Consistent Frame Buckling Analysis by Finite Element Method
Publication: Journal of Structural Engineering
Volume 117, Issue 4
Abstract
Conventional element assembly process based on the initial configuration of structures does not necessarily imply the satisfaction of compatibility conditions in the deformed state. This may result in a violation to the rule that all physical relations should be specified for deformed structures in a buckling analysis. Based on an exact consideration of the interelement compatibility for structural members, one can derive a joint matrix for internally generated moments and a moment matrix for externally applied moments, in addition to the elastic and geometric stiffness matrices commonly used in nonlinear analysis. To highlight the linking between the fundamental mechanics equations and their finite element counterparts, the present derivation will be made only for planar frames that are allowed to buckle both in and out of plane. The validity of the present procedure is confirmed in the numerical examples.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Argyris, J. H., Hilbert, O., Malejannakis, Ġ. A., and Scharpf, D. W. (1979). “On the geometrical stiffness of a beam in space—a consistent approach.” Computer Methods in Appl. Mech. and Engrg., 20, 105–131.
2.
Chajes, A. (1974). Principles of structural stability theory. Prentice‐Hall, Englewood Cliffs, N.J.
3.
Chen, W. F., and Lui, E. M. (1987). Structural stability—theory and implementation. Elsevier, New York, N.Y.
4.
Elias, Z. M. (1986). Theory and methods of structural analysis. John Wiley and Sons, New York, N.Y.
5.
Reissner, E. (1973). “On one‐dimensional large‐displacement finite‐strain beam theory.” Studies in applied mathematics, Vol. LII, No. 2, The Massachusetts Inst. of Tech.
6.
Simitses, G. J. (1976). An introduction to the elasticity stability of structures. Prentice‐Hall, Englewood Cliffs, N.J.
7.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. 2nd Ed., McGraw‐Hill, New York, N.Y.
8.
Vlasov, V. Z. (1961). Thin‐walled elastic beams. 2nd Ed., Israel Program for Sci. Translation, Jerusalem, Israel.
9.
Yang, Y. B. (1984). “Linear and nonlinear analysis of space frames with nonuniform torsion using interactive computer graphics,” thesis presented to Cornell University, at Ithaca, N.Y., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
10.
Yang, Y. B., and McGuire, W. (1986a). “Stiffness matrix for geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), 853–877.
11.
Yang, Y. B., and McGuire, W. (1986b). “Joint rotation and geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), 879–905.
12.
Yang, Y. B., and Shue, C. C. (1989). “Theory of stability for framed structures—nonconservative systems.” Proc. National Science Council, Part A: Physical Science and Engineering, Taipei, Taiwan, 13(4), 202–210.
13.
Yang, Y. B., and Kuo, S. R. (1990). “Out‐of‐plane buckling of angled frames.” Int. J. Mech. Sci., Jun.
14.
Ziegler, H. (1977). Principles of structural stability. 2nd Ed., Birkhauser Verlag Basel, Stuttgart, Germany.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 117 • Issue 4 • April 1991
Pages: 1053 - 1069
Copyright
Copyright © 1991 ASCE.
History
Published online: Apr 1, 1991
Published in print: Apr 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.