An elastic circular cylinder with displacement prescribed at the ends - axially symmetric case

The problem of a linear elastic cylinder with a stress-free curved surface and prescribed displacements at the plane ends is solved by the development in terms of eigenvalue expansions. Then, a biorthogonality relationship for the axially symmetric case is obtained, which is seen to have convergence difficulties. These are surmounted through use of a Galerkin approach, which yields a more diagonally dominant system. To obtain results at the plane ends special techniques have to be developed that correctly incorporate the singular behaviour there.