Equilibrium planar crack with contour angular points in elastic layer

The three-dimensional static problem of the elasticity theory on the elastic layer balance weakened by a flat rectangular crack is considered. The crack is located in the median layer plane; it is supported open under the normal loading applied to its edges. The layer edges are under the smooth contact with two rigid bases. The problem is converted to the solution of the known singular integro-differential equation concerning the crack opening function through the application of two-dimensional integral Fourier transformation to the equilibrium equation. The equation solution is constructed by the direct variational method. In neighborhood of the contour angular points, the solution completes the construction numerically, with regard for the early distinguished singularity. Values of the direct stress intensity factor in neighborhood of the crack periphery are obtained. The solution behavioral features in neighborhood of the contour rectilinear sites and angular points are established.