Large deformation of rigid-viscoplastic cantilevers subjected to impulsive loading
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 idealisation 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 for small displacement assumptions and then extended to incorporate geometric effects. An algorithm is given for the time integration of the motion in which the geometry of the st ructure is updated. Applications of the method are described for impulsive loading, and extended to a type of pipe-whip problem where the loading is a combination of an impulse and a pulse which acts in the direction of the tangent at the tip of the cantilever structure at each instant. Illustrative examples are presented which show that the algorithms can be used to give very good predictions of the displaced shape of the structures under consideration.
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