Axisymmetric Problem of Torsion of an Elastic Space with Smooth and Acute-Angled Notches

Abstract

We develop a unified approach to the solution of the problems of stress concentration near sharp and rounded vertices in axisymmetric cavities under the conditions of torsion of an elastic space. We use the method of singular integral equations for smooth open contours whose ends reach the axis of torsion of the elastic body. As a result, we determine the distributions of stresses on the surfaces of the cavities well as the stress concentration and stress intensity factors at rounded and sharp vertices. Numerical results are obtained for cavities of different configurations (rhombic, hyperbolic, oval, and rectangular) in broad ranges of variation of rounding radii at the vertices of the boundary contour.