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Mechanical Sciences An open-access journal for theoretical and applied mechanics
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Volume 4, issue 2
Mech. Sci., 4, 279-289, 2013
https://doi.org/10.5194/ms-4-279-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Recent advances and current trends in numerical multibody...

Mech. Sci., 4, 279-289, 2013
https://doi.org/10.5194/ms-4-279-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 01 Aug 2013

Research article | 01 Aug 2013

A novel director-based Bernoulli–Euler beam finite element in absolute nodal coordinate formulation free of geometric singularities

P. G. Gruber1, K. Nachbagauer2, Y. Vetyukov1, and J. Gerstmayr1 P. G. Gruber et al.
  • 1Linz Center of Mechatronics GmbH, Altenberger Straß e 69, 4040 Linz, Austria
  • 2Institute of Technical Mechanics, Johannes Kepler Universität Linz, Altenbergerstraß e 69, 4040 Linz, Austria

Abstract. A three-dimensional nonlinear finite element for thin beams is proposed within the absolute nodal coordinate formulation (ANCF). The deformation of the element is described by means of displacement vector, axial slope and axial rotation parameter per node. The element is based on the Bernoulli–Euler theory and can undergo coupled axial extension, bending and torsion in the large deformation case. Singularities – which are typically caused by such parameterizations – are overcome by a director per element node. Once the directors are properly defined, a cross sectional frame is defined at any point of the beam axis. Since the director is updated during computation, no singularities occur. The proposed element is a three-dimensional ANCF Bernoulli–Euler beam element free of singularities and without transverse slope vectors. Detailed convergence analysis by means of various numerical static and dynamic examples and comparison to analytical solutions shows the performance and accuracy of the element.

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