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Bifurcation buckling of spherical caps
Author(s) -
Reiss Edward L.
Publication year - 1965
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160180109
Subject(s) - citation , buckling , government (linguistics) , library science , mathematics , mathematical economics , operations research , combinatorics , computer science , sociology , engineering , philosophy , linguistics , structural engineering
: A nonlinear boundary value problem was considered for the axisymmetric buckling of thin spherical shells subjected to uniform external pressure. The uniformly compressed spherical state is a solution of this problem for all values of the pressure. It was proven, using Poincare's method, that for pressures sufficiently near each simple eigenvalue of the linearized shell buckling theory, there is another (buckled) solution of the nonlinear problem. A convergent perturbation expansion was used to analyze the buckled solutions near the eigenvalues. For a limited range of caps, it was proven that one or three buckled solutions bifurcate from the multiple (double) eigenvalues depending on their order. The existence of a lowest intermediate buckling was established and precise upper and lower bounds were given on its magnitude.