| description abstract | An edgecracked halfplane 0 < x < A and a halfplane x > 0 with a semiinfinite crack x > a perpendicular to the edge are examined in this paper. Uniform crackface loading is thoroughly examined, with a thorough exposition of the Koiter Wiener–Hopf approach (Koiter, 1956, “On the Flexural Rigidity of a Beam Weakened by Transverse Saw Cuts,†Proc. Royal Neth. Acad. of Sciences, B59, pp. 354–374); an analytical expression for the corresponding Tstress is obtained. For the additional cases of (i) nonuniform edgecrack crackface loading دƒ(x/A)k (â„œ(k)>1), (ii) concentrated loading at the edgecrack crack mouth, the Wiener–Hopf solutions and analytical Tstress expressions are provided, and tables of Tstress results for دƒ(x/A)k and دƒ(1x/A)k are presented. A Green's function for the edgecrack Tstress is developed. The differing developments made by Koiter (1956, “On the Flexural Rigidity of a Beam Weakened by Transverse Saw Cuts,†Proc. Royal Neth. Acad. of Sciences, B59, pp. 354–374, Wigglesworth (1957, “Stress Distribution in a Notched Plate,†Mathematika, 4, pp. 76–96), and Stallybrass (1970, “A Crack Perpendicular to an Elastic HalfPlane,†Int. J. Eng. Sci., 8, pp. 351–362) for the case of an edgecracked halfplane are enhanced by deducing a quantitative relationship between the three different Wiener–Hopf type factorizations. An analytical universal Tstress expression for edgecracks is derived. Finally, the case of a vanishing uncracked ligament in a halfplane is examined, and the associated Wiener–Hopf solution and analytical Tstress expression are again provided. Several limiting cases are examined. | |
