Analytical and numerical observations on the Hetényi solution for buckling of beams on elastic foundations

Title: Analytical and numerical observations on the Hetényi solution for buckling of beams on elastic foundations
Creator: Griffiths, D. V.; Bee, G.
Relation: Journal of Engineering Mechanics Vol. 141, Issue 1
Publisher Link: http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0000827
Publisher: American Society of Civil Engineers
Resource Type: journal article
Date: 2015
Description: 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.
Subject: beam; elastic foundation; buckling; finite elements; analytical solution
Identifier: http://hdl.handle.net/1959.13/1334483
Identifier: uon:27298
Identifier: ISSN:0733-9399
Language: eng
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