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