Plastic Buckling of Imperfect Hemispherical Shells Subjected to External Pressure

1987 ◽  
Vol 201 (3) ◽  
pp. 153-170 ◽  
Author(s):  
G D Galletly ◽  
J Blachut ◽  
J Kruzelecki
Keyword(s):  
Lower Bound ◽  
Legendre Polynomial ◽  
Initial Imperfection ◽  
External Pressure ◽  
Plastic Shell ◽  
Test Results ◽  
Algebraic Equations ◽  
Plastic Buckling ◽  
Spherical Shells ◽  
Hemispherical Shells

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.

Effect of Weather, Age, and Cyclic Pressurizations on Structural Performance of Acrylic Plastic Spherical Shells Under External Pressure Loading

1982 ◽  
Vol 104 (2) ◽  
pp. 190-200
Author(s):  
J. D. Stachiw ◽  
R. B. Dolan
Keyword(s):  
Surface Layer ◽  
Critical Pressure ◽  
External Pressure ◽  
Thin Surface Layer ◽  
Ambient Atmosphere ◽  
Plastic Shell ◽  
Spherical Shells ◽  
Acrylic Plastic ◽  
Operational Life ◽  
Physical And Chemical

Weathering, aging, and cyclic application of stresses to acrylic plastic degrades its physical properties. The rate of degradation must be known if the useful life of load-carrying acrylic structures is to be predicted with accuracy. Physical and chemical tests conducted by the authors on thick spherical shells indicate that the weathering affects only a thin surface layer of material, which after 10 years is still less than 0.020 in. thick. Similarly, pollutants in the ambient atmosphere of the pressure chamber affect the surface layer of the spherical shell facing the interior of the chamber. The physical and chemical properties of the thin surface layer affected by weathering differed significantly from those in the middle of 2.5-in.-thick Plexiglas G plate; the decrease in properties was: 40 percent in tensile elongation, 34 percent in flexure strength, 21 percent in tensile strength, and 79 percent in molecular weight. Since the interior body of the thick plastic shell is not affected by weathering or chemical attack and the affected surface layers are very thin, the ability of the shell to carry compressive loads is not significantly diminished after 10 years of service. Only an 11 percent decrease of critical pressure was observed in spherical shells with thickness of 1 in. subjected to 10 years of weathering and 2000 pressure cycles of 8 hour duration each to 30 percent of its original critical pressure. Based on the preceding data it appears safe to extend the operational life from 10 to 20 years of all acrylic plastic spherical shells with bearing surfaces normal to spherical surface designed on the basis of ANSI/ASME PVHO-1 Safety Standard for external pressure service.

Buckling Design of Imperfect Welded Hemispherical Shells Subjected to External Pressure

1991 ◽  
Vol 205 (3) ◽  
pp. 175-188 ◽  
Author(s):  
G D Galletly ◽  
J Blachut
Keyword(s):  
Experimental Information ◽  
External Pressure ◽  
Design Stage ◽  
Arc Length ◽  
Spherical Shells ◽  
Geometric Imperfections ◽  
Collapse Pressure ◽  
Buckling Resistance ◽  
Initial Geometric Imperfections ◽  
Hemispherical Shells

