Axisymmetric problem for rigid disc in an infinite elastic cylinder embedded in an infinite elastic material surrounding it (Q802343)

Axially symmetric stress distribution in an embedded infinite elastic cylinder containing a rigid disc is considered. A representation of the displacement at a point can be constructed as a sum of two terms involving harmonic functions. This representation after satisfying the boundary conditions on the disc and continuity conditions on the curved surface of the cylinder reduces to an unknown function which is the solution of a Fredholm integral equation of the second kind. Iterative solutions of this integral equation are obtained for a small value of the ratio of the radius of disc to the radius of the cylinder. These solutions are used for calculating the force required to shift the disc through a finite distance along the axis of the cylinder.