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Kinetic aspects of discrete cosserat rods based on the difference geometry of framed curves

: Linn, J.; Hermansson, T.; Andersson, F.; Schneider, Fabio

Fulltext urn:nbn:de:0011-n-4772833 (1.7 MByte PDF)
MD5 Fingerprint: 82b4b67aaa90357ffc1de774c7f161f7
Created on: 24.9.2019

Valasek, M. ; Czech Technical University, Prag; European Community on Computational Methods in Applied Science -ECCOMAS-:
8th ECCOMAS Thematic Conference on Multibody Dynamics 2017. Conference Proceedings : Prague, June 19 - 22, 2017
Prag: Czech Technical University, 2017
ISBN: 978-80-01-06173-2 (Online)
ISBN: 978-80-01-06174-9 (Print)
Thematic Conference on Multibody Dynamics <8, 2017, Prague>
Conference Paper, Electronic Publication
Fraunhofer ITWM ()

The theory of Cosserat rods provides a self consistent framework for modeling large spatial deformations of slender flexible structures at small local strains. Discrete Cosserat rod models [1, 2] based on geometric finite differences preserve essential properties of the continuum theory. The present work investigates kinetic aspects of discrete quaternionic Cosserat rods defined on a staggered grid within the framework of Lagrangian mechanics. Assuming hyperelastic constitutive behaviour, the Euler–Lagrange equations of the model are shown to be equivalent to the (semi)discrete balance equations of forces, moments and inertial terms obtained from a direct discretization of the continuous balance equations via spatial finite differences along the centerline curve. Therefore, equilibrium configurations obtained by energy minimization correspond to solutions of the quasi-static balance equations. We illustrate this approach by two academic examples (Euler’s Elastica and Kirchhoff’s helix) and highlight its utility for practical applications with a use case from automotive industry (analysis of the layout of cooling hoses in the engine compartment of a passenger car).