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Lie Group Modeling of Nonlinear Helical Beam Elements

[+] Author Affiliations
Ralph Jödicke, Uwe Jungnickel

Institute of Mechatronics, Chemnitz, Germany

Andreas Müller

University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai, China

Paper No. DETC2014-34355, pp. V006T10A030; 10 pages
doi:10.1115/DETC2014-34355
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4639-1
  • Copyright © 2014 by ASME

abstract

A viscoelastic beam model is presented based on SE(3) group theory. We discretize a rod with beams between finite frames on the rod and regard the configurations of these frames as elements of the SE(3) Lie group. Two subsequent frames are connected by a beam. The curvatures and strains are assumed to be constant on the trajectory between them. If the deflection curve of the beam is modeled as a helix, the resulting beam model is geometrical exact for large bending deformations. The stiffness matrices of the discrete beam elements result from the potential extensional and shearing energy as well as from the potential bending and torsion energy. The benefit of this SE(3) modeling for translational elastic coordinates and for translational forces in comparison to an SO(3) × ℝ3 variant is demonstrated.

Copyright © 2014 by ASME
Topics: Modeling

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