Analytical and Numerical Observations on the Hetényi Solution for Buckling of Beams on Elastic Foundations
Publication: Journal of Engineering Mechanics
Volume 141, Issue 1
Abstract
This paper considers the minimum buckling load and mode shape of a simply supported beam on an elastic foundation. Solutions are obtained by solving the eigenvalue problem delivered by a finite-element formulation and by using the analytical solutions involving (1) trials and (2) rounding of real numbers to integers as described by Hetényi [Hetényi, M. (1946). Beams on Elastic Foundations, University of Michigan Press, Ann Arbor, MI]. The comparison shows that the solution by rounding can lead to overestimation of the buckling load close to the transition zone between mode shapes. The paper explains the reason for the overestimation and offers a simple direct algorithm that always leads to the correct mode shape and minimum buckling load.
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Acknowledgments
The authors acknowledge the support of National Science Foundation grant CMMI-0970122 on GOALI: Probabilistic Geomechanical Analysis in the Exploitation of Unconventional Resources.
References
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 141 • Issue 1 • January 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 5, 2013
Accepted: May 22, 2014
Published online: Jul 1, 2014
Published in print: Jan 1, 2015
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