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On the Issue of Redundancy in the Large Rotation Vector Formulation

[+] Author Affiliations
Jieyu Ding

Qingdao University, Qingdao, China

Michael Wallin, Antonio M. Recuero, Ahmed A. Shabana

University of Illinois at Chicago, Chicago, IL

Cheng Wei

Harbin Institute of Technology, Harbin, China

Paper No. DETC2014-34392, pp. V006T10A031; 6 pages
doi:10.1115/DETC2014-34392
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

In the large rotation vector formulations (LRVF), two independent interpolations are used in the nonlinear large displacement analysis of beams. This kinematic description leads to a fundamental redundancy problem. This paper examines this fundamental issue and demonstrates that the use of two geometrically independent meshes can lead to coordinate and geometric invariant redundancy that cannot be solved using constraints or forces. It is demonstrated in this paper that the two geometry meshes can define different space curves, which can differ by arbitrary rigid body displacements. The material points of the two meshes occupy different positions in the deformed configuration, and as a consequence, the geometries of the two meshes can differ significantly. Simple examples are presented in order to shed light on these fundamental issues.

Copyright © 2014 by ASME

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