On the relation between rigid-plastic and elastic-plastic predictions of response to pulse loading

Using a simple model, comparisons are shown between the predictions of elastic-plastic and rigid-plastic analyses as to the permanent displacements due to pulse loading. Several pulse shapes are considered, and the comparisons are made over a large range of the ratio τ/T (pulse duration time/natural period of the structure). When the rise time of the pulse is not zero, these show a wavy character that was not seen in earlier comparisons of this type, where smaller ranges were used. Thus the two predictions are found to be very close at regular intervals, while the rigid-plastic prediction has negative (unconservative) errors in between, relative to the elastic-plastic one. These errors may be large even though the plastic deformation greatly exceeds the elastic displacement at yield. The ‘energy ratio’ criterion for validity of rigid-plastic analysis must be supplemented, for ‘long’ pulses, by consideration of the effect of pulse duration. The waviness of the elastic-plastic spectral plots is explained in terms of the similar shapes of the ‘dynamic amplification’ spectra of wholly elastic shock analysis.