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.
Highlights
During the last decades, the room available in car vehicles has plummeted because of the rapid development of on-board electronics
Taking advantage of the polynomial form of the system of equations obtained when using quaternion parameters an alternative consists in replacing the predictor-corrector method (PCM) by the asymptotic numerical method (ANM) firstly presented by Damil and Potier-Ferry [18] and by Cochelin [19]
We propose here to set up the technique on the finite-element based geometrically exact beam model, in what constitutes the main originality of this paper
Summary
The room available in car vehicles (e.g. in engine compartment) has plummeted because of the rapid development of on-board electronics. Used only for storage in the numerical models, Zupan et al [12] have recently shown their utility when used as primary variables They have developed a model without rotation matrices exploiting the high potential of quaternion algebra, and very efficient for numerical purposes [15]. Taking advantage of the polynomial form of the system of equations obtained when using quaternion parameters an alternative consists in replacing the PCM by the asymptotic numerical method (ANM) firstly presented by Damil and Potier-Ferry [18] and by Cochelin [19]. This technique is very robust, does not require any tuning parameters and is well suited for an industrial use. A critical evaluation and future researches are presented by way of conclusion
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