Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The axisymmetric branching behavior of complete spherical shells


Authors: Charles G. Lange and Gregory A. Kriegsmann
Journal: Quart. Appl. Math. 39 (1981), 145-178
MSC: Primary 73L99; Secondary 35B32, 73H05
DOI: https://doi.org/10.1090/qam/625467
MathSciNet review: 625467
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Abstract: The purpose of this paper is to describe the axisymmetric branching behavior of complete spherical shells subjected to external pressure. By means of an asymptotic integration technique (based on the smallness of the ratio of the shell thickness to the shell radius) applied directly to a differential equation formulation, we are able to continue the solution branches from the immediate vicinity of the bifurcation points, where the solution has the functional form predicted by the linear buckling theory, to the region where the solution consists of either one or two ``dimples'' with the remainder of the shell remaining nearly spherical. The analysis deals with a novel aspect of bifurcation theory involving ``closely spaced'' eigenvalues.


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DOI: https://doi.org/10.1090/qam/625467
Article copyright: © Copyright 1981 American Mathematical Society


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