An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics

We present in this paper a new nite element formulation of geometrically exact rod models in the threedimensional dynamic elastic range. The proposed formulation leads to an objective (or frame-indi erent under superposed rigid body motions) approximation of the strain measures of the rod involving nite rotations of the director frame, in contrast with some existing formulations. This goal is accomplished through a direct nite element interpolation of the director elds de ning the motion of the rod’s crosssection. Furthermore, the proposed framework allows the development of time-stepping algorithms that preserve the conservation laws of the underlying continuum Hamiltonian system. The conservation laws of linear and angular momenta are inherited by construction, leading to an improved approximation of the rod’s dynamics. Several numerical simulations are presented illustrating these properties