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Accuracy of Co-rotational Formulation for 3-D Timoshenko's Beam

M. Iura1, Y. Suetake2, S. N. Atluri3
Tokyo Denki University, Hatoyama, Hiki, Saitama, Japan
Ashikaga Institute of Technology, Ashikaga, Tochigi, Japan
Center for Aerospace Research & Education, University of California, Irvine, Irvine, CA. 92697, USA

Computer Modeling in Engineering & Sciences 2003, 4(2), 249-258. https://doi.org/10.3970/cmes.2003.004.249

Abstract

An accuracy of finite element solutions for 3-D Timoshenko's beams, obtained using a co-rotational formulation, is discussed. The co-rotational formulation has often been used with an assumption that the relative deformations are small. A fundamental question, therefore, has been raised as to whether or not the numerical solutions obtained approach the solutions of the exact theory. In this paper, from theoretical point of view, we investigate the accuracy of the co-rotational formulation for 3-D Timoshenko's beam undergoing finite strains and finite rotations. It is shown that the use of the conventional secant coordinates fails to give satisfactory numerical solutions. We introduce a new local coordinate system in which a linear beam theory is used to construct the strain energy function. It is shown that the finite element solutions obtained converge to those of the exact beam theory as the number of element increases.

Keywords

Co-rotational Formulation, Timoshenko's Beam, Finite Element Method, Finite Rotations.

Cite This Article

Iura, M., Suetake, Y., Atluri, S. N. (2003). Accuracy of Co-rotational Formulation for 3-D Timoshenko's Beam. CMES-Computer Modeling in Engineering & Sciences, 4(2), 249–258.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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