Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Symmetric and unsymmetric buckling of circular arches

Authors: R. W. Dickey and Joseph J. Roseman
Journal: Quart. Appl. Math. 54 (1996), 759-775
MSC: Primary 73H05; Secondary 73C50, 73G05, 73K05, 73V25
DOI: https://doi.org/10.1090/qam/1417238
MathSciNet review: MR1417238
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Abstract: A nonlinear geometrically exact inextensible elastica theory is used to derive a mathematical system which models a clamped circular arch of central angle $ 2\alpha $ under the action of a vertical force field of amplitude $ P$ (e.g., gravity). The equilibria of the arch are studied for various values of $ \alpha , 0 < \alpha < \pi $. The existence of a solution of symmetric form for all fixed values of $ P$ and $ \alpha $ is proved analytically by arguments based on variational principles. Numerical solutions are calculated for a variety of choices of $ \alpha $, and in each case buckling (nonuniqueness) is shown to occur when $ P$ is sufficiently large. In some cases, both symmetric and unsymmetric configurations are found, but each unsymmetric configuration obtained is found to be an unstable equilibrium, having energy greater than that of the symmetric configuration. Implications concerning the relative strengths and weaknesses of the various arches are discussed.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1417238
Article copyright: © Copyright 1996 American Mathematical Society

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