The end problem for a torsionless hollow circular elastic cylinder

A class of axisymmetric boundary value problems for a torsionless semi-infinite hollow circular cylinder is considered; the lateral surface of the cylinder is assumed to be traction free, whereas its end-section is subjected to given self-equilibrated loads, given displacements or to mixed boundary conditions. The solution utilizes Love's stress representation - - known to be complete - - to generate an aggregate of biorthogonal eigenfunctions in the interval a≤π≤b. The problem is formally reduced to an infinite system of linear algebraic equations; explicit expressions being given in the case of mixed boundary conditions. The close association of the problem with two classical ones, namely, Saint-Venant's problems and Salnt-Venant's principle is discussed and supplemented with substantial references.