Skip to main content
Article
A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization
Computational Mechanics (2009)
  • Susanta Ghosh, Indian Institute of Science, Bangalore
  • D. Roy, Indian Institute of Science, Bangalore
Abstract
While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.
Keywords
  • geometrically exact beam,
  • finite rotation,
  • rotation manifold,
  • tangent space,
  • relative rotation,
  • objective strain,
  • path-independence
Disciplines
Publication Date
January 8, 2009
DOI
10.1007/s00466-008-0358-z
Publisher Statement
© Springer-Verlag 2009
Citation Information
Susanta Ghosh and D. Roy. "A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization" Computational Mechanics Vol. 44 Iss. 103 (2009) ISSN: 0178-7675
Available at: http://works.bepress.com/susanta-ghosh/9/