On the stresses in the vicinity of an elliptic hole in a cylindrical shell under torsional loading

A perturbation solution is presented for the stresses around a small elliptic hole in an infinitely long circular cylindrical shell subjected to torsion. The major axis of the whole is taken to be parallel to the shell axis. For the limiting case of a crack, the general solutions in elliptic coordinates are expanded at the crack tip in polar coordinates to obtain stresses in the form usual to solutions for crack problems.