Plastic Flow Buckling of Cylindrical Shells Due to Impulsive Loading

Abstract

A theory is postulated to explain the plastic buckling of cylindrical shells caused by uniform radially inward impulses. Experimental results are presented which show that the number of buckles increases with the shell length. A simple formula is derived which predicts preferred mode numbers in agreement with the experimental results for shells with lengths up to about 1 1/2 dia. For longer shells, mode numbers may be obtained by numerical integration of the equation of motion. The increase in mode number with shell length is attributed to the relative effects of the “directional” and hardening contributions to the reactive bending moment, the former stemming from yielding in a biaxial plastic state of stress. In short shells (length < dia), it is shown that the directional moment dominates, whereas in long shells (length > 3 dia) the hardening moment dominates. The mode prediction formula just mentioned applies whenever the directional moment dominates and the difficulty in treating cases where the hardening moment is significant is indicated. Again, for the former case, a simple threshold impulse formula is derived conforming to the experiments.