Closed form solutions for the dynamics of a pressurized elastoplastic thin-walled tube

This paper provides analytic solutions for the dynamics of a pressurized elastoplastic thin-walled tube at small strains. The closed-form expressions of the stress and displacement fields are derived within the framework of thin cylindrical shell theory. Three dynamic load-processes are considered: an the increasing-constant internal pressure, a rectangular and a triangular pulse loads. It is found that, depending on the external load function, the ductility limit of the solid may be reached and the displacement is unbounded. In this case, the structure collapses by plastic strain accumulation. However, if the ductility limit is not reached, plastic strains stabilize after a transient phase and the tube exhibits an elastodynamic response function. The analytical results are compared with numerical predictions derived by the standard Finite Element Method (FEM).