Bifurcation Buckling of Spherical Caps

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Bifurcation Buckling of Spherical Caps
Edward L Reiss
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Rl v'l^vt ■? ;?: H' ♦IlSnO.^Hl Hi t X -■>n 7 26 . 2^2 iS. S) I ff'(x) -oJf'^(x)Jx^dx >, for all f(x)^ A .
p Here ^-', is also the lovrest eigenvalue of the linearized buckling problem for the sy/imetric deformations of radially compressed and clamped circular plates: (5o6) Gf(x) +Af(x) =, f'(0) = f(l) = .
V/e call (5»6) the "equivalent" circular plate problem. The inequality (^oS) and the functional V given in (5»h-) and (5. 1) immediately yield LEI-MA 1. If >^ ? then only f (x) = mi nimizes V,
... The form of the functional V and the properties of the eigenvalues (3«5a) and eigenvectors (3c7) of the linear shell buckling problem yield LEIIIIA 2. If X = X(p) then there exist for each p > a function f(x)£A such that V[f(x)J B > -2B /a, n = 1, 2, . , . . The constants n nn a and 6^ are defined by n n " a2 = .

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