Elastic Buckling of Externally-pressurized Imperfect Toroidal Shells

This paper summarizes the results of numerical studies into the effects of initial geometric imperfections on the elastic buckling behaviour of steel circular and elliptic toroidal shells subjected to follower-type external pressure. The types of initial imperfection studied are (a) axisymmetric localized ones and (b) sinusoidal buckling modes. The principal localized imperfections studied are (i) circular increased-radius "flat spots" and (ii) smooth dimples. The buckling pressures p_crof circular toroidal shells were not very sensitive to initial imperfections. With elliptic toroids, whether the shell was sensitive to initial imperfections or not depended on the ratio k(≡ a/b) of major to minor radii of the section. The shells on the ascending part of the p_crversus k curve behaved like circular toroidal shells, i.e. they were not sensitive to initial imperfections. However, the behaviour of elliptic toroids on the descending part of the versus k curve was very different. The numerical results quoted in the paper are for limited ranges of the geometric parameters. It would be useful to extend these ranges, to explore the effects of plasticity and to conduct model tests on imperfect steel models to verify the conclusions of the numerical studies.