Analytical evaluation of the transverse displacement at the tip of a semi-infinite crack in an elastic plate

In this paper, a general approach is developed for evaluating the transverse displacements in an angular sector. The problem is investigated within the first order plate theory, which can be considered as an elementary extension of the classical plane theories of elasticity. Based on this approach, a new analytical solution for a semi-infinite crack subjected to mode I loading is obtained and this solution is verified against previous three-dimensional Finite Element studies. This approach can also be useful in the analysis of other problems, which can be reduced to a modified Helmholtz (or Yukawa) equation in an angular sector.