A long cylindrical shell without end loads or restraints is considered to be loaded uniformly by external pressure applied as a rectangular-shaped pulse in time. It is assumed that the shell material is elastic and perfectly plastic, that the material points in the shell are displaced only in the radial direction, and that all points on the middle surface of the shell have the same motion in time. This paper investigates the total impulse which must be delivered to the shell in order to bring the inward radial displacement to a prescribed maximum value. The impulse needed to cause the prescribed displacement is calculated as a function of pulse-duration time and compared with the impulse for zero-pulse-duration time, which is calculated using the Dirac delta function. The ratio, a function of maximum displacement and pulse-duration time, always increases with increasing pulse-duration time, but the rate of increase is relatively less severe for more ductile materials. The duration of the plastic regime is also calculated, since this affects the growth of buckling displacements according to the analysis of Abrahamson and Goodier.2 It is found that, for a given total impulse, the plastic-regime duration time decreases with increasing pulse-duration time. Thus, buckling would be most severe for the shortest pulse-duration time.

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