Plastic Buckling of Imperfect Hemispherical Shells Subjected to External Pressure

Plastic buckling/collapse pressures for externally pressurized imperfect hemispherical shells were calculated for several values of the yield point (s_yp), 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 (p_c) for both types of imperfection were normalized and plotted versus λ (a parameter proportional to . Approximate algebraic equations were then derived which give p_c/p_yp as a function of λ and δ₀/t. The values of p_c 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 s_imp, 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 R_imp/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 R_imp/R ≥ 1.3 imposed by some Codes should also be reviewed, particularly in the plastic regime.