Axisymmetric displacement boundary value problem for a penny-shaped crack

Summary A solution is derived from equations of equilibrium in an infinite isotropic elastic solid containing a penny-shaped crack where displacements are given. Abel transforms of the second kind stress and displacement components at an arbitrary point of the solid are known in the literature in terms of jumps of stress and displacement components at a crack plane. Limiting values of these expressions at the crack plane together with the boundary conditions lead to Abel-type integral equations, which admit a closed form solution. Explicit expressions for stress and displacement components on the crack plane are obtained in terms of prescribed face displacements of crack surfaces. Some special cases of the crack surface shape functions have been given in the paper.