Three formulations for a flexible spatial beam element for dynamic analysis are compared: a Timoshenko beam with large displacements and rotations, a fully parametrized element according to the absolute nodal coordinate formulation (ANCF), and an ANCF element based on an elastic line approach. In the last formulation, the shear locking of the antisymmetric bending mode is avoided by the application of either the two-field Hellinger–Reissner or the three-field Hu–Washizu variational principle. The comparison is made by means of linear static deflection and eigenfrequency analyses on stylized problems. It is shown that the ANCF fully parametrized element yields too large torsional and flexural rigidities, and shear locking effectively suppresses the antisymmetric bending mode. The presented ANCF formulation with the elastic line approach resolves most of these problems.
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e-mail: a.l.schwab@tudelft.nl
e-mail: j.p.meijaard@utwente.nl
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January 2010
Research Papers
Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation
A. L. Schwab,
A. L. Schwab
Laboratory for Engineering Mechanics,
e-mail: a.l.schwab@tudelft.nl
Delft University of Technology
, Mekelweg 2, NL-2628 CD Delft, The Netherlands
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J. P. Meijaard
J. P. Meijaard
Laboratory of Mechanical Automation and Mechatronics, Faculty of Engineering Technology,
e-mail: j.p.meijaard@utwente.nl
University of Twente
, P.O. Box 217, NL-7500 AE Enschede, The Netherlands
Search for other works by this author on:
A. L. Schwab
Laboratory for Engineering Mechanics,
Delft University of Technology
, Mekelweg 2, NL-2628 CD Delft, The Netherlandse-mail: a.l.schwab@tudelft.nl
J. P. Meijaard
Laboratory of Mechanical Automation and Mechatronics, Faculty of Engineering Technology,
University of Twente
, P.O. Box 217, NL-7500 AE Enschede, The Netherlandse-mail: j.p.meijaard@utwente.nl
J. Comput. Nonlinear Dynam. Jan 2010, 5(1): 011010 (10 pages)
Published Online: December 8, 2009
Article history
Received:
October 28, 2008
Revised:
March 2, 2009
Online:
December 8, 2009
Published:
December 8, 2009
Citation
Schwab, A. L., and Meijaard, J. P. (December 8, 2009). "Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation." ASME. J. Comput. Nonlinear Dynam. January 2010; 5(1): 011010. https://doi.org/10.1115/1.4000320
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