Abstract

There are three basic finite element formulations which are used in the dynamics analysis of flexible beams undergoing large rotation and deformation. These are the floating frame of reference approach, the finite segment method and the large rotation vector approach. Recently, the absolute nodal coordinate formulation was proposed by A.A.Shabana et al. In this formulation, elastic forces are lead by approximating the slope of the beam at an arbitrary point on the neutral axis of the beam in terms of the slope of the simple support axis of the beam.

In this paper, we propose the mean axis of the planar Bernoulli-Euler beam for the absolute nodal coordinate approach. The origin and the orientation of this axis are selected so as to minimize the total deformation of the concerned beam. And the selected axis can be simply described by the nodal coordinates of the beam element. Using the mean axis instead of the simple support axis, the elastic forces of the beam element may be more precisely calculated. Finally, we show numerical examples to demonstrate effectiveness of this approach.

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