Abstract
We consider a contact problem of the theory of elasticity for an isotropic half plane with a system of curvilinear cracks and a rigid punch pressed into the half plane. We assume that the base of the punch has an arbitrary convex shape, that either the punch interacts with the half plane via friction forces or they are rigidly engaged, and that the crack lips are under the conditions of smooth contact. The problem is reduced to singular integral equations in unknown derivatives of singular displacements on the crack contours and contact forces under the punch. These equations are solved by the method of mechanical quadratures. We present the results of numerical analysis of the stressed state of the half plane with internal vertical crack under pressure of a flat punch without friction on the boundary of the half plane.
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