scholarly journals Imperfection Sensitivity of Externally Pressurized Spherical Shells

1967 ◽  
Vol 34 (1) ◽  
pp. 49-55 ◽  
Author(s):  
J. W. Hutchinson
Keyword(s):  
General Theory ◽  
Shell Thickness ◽  
Middle Surface ◽  
External Pressure ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Small Deviations ◽  
Severe Effect ◽  
Shell Geometry

The initial postbuckling behavior of a shallow section of a spherical shell subject to external pressure is studied within the context of Koiter’s general theory of postbuckling behavior. Imperfections in the shell geometry are shown to have the same severe effect on the buckling strengths of spherical shells as has been demonstrated for axially compressed cylindrical shells. Large reductions in the buckling pressure result from small deviations, relative to the shell thickness, of the shell middle surface from the perfect configuration.

scholarly journals Buckling of spherical shells revisited

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160577 ◽  
Author(s):  
John W. Hutchinson
Keyword(s):  
Middle Surface ◽  
External Pressure ◽  
Maximum Pressure ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Mode Localization ◽  
Axisymmetric State ◽  
New Findings ◽  
Post Buckling ◽  
The 1960S

A study is presented of the post-buckling behaviour and imperfection sensitivity of complete spherical shells subject to uniform external pressure. The study builds on and extends the major contribution to spherical shell buckling by Koiter in the 1960s. Numerical results are presented for the axisymmetric large deflection behaviour of perfect spheres followed by an extensive analysis of the role axisymmetric imperfections play in reducing the buckling pressure. Several types of middle surface imperfections are considered including dimple-shaped undulations and sinusoidal-shaped equatorial undulations. Buckling occurs either as the attainment of a maximum pressure in the axisymmetric state or as a non-axisymmetric bifurcation from the axisymmetric state. Several new findings emerge: the abrupt mode localization that occurs immediately after the onset of buckling, the existence of an apparent lower limit to the buckling pressure for realistically large imperfections, and comparable reductions of the buckling pressure for dimple and sinusoidal equatorial imperfections.

Dent Imperfections in Shell Buckling: The Role of Geometry, Residual Stress, and Plasticity

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
S. Gerasimidis ◽  
J. W. Hutchinson
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Middle Surface ◽  
External Pressure ◽  
Second Step ◽  
Elastic Buckling ◽  
Spherical Shells ◽  
Shell Buckling ◽  
Cylindrical Metal

Abstract Departures of the geometry of the middle surface of a thin shell from the perfect shape have long been regarded as the most deleterious imperfections responsible for reducing a shell’s buckling capacity. Here, systematic simulations are conducted for both spherical and cylindrical metal shells whereby, in the first step, dimple-shaped dents are created by indenting a perfect shell into the plastic range. Then, in the second step, buckling of the dented shell is analyzed, under external pressure for the spherical shells and in axial compression for the cylindrical shells. Three distinct buckling analyses are carried out: (1) elastic buckling accounting only for the geometry of the dent, (2) elastic buckling accounting for both dent geometry and residual stresses, and (3) a full elastic–plastic buckling analysis accounting for both the dent geometry and residual stresses. The analyses reveal the relative importance of the geometry and the residual stress associated with the dent, and they also provide a clear indicator of whether plasticity is important in establishing the buckling load of the dented shells.

Imperfection-Sensitivity of Long Antisymmetric Cross-Ply Cylindrical Panels Under Shear Loads

1987 ◽  
Vol 54 (2) ◽  
pp. 292-298 ◽  
Author(s):  
David Hui ◽  
I. H. Y. Du
Keyword(s):  
Modulus Ratio ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Geometric Imperfections ◽  
Material Parameters ◽  
Shear Loads ◽  
Number Of Layers ◽  
Cylindrical Panels ◽  
Shear Buckling ◽  
Shell Geometry

This paper examines the theoretical postbuckling behavior and imperfection-sensitivity of antisymmetrically laminated open, long, cylindrical panels under shear loads. The longitudinal edges may be simply-supported or clamped. It is found that the cylindrical panels may be sensitive to the presence of geometric imperfections depending primarily on the reduced-flatness parameter and Young’s modulus ratio. The shear buckling load and the postbuckling coefficients are plotted as a function of the shell geometry, number of layers, and material parameters. The paper is the first in the literature to examine the postbuckling behavior of open laminated cylindrical panels under shear loads.

Elastic Postbuckling Behavior of Stiffened and Barreled Cylindrical Shells

1969 ◽  
Vol 36 (4) ◽  
pp. 784-790 ◽  
Author(s):  
J. W. Hutchinson ◽  
J. C. Frauenthal
Keyword(s):  
General Theory ◽  
Boundary Conditions ◽  
Type Theory ◽  
Cylindrical Shells ◽  
Buckling Load ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Different Boundary Conditions ◽  
Stiffened Cylindrical Shells

The initial postbuckling behavior of axially stiffened cylindrical shells is studied with a view to ascertaining the extent to which various effects such as stringer eccentricity, load eccentricity, and barreling influence the imperfection-sensitivity of these structures to buckling. In most cases, when these effects result in an increase in the buckling load of the perfect structure, they increase its imperfection-sensitivity as well. In some instances, however, barreling can significantly raise the buckling load of the shell while reducing its imperfection-sensitivity. The analysis, which is based on Koiter’s general theory of postbuckling behavior and is made within the context of Ka´rma´n-Donnell-type theory, takes into account nonlinear prebuckling deformations and different boundary conditions.