Welded hemispherical or spherical shells in practice have initial geometric imperfections in them that are random in nature. These imperfections determine the buckling resistance of a shell to external pressure but their magnitudes will not be known until after the shell has been built. If suitable simplified, but realistic, imperfection shapes can be found, then a reasonably accurate theoretical prediction of a spherical shell's buckling/collapse pressure should be possible at the design stage. The main aim of the present paper is to show that the test results obtained at the David Taylor Model Basin (DTMB) on 28 welded hemispherical shells (having diameters of 0.75 and 1.68 m) can be predicted quite well using such simplified shape imperfections. This was done in two ways. In the first, equations for determining the theoretical collapse pressures of externally pressurized imperfect spherical shells were utilized. The only imperfection parameter used in these equations is δ0, the amplitude of the inward radial deviation of the pole of the shell. Two values for δ0 were studied but the best overall agreement between test and theory was found using δ0 = 0.05 ✓ (Rt). This produced ratios of experimental to numerical collapse pressures in the range 0.98–1.30 (in most cases the test result was the higher). The second approach also used simplified imperfection shapes, but in conjunction with the shell buckling program BOSOR 5. The arc length of the imperfection was taken as simp = k ✓ (Rt) (with k = 3.0 or 3.5) and its amplitude as δ0 = 0.05√(Rt). Using this procedure on the 28 DTMB shells gave satisfactory agreement between the experimental and the computer predictions (in the range 0.92–1.20). These results are very encouraging. The foregoing method is, however, only a first step in the computerized buckling design of welded spherical shells and it needs to be checked against spherical shells having other values of R/t. In addition, more experimental information on the initial geometric imperfections in welded spherical shells (and how they vary with R/t) is desirable. A comparison is also given in the paper of the collapse pressures of spherical shells, as obtained from codes, with those predicted by computer analyses when the maximum shape deviations allowed by the codes are employed in the computer programs. The computed collapse pressures are frequently higher than the values given by the buckling strength curves in the codes. On the other hand, some amplitudes of imperfections studied in the paper give acceptable results. It would be helpful to designers if agreement could be reached on an imperfection shape (amplitude and arc length) that was generally acceptable. Residual stresses are not considered in this paper. They might be expected to decrease a spherical shell's buckling resistance to external pressure. However, experimentally, this does not always happen.

Geometric imperfection and lower-bound analysis of spherical shells under external pressure

2019 ◽  
Vol 143 ◽  
pp. 106195 ◽  
Author(s):  
H.N.R. Wagner ◽  
C. Hühne ◽  
J. Zhang ◽  
W. Tang ◽  
R. Khakimova
Keyword(s):  
Lower Bound ◽  
External Pressure ◽  
Spherical Shells ◽  
Geometric Imperfection ◽  
Bound Analysis

On the Plastic Buckling Paradox for Cylindrical Shells

1996 ◽  
Vol 210 (5) ◽  
pp. 477-488 ◽  
Author(s):  
J Blachut ◽  
G D Galletly ◽  
S James
Keyword(s):  
Biaxial Loading ◽  
Flow Theory ◽  
External Pressure ◽  
Test Results ◽  
Plastic Buckling ◽  
Shell Buckling ◽  
Axial Tension ◽  
Plate And Shell ◽  
Shell Models ◽  
Flow Theories

Previous investigations have raised some doubts about the accuracy of flow theory predictions for a few plate and shell plastic buckling problems. The present series of buckling experiments on machined, mild steel, cylindrical shell models under non-proportional biaxial loading (axial tension plus external pressure) was designed to provide additional data for the evaluation of the J2 plasticity theories. Numerical calculations were carried out with the BOSOR 5 shell buckling program, using the J2 deformation and flow theories, and these were compared with the test results. Neither theory can be said to predict plastic buckling accurately. However, deformation theory predicted the bifurcation buckling loads reasonably well, whereas flow theory was often incorrect.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Dao Huy Bich
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Linear Buckling ◽  
Non Linear ◽  
Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

On the Nonlinear Analysis Methodologies for Thin Spherical Shells Under External Pressure with Different Finite-Element Codes

1989 ◽  
Vol 33 (04) ◽  
pp. 318-325
Author(s):  
Dario Boote ◽  
Donatella Mascia
Keyword(s):  
Finite Element ◽  
Numerical Procedure ◽  
External Pressure ◽  
Experimental Investigations ◽  
Nonlinear Analyses ◽  
Spherical Shells ◽  
Double Curvature ◽  
Load Carrying ◽  
Material Load ◽  
Structure Collapse

Submersible structures consist merely of simple and double curvature thin-walled shells. For this kind of structure, collapse occurs due to the combined nonlinear action of buckling and plasticity of material. Load-carrying capacity may then be assessed mainly by two approaches: experimental investigations and step-by-step numerical procedures. In nonlinear analyses, the results obtained are influenced by the magnitude of the load increment adopted. Solution procedures are then required in order to choose adequate parameters for material failure description as well as elastic nonlinearity. The aim of this paper is to carry out a suitable numerical procedure whose reliability does not depend on the finite-element code adopted.

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