Abstract
There is considered an infinite elastic plane with a symmetric crack that can be mapped into a circle by a rational function. It is assumed that opposite edges of the crack come into contact because of loading at infinity. it is also assumed that the vertical displacement component is known on the crack contour in the contact range; there is no tangential stress because of symmetry, and there are no stresses on the free part of the boundary. By means of a suitable selection of two piecewise-meromorphic functions, the boundary conditions result in a Riemann boundary value problem for the vector functions holomorphic on a plane slit along pairs of circular arcs, and having finite order at infinity. A solution is given in quadratures for the problem formulated. Conditions are written down which define the unknown coefficients of the general solution. A specific example is considered when the crack has the profile of a prolate ellipse.
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