This part of these two companion papers demonstrates the computer implementation of the absolute nodal coordinate formulation for three-dimensional beam elements. Two beam elements that relax the assumptions of Euler-Bernoulli and Timoshenko beam theories are developed. These two elements take into account the effect of rotary inertia, shear deformation and torsion, and yet they lead to a constant mass matrix. As a consequence, the Coriolis and centrifugal forces are identically equal to zero. Both beam elements use the same interpolating polynomials and have the same number of nodal coordinates. However, one of the elements has two nodes, while the other has four nodes. The results obtained using the two elements are compared with the results obtained using existing incremental methods. Unlike existing large rotation vector formulations, the results of this paper show that no special numerical integration methods need to be used in order to satisfy the principle of work and energy when the absolute nodal coordinate formulation is used. These results show that this formulation can be used in manufacturing applications such as high speed forming and extrusion problems in which the element cross section dimensions significantly change.
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December 2001
Technical Papers
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications
Refaat Y. Yakoub,
Refaat Y. Yakoub
Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor St., Chicago, IL 60607-7022
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Ahmed A. Shabana
Ahmed A. Shabana
Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor St., Chicago, IL 60607-7022
Search for other works by this author on:
Refaat Y. Yakoub
Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor St., Chicago, IL 60607-7022
Ahmed A. Shabana
Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor St., Chicago, IL 60607-7022
Contributed by the Reliability, Stress Analysis and Failure Prev. Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 2000. Associate Editor: J. Gao.
J. Mech. Des. Dec 2001, 123(4): 614-621 (8 pages)
Published Online: May 1, 2000
Article history
Received:
May 1, 2000
Citation
Yakoub , R. Y., and Shabana, A. A. (May 1, 2000). "Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications ." ASME. J. Mech. Des. December 2001; 123(4): 614–621. https://doi.org/10.1115/1.1410099
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