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Buckling of an externally pressurized spherical shell

This and the next several slides are for externally pressurized spherical shells.

From:
PICTURE (a) Carlson, R. L. (1), Sendelbeck, R. L. (2), Hoff, N. J. (2)
(1) School of Aerospace Engineering at the Georgia Institute of Technology, Atlanta, Georgia
(2) Department of Aeronautics and Astronautics of Stanford University, Stanford, California
Experimental studies of the buckling of complete spherical shells. Exp. Mech. 7:281-288, 1967. Also NASA CR- 550, August 1966.

ABSTRACT: Complete spherical shells with radius-to-thickness ratios of from 1570 to 2120 were produced by electroforming. For specimens of good quality and for optimum testing conditions, buckling pressures up to 86 percent of the classical value were obtained. The effect of loading-system characteristics was examined by pressurizing spherical shells in rigid and soft systems and no difference in buckling pressure was observed. It was found that buckling behavior is strongly influenced by the nature and severity of flaws or imperfections; i.e., low buckling pressures can be correlated with the presence of severe flaws or nonuniformities.

The load-carrying capacity of an externally pressurized thin monocoque spherical shell behaves analogously to that of a thin cylindrical shell under uniform axial compression.

As with the buckled axially compressed thin cylindrical shell displayed two slides ago, there are many, many buckles over the entire surface of the shell, the characteristic size of which is very small compared to the dimensions of the test specimen.

(In the photograph (a) the post-buckling pattern is “artificially” stabilized because there is a solid mandrel inside the shell).

PICTURE (b) Thompson, J. M. T. (1962) The elastic instability of a complete spherical shell, Aero. Quart., 13, 189-201.

PICTURES (a) and (b):
J. Michael T. Thompson [(1)Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK, (2) School of Engineering, University of Aberdeen, Aberdeen AB24 3FX, UK], "Advice to a young researcher: with reminiscences of a life in science", Philosophical Transactions of the Royal Society A, Vol. 371, no. 1993, 20120425, 28 June 2013, doi: 10.1098/rsta.2012.0425,
http://rsta.royalsocietypublishing.org/content/371/1993/20120425.short
ABSTRACT: This paper provides an informal guide to young researchers in science and engineering as they progress for their first 10 or so years from the time that they first started thinking about doing a PhD. This advice is drawn, with examples and anecdotes, from my own research career which started at the Cambridge Engineering Department in 1958, and progressed through 48 years at University College London to a part-time chair that I now hold in Aberdeen. I hope it may encourage and help tomorrow's scientists on whom the Earth's future very much depends.

PICTURE (b) again: This looks as though it might be a bifurcation buckling mode.

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