ALE beam using reference dynamics

We present a small strain beam model based on the Arbitrary Lagrangian Eulerian setting for use in multibody dynamics. The key contribution of the present paper is to provide a formulation with large flexible reference motion and small overlaid deflections. We point out that the reference motion is...

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Bibliographic Details
Published in:Multibody system dynamics 2019-06, Vol.46 (2), p.127-146
Main Authors: Grundl, Kilian, Schindler, Thorsten, Ulbrich, Heinz, Rixen, Daniel J.
Format: Article
Language:English
Subjects:
Automotive Engineering
Belt drives
Computer simulation
Continuously variable
Control
Degrees of freedom
Dry friction
Dynamical Systems
Electrical Engineering
Engineering
Formulations
Mathematical analysis
Mathematical models
Mechanical Engineering
Optimization
Rope
Strings
Transmissions (automotive)
Variations
Vibration
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Summary:We present a small strain beam model based on the Arbitrary Lagrangian Eulerian setting for use in multibody dynamics. The key contribution of the present paper is to provide a formulation with large flexible reference motion and small overlaid deflections. We point out that the reference motion is described by actual degrees of freedom of the model. Therefore, we use a vector of generalized positions and an Eulerian coordinate, which itself is a degree of freedom and in which the flow of the beam material through an arbitrary volume is represented. The additional displacements describe small fluctuations around the reference motion. With this idea it is easy to separate the motion of belt drives, cable and rope ways or strings. In particular, the overlaid deflections are described for efficient numeric computation and may be analyzed in an easy way for vibrational behavior. The guiding reference motion is arbitrary, i.e., the transmission ratios are degrees of freedom and may change dynamically affecting also the fluctuations. Contacts with dry friction are foreseen and represented in the present model. It is validated and proven to be efficient in comparison with classic co-rotational and absolute nodal coordinate formulations in our application. The simulation of pushbelt continuously variable transmissions is taken as a high-dimensional industrial example.
ISSN:1384-5640
1573-272X
DOI:10.1007/s11044-019-09671-7