Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The parabolic umbilic catastrophe and its application in the theory of elastic stability

Authors: David Hui and Jorn S. Hansen
Journal: Quart. Appl. Math. 39 (1981), 201-220
MSC: Primary 73H05; Secondary 58C28
DOI: https://doi.org/10.1090/qam/625469
MathSciNet review: 625469
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Abstract: The implications of the parabolic umbilic catastrophe in the theory of elastic stability are investigated. In particular, the influence of terms in the potential energy which are deemed necessary for a complete analysis and the isolation of primary critical surfaces are considered. The results are demonstrated for the example of the buckling and initial post-buckling of a spherical shell under the influence of a constant as well as a spatially variable pressure.

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DOI: https://doi.org/10.1090/qam/625469
Article copyright: © Copyright 1981 American Mathematical Society

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