A finite element formulation for sliding beams, Part I

We use the updated Lagrangian and the co-rotational Þnite element methods to obtain solutions for geometrically non-linear ßexible sliding beams. Finite element formulations are normally carried out for Þxed domains. Since the sliding beam is a system of changing mass, Þrst we discretize the system by introducing a variable-domain beam element and model the sliding beam by a Þxed number of elements with changing length. Second, we transform the system governing equations of motion to a Þxed domain and use conventional Þnite elements (Þxed size and number) to discretize the system. Then our investigation is followed by a comparison between two formulations. Finally, we use the co-rotational method in conjunction with a variable domain beam element to obtain the discretized system equations. To do so, we consider the beam to slide with respect to a Þxed channel and later we consider a formulation in which the beam remains at rest and the channel slides with a prescribed velocity. We show that both formulations end up with identical discretized equations of motion