THE PROBLEM OF AN EDGE CRACK IN A HALF-PLANE

The problem of stretching a half-plane with an edge crack by a distributed load was solved by Koiter and Wigglesworth. Their solutions obtained using integral transformations are very complex; therefore, attempts have been made to solve the problem by other methods. These methods are also more complicated than the classical methods of Kolosov and Muskhelishvili and are suitable only for a narrow class of problems. But there may be an idea that it is impossible to solve the problem of a crack in a half-plane and similar problems using classical methods. However, this is not the case, which is confirmed by the present work. The problem is solved by decomposing derivatives of complex potentials into power series, in combination with a conformal mapping of the unit circle to the area under consideration. For the coefficients of the series, an infinite system of linear algebraic equations is obtained. The advantages of the resulting solution lie both in the generality of the method by which it was obtained and in its simplicity: it makes it easy to find not only the intensity factor of the strain.