An infinitely large plate weakened by a circular-arc crack subjected to partially distributed loads

On the basis of the complex-variable approach for the first boundary condition problems, a mapping function is proposed to transform the contour surface of a circular are crack into a unit circle. By this mapping, direct stress integration along the contour surface can be performed for the case when uniform tractions are applied on part of the crack edge. General complex stress functions are obtained by evaluating the Cauchy integral for the governing boundary equation. After the obtained stress functions are differentiated with respect to a reference angle in the mapped plane, the general complex stress functions for the circular-arc crack problem, when concentrated loads are applied on the crack surface, can be obtained. The importance of this solution lies in its general applicability to crack problems with arbitrary loading.