Correlation Parameters for Eliminating the Effect of Pulse Shape on Dynamic Plastic Deformation

Abstract

The solutions to four classical problems in dynamic plasticity—the circular plate under uniform pressure, the reinforced circular cylindrical shell under uniform pressure, the free-free beam with a central concentrated force, and the circular cylindrical shell with a ring load—are examined to determine the effect of pulse shape on final plastic deformation. It is found that there is a strong dependence on pulse shape for pulses which have the same total impulse and maximum load; however, the effect of the pulse shape is virtually eliminated if the pulses have the same total impulse and “effective load.” The “effective load” is defined as the impulse divided by twice the mean time of the pulse, where the mean time is the interval between the onset of plastic deformation and the centroid of the pulse.

Large viscoplastic deflections of impulsively loaded plane frames

“…It is well known that this idealization leads to over-estimates of major deflect ions (15] when app lied to rigid-perfectly plastic structures using small deflection equat ions. The error in the over-estimate in those cases can be shown to be given approximately…”

On dimensionless numbers for dynamic plastic response of structural members

“…However, when the loading time is comparable with the structural response time, then the effect of the loading shape must be considered. Normally, the two effective loading parameters introduced by Youngdahl [30] could be used to eliminate the strong dependence of the dynamic plastic response on the pulse loading shape, i.e.…”

Joining zone design for electromagnetically crimped connections

“…Strain hardening and a strain-rate dependent material behavior are neglected in this approximation to find a closed-form solution for this problem. The basic idea of Youngdahl (1970) model is the transfer of an arbitrary pressure pulse into a rectangular pulse that leads to the same deflection. Because this pressure function represents the simplest dynamic loading, the mathematical description of its deformation behavior is also simpler than for any other pulse shape.…”

“…An approach to approximate the pressure pulse necessary to fill a given groove geometry offers the analytical prediction of the dynamic response of a fully clamped cylindrical shell developed by Youngdahl (1970). Strain hardening and a strain-rate dependent material behavior are neglected in this approximation to find a closed-form solution for this problem.…”