Mode Approximations for Impulsively-Loaded Rigid-Plastic Structures

This paper is concerned with impulsively-loaded metal structures which fall into the class that can be treated by the elementary rigidplastic theory. This class is defined by the condition that the initial energy (or the energy finally dissipated in plastic deformation) should be small compared to the maximum amount of energy which can be stored elastically in the structure. An attempt is made to provide a rational method of constructing one degree of freedom approximations for this class of problem. The approximation follows automatically from the choice of a mode shape, i.e., the most rational choice of the initial amplitude of the mode and the subsequent behavior of the mode involve no further arbitrary decisions. The method is based on a comparison of the behavior of two solutions involving the same structure by different initial conditions, using an argument similar to that which established uniqueness of solution. Illustrative examples are given.