Complex variable methods are applied to the plane elastic problems of semi-infinite sheet with a sharp edge notch of an arbitrary included angle 2β. The concept of the stress intensity in a crack problem is extended to the externally cut V-shaped notch. The difficulty of the problem would lie in the unavoidable introduction of a mapping function with singularities of branch-point type and related complex potentials, which is shown to be resolved by a power series development with expansion coefficients, which depend on the boundary-describing parameter, being smoothly continued from the traction-free boundary region to the local zone characterized by a stress singularity. General solutions for the stresses and the stresses local to the notch tip are given. In the light of the foregoing arguments the implications of the Westergaard solution for a crack are discussed.
stress singularity factor
strength of singularity
edge notch
conformal mapping
Schwartz-Christoffel transformation