Rigid Element Approach for Deriving the Geometric Stiffness of Curved Beams for Use in Buckling Analysis
Publication: Journal of Structural Engineering
Volume 133, Issue 12
Abstract
For a rigid element equilibrated by a set of initial forces, the geometric stiffness matrix derived is the same, whether it is straight or curved, as long as it has identical nodal degrees at the two ends. Thus, one can first derive the geometric stiffness matrix for a rigid straight beam that has the same ending points as those of the curved beam using a rigid displacement field, and then transform this matrix from the Cartesian coordinates to the cylindrical coordinates to obtain the one for the rigid curved beam. The geometric stiffness matrix so derived (for treating the rigid displacements) can be used along with the elastic stiffness matrix (for treating the natural deformations) in the buckling analysis of curved beams. The present approach is featured by the fact that no assumptions are made for the kinematic behavior of curved beams, while the procedure of derivation is simple, explicit, and physically meaningful. Good characteristics of convergence are achieved as the finite-element mesh is refined. The robustness of the proposed approach is demonstrated in the solution of some benchmark problems.
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Acknowledgments
The research reported herein is partially sponsored by the National Science Council of the Republic of China to the first writer (Grant No. UNSPECIFIEDNSC 80-0410-E002-18). This paper was written when the first writer stayed at the National University of Singapore for a period of as part of his sabbatical leave, starting from February 1, 2006. The sponsorship made available by the NUS and NSC for such a stay is greatly appreciated by the first writer.
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Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 133 • Issue 12 • December 2007
Pages: 1762 - 1771
Copyright
© 2007 ASCE.
History
Received: Feb 15, 2006
Accepted: Jun 15, 2007
Published online: Dec 1, 2007
Published in print: Dec 2007
Notes
Note. Associate Editor: Keith D. Hjelmstad
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