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The Absolute Nodal Coordinate Formulation

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Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 565))

Abstract

The key idea of the absolute nodal coordinate formulation (ANCF) is to use slope vectors in order to describe the orientation of the cross-section of structural mechanics components, such as beams, plates or shells. This formulation relaxes the kinematical assumptions of Bernoulli–Euler and Timoshenko beam theories and enables a deformation of the cross-sections. The present contribution shows how to create 2D and 3D structural finite elements based on the ANCF by employing different sets of slope vectors for approximating the cross-sections’ orientation. A specific aim of this chapter is to present a unified notation for structural mechanics and continuum mechanics ANC formulations. Particular focus is laid on enhanced formulations for such finite elements that circumvent severe issues like Poisson or shear locking. The performance of these elements is evaluated and a detailed assessment comprising the convergence order, the number of iterations, and Jacobian updates for large deformation benchmark problems is provided.

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Notes

  1. 1.

    For an example of a slope vector, see \({\mathbf {x}}_{,\xi }\), \({\mathbf {x}}_{,\eta }\) or \({\mathbf {x}}_{,\zeta }\) in Fig. 2.

  2. 2.

    http://www.hotint.org/.

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Acknowledgments

The authors Gerstmayr, Humer, and Gruber have been supported by the Linz Center of Mechatronics (LCM) in the framework of the Austrian Comet-K2 programme. K. Nachbagauer acknowledges support from the Austrian Science Fund (FWF): T733-N30.

Author information

Authors and Affiliations

  1. Leopold-Franzens-Universität Innsbruck, Technikerstraße 13, 6020, Innsbruck, Austria

    Johannes Gerstmayr

  2. Linz Center of Mechatronics GmbH, Altenberger Straße 69, 4040, Linz, Austria

    Alexander Humer & Peter Gruber

  3. Johannes Kepler University, Altenberger Straße 69, 4040, Linz, Austria

    Alexander Humer

  4. University of Applied Sciences Upper Austria, Stelzhamerstraße 23, 4600, Wels, Austria

    Karin Nachbagauer

Authors
  1. Johannes Gerstmayr
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  2. Alexander Humer
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  3. Peter Gruber
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  4. Karin Nachbagauer
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Corresponding author

Correspondence to Johannes Gerstmayr .

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Editors and Affiliations

  1. Institute of Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Peter Betsch

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Gerstmayr, J., Humer, A., Gruber, P., Nachbagauer, K. (2016). The Absolute Nodal Coordinate Formulation. In: Betsch, P. (eds) Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics. CISM International Centre for Mechanical Sciences, vol 565. Springer, Cham. https://doi.org/10.1007/978-3-319-31879-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-31879-0_4

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