Torsion of a circular cone with static and dynamic loading

Integral transformation methods—the Mellin transform for statics and the Lebedev-Kontorovich transform for dynamics—are used to construct analytic solutions of the problem of the torsion of an elastic circular cone. Assuming that external forces are concentrated in the neighbourhood of the vertex of the cone, the asymptotic behaviour of the far field is investigated. It is shown that the leading term of the asymptotic expansion is governed by the magnitude of the moment of the external forces, so that the St Venant principle is satisfied in the cases under consideration.