The Half-plane with an Edge Crack in Plane Elastostatics

The Wiener-Hopf technique is applied to the problem of a half-planewith a crack perpendicular to its edge. A closed solution isobtained giving the stress and displacement fields in the formof eigenfunction expansions, valid over the whole region, exceptthe neighbourhood of the tip of the crack. The behaviour inthis region is obtained by an asymptotic technique. The coefficientsof the expansions involve a generalized factorial function,and a method for the computation of this function is given,thus enabling numerical values of the stresses and displacementsto be obtained for the given cases of stretching and bendingthe half-plane.