. N. Dmitriev. - Sankt-Peterburg : Politekhnika, 2003. - 233 s.
2. Alexandrov, V. M., Kalker, J. J., Pozharskiy, D. A. Three-dimensional contact problem for a twolayered elastic base with an unknown contact area. Mechanics of Solids, 1999, no. 4, pp. 41-45.
3. Alexandrov, V. M., Pozharskiy, D. A. Three-dimensional contact problems. Dordrecht : Kluwer, 2001, 406 p.
