Postbuckling of Elastic Columns with Second-Mode Imperfection
Publication: Journal of Engineering Mechanics
Volume 132, Issue 8
Abstract
Initial imperfections of columns are often assumed to have the shape of the first buckling mode. In this technical note, the imperfection has the shape of the second mode. An elastica analysis is performed, and numerical results are obtained for two cases with the use of a shooting method. For the example of a pinned column, bifurcation occurs at a load slightly higher than the critical load for the perfect system. With further increase in load, the deflection changes smoothly from an antisymmetric shape with one node to a shape with no nodes. For the cantilevered-column example, a limit point occurs just beyond the critical load for the perfect system, and the equilibrium shape jumps from one state to another. As the load is increased further, the deflection passes smoothly to the other side of the column and loses its inflection point.
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Acknowledgments
This research was partially supported (R.H.P., L.N.V.) by the National Science Foundation under Grant No. NSFCMS-0301084. The writers are grateful to the reviewers for their helpful comments.
References
Allen, H. G., and Bulson, P. S. (1980). Background to buckling, McGraw–Hill, New York.
Reiss, E. L. (1977). “Imperfect bifurcation.” Applications of bifurcation theory, P. H. Rabinowitz, ed., Academic, New York, 37–71.
Virgin, L. N., and Plaut, R. H. (2004). “Postbuckling and vibration of linearly elastic and softening columns under self-weight.” Int. J. Solids Struct., 41, 4989–5001.
Wolfram, S. (1996). The Mathematica book, 3rd Ed., Cambridge University Press, Cambridge, U.K.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 132 • Issue 8 • August 2006
Pages: 898 - 901
Copyright
© 2006 ASCE.
History
Received: Mar 21, 2005
Accepted: Jan 18, 2006
Published online: Aug 1, 2006
Published in print: Aug 2006
Notes
Note. Associate Editor: Hayder A. Rasheed
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