On an Extremum Principle for Mode Form Solutions in Plastic Structural Dynamics

Abstract

An extremum principle of Lee and Martin [2], for mode form solutions of a structure deforming plastically as result of dynamic loading, is discussed with special reference to conditions for the extrema to be stationary, with vanishing first variation of a functional of kinematically admissible velocity fields. Three classes of material behavior are treated: rigid-perfectly plastic, rigid-viscoplastic, and viscous, the last having no yield function. We illustrate various forms of these which are realistic as well as convenient in problems of plastic dynamics of structures. For all three classes of material, we show that stationary extrema occur under certain conditions, but may be regarded as exceptional. The properties of the extrema for structures are illustrated by means of a simple discrete structure model with two masses.