Abstract
A continuum of ideal rigid-plastic strain rate insensitive material is considered, with surface tractions of an impulsive character described by a single time-dependent loading parameter. A general formula is derived for the lower bound of response time and the approximate determination of the displacements. A kinematically admissible velocity field is assumed, reducing the problem to a statical analysis of the continuum and to investigation of a one-degree-of-freedom system. Substituting this system for the continuum allows estimation of effects of elastic deformations, strain hardening, and changes in geometry. Detailed analysis concerns an approximate bi-linear resistance displacement parameter relationship. An investigation of circular and rectangular plates and beams illustrates the general theorems. At relatively lower peak-values of the impulsive loading the approximation is satisfactory.
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