Interaction between reflected elastic flexural waves and a plastic 'hinge' in the dynamic response of pulse loaded beams

By employing an elastic-perfectly plastic ideal sandwich beam model and solving the governing equations expressed in finite-difference form, the interaction between the reflected elastic flexural wave and the plastic hinge in the dynamic response of the beam to a suddenly applied force pulse is examined. The evolution of the plastically deforming region in the beam (the plastic hinge) is shown to be closely related to its encounter with reflected elastic waves. The correlation between the formation of a reversed hinge at the root with the notable oscillation in the position of the travelling hinge is also revealed. When the beam is loaded by a step force, the plastic hinge locates at a position close to that predicted by the rigid-plastic analysis and it is relatively stable during its interaction with the reflected elastic waves. When a rectangular pulse is applied, whether the reflected elastic waves can terminate the plastic flow in the plastic zone (i.e. whether the entire plastic zone undergoes complete elastic unloading) is shown to depend on the total impulse imparted to the beam.