Asymmetrically cracked cylinder under torsion (Q1071587)

A problem of sufficient practical interest was solved in this paper within the context of linear elastostatics. The elastic body has the form of a shaft with a circular cracked cross-section, the crack being a segment of a diameter, not necessarily in the central position. The external loading was a twisting couple or, equivalently, anti-plane stresses acting on the crack faces. The solution is effected by using complex-variable techniques and reducing the problem to the Keldysh-Sedov mixed boundary value problem. In our opinion, this approach is the most simple and straightforward as compared with previous procedures which have solved similar problems.