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Kinetic Aspects of Discrete Cosserat Rods

Joachim Linn ; Tomas Hermansson (Institutionen för produkt- och produktionsutveckling) ; Fredrik Andersson ; Fabio Schneider
Proceedings of the 8th ECCOMAS Thematic Conference on Multibody Dynamics (2017)
[Konferensbidrag, refereegranskat]

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 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).

Nyckelord: Cosserat rods, discrete balance equations, geometric finite differences, Lagrangian mechanics



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Denna post skapades 2017-09-05.
CPL Pubid: 251629

 

Institutioner (Chalmers)

Institutionen för produkt- och produktionsutveckling (1991-2017)

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Produktion
Fysik
Materialteknik

Chalmers infrastruktur