A penny-shaped crack in a layer whose upper and lower surfaces are fixed

A vertical, planar pressurized crack is located in a layer with fixed upper and lower surfaces. The integral representation for the displacement field is given, and an integral equation, which relates crack opening and applied pressure, is derived. A numerical scheme to construct the triangular boundary elements and to solve the integral equation is developed. A three-term approximative integration scheme developed by Sneddon proves to be essential for implementation of the numerical solution. Numerical examples are designed for exploring the boundary effect once the kernel of the integral is put into a suitable form. Simplifying methods to approximate the results of the exact solution are developed and prove surprisingly accurate.