Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



On the nonunique equilibrium states of a shallow arch subjected to a uniform lateral load

Authors: Arnold D. Kerr and Lotfi El-Bayoumy
Journal: Quart. Appl. Math. 28 (1970), 399-409
DOI: https://doi.org/10.1090/qam/99783
MathSciNet review: QAM99783
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Abstract | References | Additional Information

Abstract: Using the exact solutiom of a shallow elastic arch clamped at both ends and subjected to a uniform lateral load, it is shown that, in addition to the equilibrium states usually discussed in the literature, also other equilibrium states, which correspond to higher modes of deformation, do exist. It is shown that there exist only a finite number of equilibrium branches which correspond to these higher modes, the number depending upon the shallowness of the arch. A number of graphs are presented which demonstrate these findings. The paper concludes with the proof that all states of equilibrium which correspond to the branches of higher order are unstable.

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

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Additional Information

DOI: https://doi.org/10.1090/qam/99783
Article copyright: © Copyright 1970 American Mathematical Society

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