Abstract
A method is outlined to obtain the “preferred” buckled states of a (complete) spherical shell under uniform external pressure. The shell model investigated is that of the John equations, a system of six nonlinear partial differential equations. Methods in bifurcation theory and group representations are used to reduce the problem to a finite-dimensional problem whose solutions generate buckled states that are “preferred” in a certain least-energy sense. Asymptotic methods and Newton's method are used in some special cases to relate the “preferred” buckled states obtained by the above approach to actual buckled states observed in experimental studies.
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Communicated by S. Antman
G. H. Knightly's research was supported in part by the U.S. National Science Foundation Grants No. MCS 77-04927 and No. MCS 79-03555; that of D. Sather, in part by U.S. National Science Foundation Grant No. MCS 78-02140 and in part by the Council on Research and Creative Work of the University of Colorado.
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Knightly, G.H., Sather, D. Buckled states of a spherical shell under uniform external pressure. Arch. Rational Mech. Anal. 72, 315–380 (1980). https://doi.org/10.1007/BF00248522
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DOI: https://doi.org/10.1007/BF00248522