Elastic buckling of, and first yielding in, thin torispherical shells subjected to internal pressure

Abstract

With the aid of the non-linear shell buckling computer program BOSOR 4, the internal pressures at which elastic circumferential buckling (or wrinkling) take place in thin torispherical shells have been calculated. The maximum equivalent (or effective) stresses in the shells in the axisymmetric pre-buckled state were also obtained; from these, the pressures at which first yielding in the shells commences were determined for 1 < σ yp E × 10 3 < 4 The calculations were performed for shells with diameter thickness ratios of 500, 1000 and 2000; other geometric ratios, as detailed in the paper, were also varied. The computations were carried out for steel shells but the results have been presented in dimensionless form. Utilising the above results it is possible to determine whether a given torispherical end closure will buckle elastically or whether an elastic-plastic analysis of the shell is desirable. Factors which are conducive to elastic buckling are a high yield point, a low modulus of elasticity or a large value of the shell diameter-thickness ( D t ) ratio. For steel shells, elastic internal pressure buckling will occur (for some combinations of r D and R S D ) for D t = 2000 and σ yp E = 3 × 10 −3 . For D t = 1000 and 500 , first yield always precedes elastic buckling for the parameters investigated. The failure mode for these cases is either elastic-plastic buckling or plastic collapse (an axisymmetric mode with large deformations). A comparison of the results of linear and non-linear elastic axisymmetric stress analyses of the shells shows that the linear theory sometimes underestimates the first yield pressure by considerable amounts. Limit pressures obtained from small-deflection shell theories can be too low in such cases. Also given in the paper are approximate simple expressions whereby the elastic internal buckling pressures of torispherical shells may be calculated. These expressions should be useful to designers.