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 (nyp), the radius-thickness ratio (R/t) and the amplitude of the initial imperfection at Ehe pole (ao). The well-known elasticplastic shell buckling program BOSOR 5 was used in the calculations and two axisynzmetric initid imperfection shapes were studied, viz. a localized increased-radius type and a Legendre polynomial.The 8numerical collapse pressures (p,) for both types of imperfection were normalized and plotted versus , i (g parameter proportional to J{(R/tXa JE)}). Approximate algebraic equations were then derived which give pc/pyp as a.function o f 2 and dolt. The values of p, given by tiese 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 goodfor BS 5500 but was fair,for the DnV rules. The agreement with BS 5500 can be improved b y 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 6,/t x 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 limitution of Rimp/R < 1.3 imposed by some Codes should also be reviewed, particularly in the plastic regime. NOTATIONdiameter of cylindrical shell modulus of elasticity degree of Legendre polynomial [equation number of waves in the circumferential direction collapse pressure of imperfect hemispherical shell elastic buckling pressure of perfect spherical shell from linear theory = 1.21E(t/R)' for v = 0.3 elastic, or plastic, bifurcation buckling pressure of perfect clamped hemisphere (from BOSOR 5) yield pressure of spherical shell = 2(t/R)ayp Legendre polynomial of degree n radius of perfect hemispherical shell (also radial coordinate on Figs 8 and 9) radius of imperfect hemispherical shell arc length over which radial imperfections, or radii of curvature, are measured thickness of shell axial coordinate on Figs 8 and 9 semi-angle of imperfection (see Fig. 2) amplitude (inwards herein) of radial imperfection at the pole (rp = 0) {12(1 -V~)}"~IX,/(R/~) % 1.82a.,,/(Rt) for v = 0.3

Elastic buckling of imperfect circular toroidal shells under external pressure

“…Equation (3) has been used before when investigating the effects of initial geometrical imperfections in hemispherical shells [7].…”

Experimental Perspective on the Buckling of Pressure Vessel Components

“…In response to this, two research programs were carried out in Liverpool. The first program concentrated on 24 torispherical heads, some hot pressed and some cold spun, to acquire information in this range [126][127][128]. The heads had R/t ratios between 85 and 330 and they were about 0.75 m in diameter.…”

An overview of buckling and ultimate strength of spherical pressure hull under external pressure

“…Plastic buckling/collapse pressures for externally pressurized imperfect hemispherical shells were calculated by Galletly et al [12] for several values of the yield point the radius-thickness ratio and the amplitude of the initial imperfection at the pole. Using the maximum values of the geometric shape deviations allowed by some national Codes, the calculated buckling strengths were compared with an approximate lower bound of test results obtained on externally pressurized spherical shells.…”