Abstract
The three - dimensional Galin’s type contact problem for a two - layered elastic base (a layer completely attached t o a half - space from another material) is investigated when an extra loading (concentrated force) is applied o utside the contact area. The contact zone is supposed to be unknown. The punch foot form is an elliptic parabol oid. The pro blem is reduced to an in tegral 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 con tact pressure and the contact zone simultaneously. Calculations made for various values of elastic and geometric parameters a llow estimating an extra force input to the dependence between the punch settlement and the force app lied to the punch. The problem is important for the strength analysis of coated surfaces of variou s elastic solids subjected to contact and extra loadings. The solution can be also useful in the frame of the discrete contact the ory for bodies with rough surfaces.
Highlights
Bodies with coverings represent a widespread class of materials, so their study has the great theoretical and practical significance
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
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
Summary
Bodies with coverings represent a widespread class of materials, so their study has the great theoretical and practical significance. 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]. 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. Consider the contact problem of the indentation of a punch into an elastic layer of the thickness h completely attached to an elastic half-space. By means of the methods of the operational calculus [2], one can derive the following integral equation with respect to the normal contact pressure q (x, y):
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