Buckling and Postbuckling Behavior of Clamped Shallow Spherical Shells Under Axisymmetric Ring Loads

1971 ◽  
Vol 38 (4) ◽  
pp. 996-1002 ◽  
Author(s):  
N. Akkas ◽  
N. R. Bauld
Keyword(s):  
Numerical Study ◽  
Postbuckling Behavior ◽  
Spherical Shells ◽  
Concentrated Load ◽  
Fixed Ring ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Post Buckling ◽  
Shell Parameter ◽  
Shell Geometry

This paper presents the results of a numerical study of the buckling and initial post-buckling behavior of clamped shallow spherical shells under axisymmetric ring loads. This behavior is studied for a cap with fixed geometry when the location of the ring load is allowed to vary from the equivalent of a concentrated load at the apex to a location near the midpoint of the shell base radius, and for a fixed ring load location when the shell geometry is allowed to vary. It is found in both studies that a significant range of the geometric shell parameter λ exists such that buckling is accompanied by a loss in load-carrying capacity.

On the Buckling Design of Spherical Shells

1981 ◽  
Vol 103 (3) ◽  
pp. 261-266 ◽  
Author(s):  
J. Morton ◽  
P. R. Murray ◽  
C. Ruiz
Keyword(s):  
Biaxial Tension ◽  
External Pressure ◽  
Design Codes ◽  
Safety Factors ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
State Of Stress ◽  
Biaxial Load ◽  
Loading Case ◽  
Selection Of

Experimental results are interpreted in the light of numerical analaysis, imperfection sensitivity and Design Codes. Two cases are discussed: spherical shells under uniform external pressure and partly filled spherical shells, supported on a continuous equatorial ring. The imperfection sensitivity associated with the first loading case leads to the selection of safety factors that depend on the actual shell stiffness. The second case, in which the load results in a biaxial tension-compression state of stress, is treated approximately in terms of a plate under biaxial load.

scholarly journals Nonlinear dynamics of spherical shells buckling under step pressure

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180884 ◽  
Author(s):  
Jan Sieber ◽  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Nonlinear Dynamics ◽  
External Pressure ◽  
Dynamic Buckling ◽  
Spherically Symmetric ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Buckling Mode ◽  
Geometric Imperfections ◽  
Pressure Threshold ◽  
Initial Geometric Imperfections

Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric ‘breathing’ mode and the buckling mode. In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead, there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections, the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure.

On the Stability Analysis of Imperfect Spherical Shells

1970 ◽  
Vol 37 (3) ◽  
pp. 629-634 ◽  
Author(s):  
A. Kalnins ◽  
V. Biricikoglu
Keyword(s):  
Stability Analysis ◽  
General Theory ◽  
Spherical Shell ◽  
Nonlinear Theory ◽  
Geometric Parameters ◽  
Postbuckling Behavior ◽  
Spherical Shells ◽  
The Stability ◽  
Asymptotic Character

A procedure is given for the analysis of axisymmetrically imperfect spherical shells which is not limited by the magnitude of the imperfections. The geometric parameters of the imperfect shell are expressed in terms of those of the perfect shell and known imperfection distribution, and the imperfect shell is solved directly by means of a nonlinear theory. As an application of the proposed procedure, the critical pressures for an axisymmetrically imperfect complete spherical shell are calculated. The results are compared with those predicted by Koiter’s general theory of initial postbuckling behavior, and their asymptotic character is verified.

Axisymmetrical Creep Buckling of Clamped Shallow Spherical Shells

1965 ◽  
Vol 32 (2) ◽  
pp. 323-330 ◽  
Author(s):  
Nai Chien Huang
Keyword(s):  
Large Deformations ◽  
Correspondence Principle ◽  
Applied Pressure ◽  
Critical Time ◽  
External Pressure ◽  
Governing Equations ◽  
Spherical Shells ◽  
Relaxation Of Stresses ◽  
Viscoelastic Shells ◽  
Shell Geometry

For a viscoelastic clamped shallow spherical shell, the vertical deflection due to uniformly distributed external pressure is a function of time. When time reaches a critical value, the shell may snap through suddenly. This critical time depends on the magnitude of the applied pressure as well as the shell geometry. The governing equations for large deformations of viscoelastic shells can be derived by applying the correspondence principle to the equivalent equations in the elastic case. The critical times for various shells under different pressures are evaluated numerically. If the deflection volume of the shell is a constant throughout the deformation process, the external pressure decreases due to relaxation of stresses in the viscoelastic shell. This decreasing external pressure is also calculated in this paper.

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