The Effect of Initial Imperfections on the Collapse Strength of Deep Spherical Shells

Krenzke, Martin A.; Kiernan, Thomas J.

doi:10.21236/ad0612100

Cited by 25 publications

(23 citation statements)

References 7 publications

(13 reference statements)

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“…Hemispherical shells considered here are those of 36 Series FS models tested in Ref. [3]. These shell structures have flat spots at their apex.…”

Section: Theoretical Solutions and Comparison With Empirical And Expementioning

confidence: 99%

“…[3]. Based on the classical buckling equation, empirical formulas were also proposed in the same reference, using local geometry rather than nominal shell dimensions to account for the effect of initial imperfections on the collapse strength.…”

Section: Introductionmentioning

confidence: 99%

“…The present analysis has following purposes. First, through a comparison of present analytical solutions with empirical and test results of [3], it is intended to varify the validity of the computer code developed in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…[2] were formed from flat plates, which inevitable introduced significant departures from sphericity as well as variations in thickness and residual stresses. Since the initial imperfection among these adverse factors introduced has been assumed to be the primary source that affects the collapse strength of shell structures [3][4][5][6], the discrepancy is consequential and their comparison is inappropriate.To eliminate or at least partially reduce the adverse effect from flat plates, a series of nearly perfect machined shells were made in Refs.[7-9].The test results showed their collapse -2-strength was nearly 90% of the classical buckling pressure.These tests not only provide a strong support to the classical small deflection buckling theory of initially perfect spherical shells, but indicate that the initial imperfection does play a significant role in reducing shell load-carrying capacity.In view of the practicality, it is very difficult, if not impossible, to manufacture or measure most spherical shells with sufficient accuracy to justify the use of classical shell buckling formulas in design. It thus becomes evident that we should consider the unevenness factors in the shell buckling analysis.…”

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A comparative study on the elastic-plastic collapse strength of initially imperfect deep spherical shells

1982

Computer-Aided Design

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Unfortunately, earlier tests conducted in Ref.[2] provided only one-fourth of the collapse strength predicted by the classical buckling theory. The huge discrepancy existed between the theory and the test is traceable. The test specimens used in Ref. [2] were formed from flat plates, which inevitable introduced significant departures from sphericity as well as variations in thickness and residual stresses. Since the initial imperfection among these adverse factors introduced has been assumed to be the primary source that affects the collapse strength of shell structures [3][4][5][6], the discrepancy is consequential and their comparison is inappropriate.To eliminate or at least partially reduce the adverse effect from flat plates, a series of nearly perfect machined shells were made in Refs.[7-9].The test results showed their collapse -2-strength was nearly 90% of the classical buckling pressure.These tests not only provide a strong support to the classical small deflection buckling theory of initially perfect spherical shells, but indicate that the initial imperfection does play a significant role in reducing shell load-carrying capacity.In view of the practicality, it is very difficult, if not impossible, to manufacture or measure most spherical shells with sufficient accuracy to justify the use of classical shell buckling formulas in design. It thus becomes evident that we should consider the unevenness factors in the shell buckling analysis. Since most contributions to the unevenness factors, such as variation in thickness, residual stress, boundary conditions, etc. may be, at least on occasions, are fairly well controlable, the effect of initial departures from sphericity appears most worthy of investigation.In connection with this investigation, the large deflection elastic buckling analysis was performed in Ref.[5] for complete spherical shells with a dimple type of initial imperfections.Focused only on shallow spherical portions of these complete shells, numerical solutions of these modified shell structures[6] compare quite satisfactorily with those of [5].The comparison by itself prompts a basic assumption that the collapse of initially imperfect shell structures is primarily a local phenomenon and therefore critically dependent on local geometry.For the purpose of the same investigation with an extension -3- As mentioned in the previous Section, the large deformation elastic-plastic thin shallow spherical shell theory [4] is utilized in this paper to predict the collapse strength of initially imperfect deep spherical shells. A shell is called "thin" if the ratio of its thickness to the radius of curvature of its middle surface is much less than unity; and a spherical shell is called "shallow" if its rise at the center is less than, say, one-eight of its base diameter.The geometry of a clamped spherical cap is shown in Fig. l(a), in which H is the central height, R the shell radius to the midsurface of the shell, a the base radius, and h the shell thickness; W(r) and U(r) are displacement components al...

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“…Hemispherical shells considered here are those of 36 Series FS models tested in Ref. [3]. These shell structures have flat spots at their apex.…”

Section: Theoretical Solutions and Comparison With Empirical And Expementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A comparative study on the elastic-plastic collapse strength of initially imperfect deep spherical shells

1982

Computer-Aided Design

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A comparative study on the elastic‐plastic collapse strength of initially imperfect deep spherical shells

Kao

1981

Numerical Meth Engineering

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Ultimate Strength Assessment of Steel-Welded Hemispheres under External Hydrostatic Pressure

Cho

Muttaqie

Lee

et al. 2020

J. Marine. Sci. Appl.

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This paper focusses on steel-welded hemispherical shells subjected to external hydrostatic pressure. The experimental and numerical investigations were performed to study their failure behaviour. The model was fabricated from mild steel and made through press forming and welding. We therefore considered the effect of initial shape imperfection, variation of thickness and residual stress obtained from the actual structures. Four hemisphere models designed with R/t from 50 to 130 were tested until failure. Prior to the test, the actual geometric imperfection and shell thickness were carefully measured. The comparisons of available design codes (PD 5500, ABS, DNV-GL) in calculating the collapse pressure were also highlighted against the available published test data on steel-welded hemispheres. Furthermore, the nonlinear FE simulations were also conducted to substantiate the ultimate load capacity and plastic deformation of the models that were tested. Parametric dependence of the level of sphericity, varying thickness and residual welding stresses were also numerically considered in the benchmark studies. The structure behaviour from the experiments was used to verify the numerical analysis. In this work, both collapse pressure and failure mode in the numerical model were consistent with the experimental model.

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The Effect of Initial Imperfections on the Collapse Strength of Deep Spherical Shells

Cited by 25 publications

References 7 publications

A comparative study on the elastic-plastic collapse strength of initially imperfect deep spherical shells

A comparative study on the elastic-plastic collapse strength of initially imperfect deep spherical shells

A comparative study on the elastic‐plastic collapse strength of initially imperfect deep spherical shells

Ultimate Strength Assessment of Steel-Welded Hemispheres under External Hydrostatic Pressure

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