Large deformations of rigid-viscoplastic cantilevers under impulsive loading

Abstract

The problem of a ductile metal cantilever structure (not necessarily initially straight) subjected to dynamic loads leading to deformations of the order of the dimensions of the structure is considered. The material is treated as rigid-viscoplastic; in this idealization elastic effects are ignored, and the dependence of the yield stress on the rate of strain is taken into account. The problem is first analysed as one of impulsive loading, using the concepts of the mode approximation technique. A new algorithm for the determination of mode shapes is presented, together with an algorithm for the time integration of the motion in which the geometry of the structure is updated. Applications of the method are described for impulsive loading, and extended to the pipe-whip problem where the loading is in the form of a pulse which acts in the direction of the tangent at the tip of the cantilever structure at each instant.