The Preferred Mode Shape in the Linear Buckling of Circular Cylindrical Shells Under Axial Compression

1965 ◽  
Vol 32 (4) ◽  
pp. 793-802 ◽  
Author(s):  
P. Mann-Nachbar ◽  
W. Nachbar
Keyword(s):  
Cylindrical Shell ◽  
Aspect Ratio ◽  
Axial Compression ◽  
Probability Distributions ◽  
Thin Shells ◽  
Thin Cylindrical Shell ◽  
Linear Buckling ◽  
Manufacturing Tolerances ◽  
Circular Cylindrical Shells ◽  
Circumferential Waves

The chessboard buckle pattern in the solution of the linearized Donnell equations for buckling of a thin, cylindrical shell under axial compression is so sensitive to uncertainties in shell dimensions that the number of circumferential waves and the aspect ratio of the buckles is indeterminate. This problem is treated statistically. Shell dimensions are treated as random variables with probability distributions dependent on nominal values and manufacturing tolerances. Distributions for aspect ratio and number of circumferential waves are found by a Monte-Carlo technique. It is found that the linear theory does contain a mechanism for distinguishing among buckle modes. There is always a preferred buckle mode. For thin shells and attainable manufacturing tolerances, the aspect ratio of the preferred mode is closer to one than that of any other possible mode, and the corresponding number of buckles is large.

Effect of an Axisymmetric Imperfection on the Plastic Buckling of an Axially Compressed Cylindrical Shell

1979 ◽  
Vol 46 (1) ◽  
pp. 125-131 ◽  
Author(s):  
S. Gellin
Keyword(s):  
Cylindrical Shell ◽  
Axial Compression ◽  
Thin Shells ◽  
Plastic Range ◽  
Imperfection Sensitivity ◽  
Plastic Buckling ◽  
Elastic Range ◽  
Long Cylindrical Shell ◽  
Axisymmetric Shape ◽  
Shape Imperfection

The effect of a sinusoidal axisymmetric shape imperfection on the plastic buckling of a long cylindrical shell under axial compression is studied. The load at which nonaxisymmetric bifurcation from the axisymmetric state occurs is determined as a function of the imperfection amplitude for relatively thin shells. Imperfection-sensitivity in the plastic range is contrasted with that in the elastic range.

Creep Buckling Analyses of Circular Cylindrical Shells Under Axial Compression—Bifurcation Buckling Analysis by the Finite Element Method

1987 ◽  
Vol 109 (2) ◽  
pp. 179-183 ◽  
Author(s):  
N. Miyazaki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Axial Compression ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
The Finite Element Method ◽  
Bifurcation Buckling ◽  
Creep Buckling ◽  
Circular Cylindrical Shells

The finite element method is applied to the creep buckling of circular cylindrical shells under axial compression. Not only the axisymmetric mode but also the bifurcation mode of the creep buckling are considered in the analysis. The critical time for creep buckling is defined as either the time when a slope of a displacement versus time curve becomes infinite or the time when the bifurcation buckling occurs. The creep buckling analyses are carried out for an infinitely long and axially compressed circular cylindrical shell with an axisymmetric initial imperfection and for a finitely long and axially compressed circular cylindrical shell. The numerical results are compared with available analytical ones and experimental data.

Stresses around large circular holes in uniform circular cylindrical shells

1982 ◽  
Vol 17 (1) ◽  
pp. 9-12 ◽  
Author(s):  
J W Bull
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Element Analysis ◽  
Three Point Bending ◽  
Circular Holes ◽  
Circular Cylindrical Shells ◽  
Good Agreement

An experimental and finite element analysis of a uniform cylindrical shell with a large circular cut-out is presented. In this analysis three hole sizes are considered, namely μ = 2.037, 4.084, and 6.344 (where μ = {[12(1 - y2)]1/4/2} × [ a/( Rt)1/2]), for loadings of axial compression, torsion and three point bending. The experimental results are the only ones available for cylindrical shells with large values of μ (except for one graph by Savin (1)†), while for three point bending there is no previously published theoretical or analytical results. Good agreement is found between the calculated and experimental stresses around the holes.

Limit Analysis of Symmetrically Loaded Thin Shells of Revolution

1959 ◽  
Vol 26 (1) ◽  
pp. 61-68
Author(s):  
D. C. Drucker ◽  
R. T. Shield
Keyword(s):  
Cylindrical Shell ◽  
Lower Bounds ◽  
Yield Surface ◽  
Limit Analysis ◽  
Thin Shell ◽  
Upper And Lower Bounds ◽  
Thin Shells ◽  
Hexagonal Prism ◽  
Shells Of Revolution ◽  
Thin Cylindrical Shell

Abstract The yield surface for a thin cylindrical shell is shown to be a very good approximation to the yield surface for any symmetrically loaded thin shell of revolution. Hexagonal prism approximations to this yield surface, appropriate for pressure vessel analysis, are described and discussed in terms of limit analysis. Procedures suitable for finding upper and lower bounds on the limit pressure for the complete vessel are developed and evaluated. They are applied for illustration to a portion of a toroidal zone or knuckle held rigidly at the two bounding planes. The combined end force and moment which can be carried by an unflanged cylinder also is discussed.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals Fully localized post-buckling states of cylindrical shells under axial compression

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170177 ◽  
Author(s):  
Tobias Kreilos ◽  
Tobias M. Schneider
Keyword(s):  
Axial Compression ◽  
Stability Boundary ◽  
Axial Direction ◽  
Edge State ◽  
Equilibrium Solutions ◽  
Thin Cylindrical Shell ◽  
Nonlinear Force ◽  
Post Buckling ◽  
The Stability ◽  
Nonlinear Solutions

We compute nonlinear force equilibrium solutions for a clamped thin cylindrical shell under axial compression. The equilibrium solutions are dynamically unstable and located on the stability boundary of the unbuckled state. A fully localized single dimple deformation is identified as the edge state —the attractor for the dynamics restricted to the stability boundary. Under variation of the axial load, the single dimple undergoes homoclinic snaking in the azimuthal direction, creating states with multiple dimples arranged around the central circumference. Once the circumference is completely filled with a ring of dimples, snaking in the axial direction leads to further growth of the dimple pattern. These fully nonlinear solutions embedded in the stability boundary of the unbuckled state constitute critical shape deformations. The solutions may thus be a step towards explaining when the buckling and subsequent collapse of an axially loaded cylinder shell is triggered.

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