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.

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Verfasserangaben:H. Lang, J. Linn, M. Arnold
URN (Permalink):urn:nbn:de:hbz:386-kluedo-16005
Schriftenreihe (Bandnummer):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (159)
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2009
Jahr der Veröffentlichung:2009
Veröffentlichende Institution:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Datum der Publikation (Server):20.05.2009
Freies Schlagwort / Tag:Constrained mechanical systems; Finite rotations; Flexible multibody dynamics; Large deformations
Fachbereiche / Organisatorische Einheiten:Fraunhofer (ITWM)
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011