Abstract
The solutions of the contact problems of the theory of elasticity in the presence of wear is given for two cases. In Sect. 1 we consider the problems in which an initially curved beam comes in contact with a half-plane. One of the initial assumptions is that the distance between certain directrices along which the body in contact is sliding and the boundary of the half-plane remains constant. In Sect. 1 the contact between the curved beam and the half-plane is discussed at the assumption that the half-plane is subject to wear. As the result of the wear, the pressure between the beam and the half-plane is gradually reduced. It is naturally assumed that the pressure at the terminal points of the contact area will, in this case, be zero. The conditions characterizing the pressure at these terminal points can be established for various types of contact problems only under certain additional assumptions; this will be discussed below.
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