Assessment of large displacement of a rigid-plastic shell withholding a localized impact

A method is derived allowing to assess large deflection of a rotationally-symmetric rigid-plastic shell impacted by a concentrated mass. Assuming a kinematically admissible mechanism of motion of the deforming portion of the shell the final shape of the shell and the time to rest are evaluated. The principle of virtual work is employed to derive the non-linear differential equation of motion of the impacting mass withheld by the shell. The maximum central deflection in terms of kinetic energy of the striking mass and of the dissipative properties of the shell is given. For a point impact an analytic solution is obtained. A numerical technique is used in the case of impact by a finite stamp and the central deflection of the shell is plotted in terms of velocity, mass and kinetic energy of the striking object.