Semi-inverse method for solving circular arc crack problems

A new approach to a certain class of circular arc crack problems is proposed in this paper. The problems are reduced to the problem of linear relationship of the boundary value (the Hilbert problem). By means of the harmonic measure and conformal mapping technique, the closed solutions are given for a plane with a single circular arc crack subjected to the uniform normal and tangential loads on the part near one end of the crack and for the same plane under concentrated normal and tangential loads at an arbitrary point on the arc crack surface. The stress intensity factors at the crack tips under consideration are determined. Some known results for the plane with the central straight crack are shown as the limiting cases of the present solutions.