Stress Concentration near Holes in the Elastic Plane Subjected to Antiplane Deformation

By the method of singular integral equations, we determine the solutions of antiplane problems of the theory of elasticity for a plane weakened by curvilinear holes with rounded and sharp vertices. The stress intensity factors at sharp vertices are found as a result of the limit transition from rounded vertices by using the relation between the stress intensity factors and stress concentration factors at the sharp and rounded tips of a V-shaped notch. We also obtain numerical results for the holes of various configurations: elliptic, in the form of physical slots, oval, rhombic, and rectangular.