Multibody dynamics simulation of geometrically exact Cosserat rods

  • In this paper, we present a viscoelastic rod model that is suitable for fast and sufficiently accurate dynamic simulations. It is based on Cosserat’s geometrically exact theory of rods and is able to represent extension, shearing (’stiff ’ dof), bending and torsion (’soft’ dof). For inner dissipation, a consistent damping potential from Antman is chosen. Our discrete model is based on a finite difference discretisation on a staggered grid. The right-hand side function f and the Jacobian ∂f/∂(q, v, t) of the dynamical system q˙ = v, v˙ = f(q, v, t) – after index reduction from three to zero – is free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore cheap to evaluate. For the time integration of the system, we use well established stiff solvers like RADAU5 or DASPK. As our model yields computation times within milliseconds, it is suitable for interactivemanipulation in ’virtual reality’ applications. In contrast to fast common VR rod models, our model reflects the structural mechanics solutions sufficiently correct, as comparison with ABAQUS finite element results shows.

Download full text files

Export metadata

Additional Services

Search Google Scholar
Metadaten
Author:H. Lang, J. Linn, M. Arnold
URN:urn:nbn:de:hbz:386-kluedo-16005
Series (Serial Number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (159)
Document Type:Report
Language of publication:English
Year of Completion:2009
Year of first Publication:2009
Publishing Institution:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2009/05/20
Tag:Constrained mechanical systems; Finite rotations; Flexible multibody dynamics; Large deformations
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011