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A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables

Type
Articles dans des revues avec comité de lecture
Author
COTTANCEAU, Emmanuel
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
133641 Technocentre Renault [Guyancourt]
THOMAS, Olivier
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
VERON, Philippe
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
ALOCHET, Marc
133641 Technocentre Renault [Guyancourt]
300520 RENAULT
DELIGNY, Renaud
133641 Technocentre Renault [Guyancourt]

URI
http://hdl.handle.net/10985/14335
DOI
10.1016/j.finel.2017.10.002
Date
2018
Journal
Finite Elements in Analysis and Design

Abstract

In this paper, a method for the quasi-static simulation of flexible cables assembly in the context of automotive industry is presented. The cables geometry and behavior encourage to employ a geometrically exact beam model. The 3D kinematics is then based on the position of the centerline and on the orientation of the cross-sections, which is here represented by rotational quaternions. Their algebraic nature leads to a polynomial form of equilibrium equations. The continuous equations obtained are then discretized by the finite element method and easily recast under quadratic form by introducing additional slave variables. The asymptotic numerical method, a powerful solver for systems of quadratic equations, is then employed for the continuation of the branches of solution. The originality of this paper stands in the combination of all these methods which leads to a fast and accurate tool for the assembly process of cables. This is proved by running several classical validation tests and an industry-like example.

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