Abstract
This paper considers the stability of a toroidal shell subjected to uniform external pressure. Stability equations for a toroidal shell are solved by use of series expansions in the circumferential and meridional directions for the displacement components that develop during buckling. Axially symmetric as well as asymmetric buckling modes are considered. Design curves that give nondimensional buckling pressures for a wide range of the toroidal shell's geometric parameters are presented. In addition, the variation of the mode shapes with the geometric parameters is illustrated. In a comparison between the results of the present theory and the few available tests on toroidal shells, it is shown that test and theory agree to within 10%. For the limiting case of a sphere under external pressure, the well-known classical result (p — 1.21 Eh/a) is obtained numerically for both the asymmetric and axially symmetric buckling modes.
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