Abstract
The paper is concerned with a hybrid finite element formulation for the geometrically exact dynamics of rods with applications to chaotic motion. The rod theory is developed for in-plane motions using the direct approach where the rod is treated as a one-dimensional Cosserat line. Shear deformation is included in the formulation. Within the elements, a linear distribution of the kinematical fields is combined with a constant distribution of the normal and shear forces. For time integration, the mid-point rule is employed. Various numerical examples of chaotic motion of straight and initially curved rods are presented proving the powerfulness and applicability of the finite element formulation.
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Sansour, C., Sansour, J. & Wriggers, P. A finite element approach to the chaotic motion of geometrically exact rods undergoing in-plane deformations. Nonlinear Dyn 11, 189–212 (1996). https://doi.org/10.1007/BF00045001
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DOI: https://doi.org/10.1007/BF00045001