Rigid-plastic membrane response of thin plates under impulsive blast loads using the extended Hamilton principle

The response of plates subjected to blast loads is of considerable scientific interest. The loading imparted to a structure following a close-in detonation of a high explosive is typically high in magnitude, near-impulsive, spatially non-uniform, with localised variability and a high dependence on factors such as charge shape, position, and composition. The resulting structural response may induce large displacements in materials whose properties may not be fully characterised. In order to properly account for the effects of such intrinsic and extrinsic uncertainties, modelling approaches must balance the competing demands of accuracy and low computational demand. This article applies the extended Hamilton's principle to rigid-plastic thin plates subjected to impulsive blast loads to derive the governing equation of motion without a prior assumption of the initial specific impulse distribution. Closed-form solutions to predict the plastic response are derived for rectangular and circular plates. The analytical models for uniform specific impulses are found to be in good agreement with high-fidelity numerical simulations performed using LS-DYNA and experimental data available in the literature.