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This and the next several slides are for INTERNALLY pressurized torispherical and ellipsoidal shells.
This metal torispherical pressure vessel is 3 meters in diameter. Incipient buckling occurs in the knuckle region where there exists meridional tension combined with hoop compression. Incipient buckling occurs in a mode in which the circumferential variation of the incipient buckling pattern varies trigonometrically, for example as sin(nxtheta), in which the number n of circumferential waves is very large, something like 100. In the post-buckled state the incipient (bifurcation) sin(nxtheta) pattern becomes localized at one or at only a few isolated values of the circumferential coordinate, theta. Buckling and localized post-buckling of the metallic shell typically occurs at pressures for which both nonlinear material behavior (plasticity) and nonlinear geometric effects (large deflections) must be accounted for in order to obtain accurate predictions.
Perhaps this photograph is from:
P.R. Patel and S.S. Gill (Mechanical Engineering Department, University of Manchester Institute of Science and Technology, Manchester, England), “Experiments on the buckling under internal pressure of thin torispherical ends of cylindrical pressure vessels”, International Journal of Mechanical Sciences, Vol. 20, No.3, 1978, pp. 159-175
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