Dynamic plastic deformation of a free ring subjected to a point load

The permanent deformation of a rigid perfectly-plastic unsupported thin ring subjected to a concentrated time-dependent force acting along a diameter is calculated. The analysis is developed for a force pulse of arbitrary shape, and numerical results are obtained for the special case of a triangular force pulse. It is shown that, for sufficiently large values of the applied force, four plastic hinges develop along the ring. Two of the hinges are fixed, and the other two move along the ring as the force varies with time. The motion of the hinges is governed by a system of coupled nonlinear ordinary differential equations that are solved numerically. The parameters that describe the final plastic deformation of the ring are evaluated and shown graphically. Previous studies of this problem provided a numerical solution for the case of a rectangular pulse only