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Research Papers

A Detailed Comparison of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation in Deformable Multibody Systems

[+] Author and Article Information
Markus Dibold

 Linz Center of Mechatronics GmbH, Altenbergerstrasse 69, A-4040 Linz, Austriamarkus.dibold@lcm.at

Johannes Gerstmayr

 Linz Center of Mechatronics GmbH, Altenbergerstrasse 69, A-4040 Linz, Austriajohannes.gerstmayr@lcm.at

Hans Irschik

Institute of Technical Mechanics, Johannes Kepler University of Linz, Altenbergerstrasse 69, A-4040 Linz, Austriahans.irschik@jku.at

J. Comput. Nonlinear Dynam 4(2), 021006 (Mar 09, 2009) (10 pages) doi:10.1115/1.3079825 History: Received November 27, 2007; Revised March 31, 2008; Published March 09, 2009

In extension to a former work, a detailed comparison of the absolute nodal coordinate formulation (ANCF) and the floating frame of reference formulation (FFRF) is performed for standard static and dynamic problems, both in the small and large deformation regimes. Special emphasis is laid on converged solutions and on a comparison to analytical and numerical solutions from the literature. In addition to the work of previous authors, the computational performance of both formulations is studied for the dynamic case, where detailed information is provided, concerning the different effects influencing the single parts of the computation time. In case of the ANCF finite element, a planar formulation based on the Bernoulli–Euler theory is utilized, consisting of two position and two slope coordinates in each node only. In the FFRF beam finite element, the displacements are described by the rigid body motion and a small superimposed transverse deflection. The latter is described by means of two static modes for the rotation at the boundary and a user-defined number of eigenmodes of the clamped-clamped beam. In numerical studies, the accuracy and computational costs of the two formulations are compared for a cantilever beam, a pendulum, and a slider-crank mechanism. It turns out that both formulations have comparable performance and that the choice of the optimal formulation depends on the problem configuration. Recent claims in literature that the ANCF would have deficiencies compared with the FFRF thus can be refuted.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

FFRF model of a finite element

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Figure 2

(a) Static modes and (b) first two eigenmodes of the FFRF finite element

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Figure 3

ANCF model of a finite element

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Figure 4

Example of a cantilever beam

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Figure 5

Relative error of the tip displacements in the cantilever example versus the number of elements

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Figure 6

Example of flexible pendulum under gravity

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Figure 7

Midspan deflection w for the ANCF and the FFRF models with 128 finite elements

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Figure 8

Relative integral error of the deflection in the pendulum with small deformations

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Figure 9

Example of a slider crank, deformed configuration

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Figure 10

Time evolution of (a) the X-position of the right end and (b) the Y-position of the midpoint of the connection rod in the slider crank

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Figure 11

Relative integral error in (a) the X-position of the right end and (b) the Y-position of the midpoint of the connection rod; slider-crank mechanism

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