Analytical solution for the elastic plane problem with a symmetric parabolic crack

The problem of an elastic plane having symmetric parabolic crack is discussed. Classical complex variable method is followed, but a conformal mapping formula is proposed so that the exterior part of the parabolic crack is mapped into a unit circle. An analytical solution for the mode I stress intensity factor at the crack tip of a symmetric parabolic crack is thus obtained. This solution analytically reduces to the classical solution for the line crack in a special case. It is found that the size and the shape of the parabolic crack affect the mode I stress intensity factor at the crack tips.