Complete Solution of Large Plastic Deformation of Square Plates Under Exponentially Decaying Pulse Loading

The rigid-plastic assumption has greatly simplified the theoretical analysis of dynamic plastic response of structures. Within this framework, a common tool is the modal technique using approximate independent yield criteria, which leads to upper- and lower-bound solutions, but usually with poor accuracy. In this paper, by utilizing the membrane factor method (MFM), the large-deflection dynamic plastic response of square plates subjected to exponentially decaying pulse loading is analyzed by taking both the transient response phase and the exact yield criterion into account. Based on the combination of saturation analysis (SA) and MFM, the complete solutions and regressive formulae of saturated deflection and saturated impulse are obtained. As the dynamic behavior of plates under rectangular pulse loading serves as a benchmark of pulse-equivalent techniques, the large plastic deformation of square plates under short-duration rectangular pulse is also analyzed in detail. Moreover, by comparing the SA results of pulse-loaded square plates with different boundary conditions, it is found that the saturated deflection and saturated impulse of the fully clamped and simply supported square plates both increase linearly with the pulse amplitude, and the slopes are approximately the same, so the conversion between the SA quantities of plates with different boundary conditions can be easily achieved.