Plastic Buckling of Imperfect Hemispherical Shells Subjected to External Pressure

Abstract

Plastic buckling/collapse pressures for externally pressurized imperfect hemispherical shells were calculated for several values of the yield point ( syp), the radius–thickness ratio ( R/t) and the amplitude of the initial imperfection at the pole (δ0). The well-known elastic–plastic shell buckling program BOSOR 5 was used in the calculations and two axisymmetric initial imperfection shapes were studied, viz. a localized increased-radius type and a Legendre polynomial. The numerical collapse pressures ( pc) for both types of imperfection were normalized and plotted versus λ ( a parameter proportional to[Formula: see text]. Approximate algebraic equations were then derived which give pc/ pyp as a function of λ and δ0/t. The values of pc given by these equations agree well with the computer results. Using the maximum values of the geometric shape deviations allowed by some national Codes, the corresponding theoretical buckling strengths were calculated. These were then compared with an approximate lower bound of test results obtained on externally pressurized spherical shells. The agreement between the two curves was not very good for BS 5500 but was fair for the DnV rules. The agreement with BS 5500 can be improved by increasing simp, the arc length over which the initial imperfections are measured. The foregoing lower bound of test results on externally pressurized spherical shells can also be obtained, approximately, using increased-radius and Legendre polynomial imperfections in which the ratio Rimp/ R is not restricted. The magnitude of the initial imperfection required for approximate agreement between the experimental and theoretical results was δ0/t ∼ 0.5. This seems a reasonable value. However, more study of this aspect of the problem is required in both the elastic and plastic buckling regions. The limitation of Rimp/ R ≥ 1.3 imposed by some Codes should also be reviewed, particularly in the plastic regime.