The paper discusses the issue of discretization of the strain-configuration relationships in the geometrically exact theory of three-dimensional (3D) beams, which has been at the heart of most recent nonlinear finite-element formulations. It is demonstrated that the usual discretization procedures for implementing these strain measures within a finite-element framework violate the important property of objectivity: invariance to rigid-body rotations. A method is proposed for overcoming this limitation, which paves the way for an objective finite-element formulation of the geometrically exact 3D beam theory. For a two-noded element, this method involves obtaining the relative rotation matrix that rotates one nodal triad onto the other and then interpolating the resulting rotation vector.
This paper discusses different types of implicit time integration algorithms for the dynamics of spatial beams. The algorithms are based on a form of co-rotational technique which is external to the element. Both end-point and mid-point formulations are presented. The latter can be considered as an`approximately energy conserving algorithm'. A new method is described for introducing numerical damping. Finally some numerical examples are presented in order to illustrate the differences in performance of the different integration schemes.
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