The Effect of Shape, Thickness and Boundary Imperfections on Plastic Buckling of Cones

2011 ◽  
Author(s):  
O. Ifayefunmi ◽  
J. Błachut
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Wall Thickness ◽  
Thickness Distribution ◽  
Radial Pressure ◽  
External Pressure ◽  
Combined Loading ◽  
Small Radius ◽  
Worst Case ◽  
Buckling Strength

Three types of imperfections are analysed in the current paper, and they are: (i) Initial geometric imperfections, i.e., deviations from perfect geometry, (ii) Variations in the wall thickness distribution, and (iii) Imperfect boundary conditions. It is assumed that cones are subject to: (a) axial compression only, (b) radial pressure only, and (c) combined loading, i.e., axial compression and external pressure acting simultaneously. Buckling strength of imperfect cones is obtained for all of the cases above. It is shown that the buckling strength is differently affected by imperfections, when cones are subjected to axial compression or to radial external pressure. The response to imperfections along the combined stability envelope is also provided, and these results are first of this type. The finite element analysis, using the proprietary code is used as the numerical tool. Cones are assumed to be from mild steel and the material is modelled as elastic perfectly plastic. Geometrical imperfection profiles are affine to eigenshapes. A number of them are tried in calculations, as well as the effect of them being superimposed. The results indicate that imperfection amplitude and its shape strongly affect the load carrying capacity of conical shells. Also, it is shown that the buckling loads of analyzed cones are more sensitive when subjected to combined loading as compared to their sensitivity under single load conditions. At the next stage, uneven thickness distribution along the cone slant was considered. Variation of wall thickness was assumed to vary in a piece-wise constant fashion. This appears to have a large effect on the buckling strength of cones under axial compression only as compared with that of cones subjected to radial external pressure only. Finally, the effect of variability of boundary conditions on failure load of cones was investigated for two loading conditions, i.e., for axial compression and for radial pressure, only. Results indicate that change of boundary conditions influences the magnitude of buckling load. For axially compressed cones the loss of buckling strength can be large (about 64% for the worst case (beta = 30 deg, the cone not restrained at small radius end). Calculations for radial pressure indicate that the loss of buckling strength is not as acute — with 34% for the worst case (beta = 40 deg, relaxed boundary conditions at the larger radius end). This is an entirely numerical study but references to accompanying experimental programme are provided.

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.

Buckling of Truncated Cones With Localized Imperfections

2012 ◽  
Author(s):  
J. Błachut
Keyword(s):  
Axial Compression ◽  
Wall Thickness ◽  
External Pressure ◽  
Buckling Load ◽  
Buckling Loads ◽  
Conical Shells ◽  
Buckling Strength ◽  
Shape Deviations ◽  
Combined Action ◽  
Axisymmetric Shape

The paper shows that both the inward and outward bulge-type axisymmetric shape imperfections can significantly lower the buckling strength of steel conical shells. The FE results are provided for: (i) axial compression, (ii) external pressure, and (iii) combined action of both loads. Sensitivity of buckling loads to outward bulges has not been generally known or expected. It is shown that the sensitivity of buckling load depends not only on the shape, amplitude but also on the position of the imperfection along the slant. Geometry of recently tested cones was also used in order to assess the influence of measured shape deviations on the buckling strength. The amplitudes of imperfections in these machined models were small (up to 5 % of wall thickness). As a result their influence on the buckling strength was found to be negligible.

Buckling of Unstiffened Steel Cones Subjected to Axial Compression and External Pressure

2010 ◽  
Author(s):  
J. Blachut ◽  
O. Ifayefunmi
Keyword(s):  
Axial Compression ◽  
Wall Thickness ◽  
Degrees Of Freedom ◽  
Static Stability ◽  
Stability Domain ◽  
External Pressure ◽  
The Other ◽  
Combined Loading ◽  
Elastic Behavior ◽  
Geometrical Parameters

The paper considers buckling of unstiffened truncated conical shells under simultaneously acting quasi-static axial compression and an independent external hydrostatic pressure. This is both numerical and experimental study. Domains of combined stability were obtained using the finite element method for a range of geometrical parameters. Cones are clamped at one end and free to move axially at the other end, where all the other degrees of freedom remain constrained. Shells are assumed to be from mild steel and the material is modeled as elastic perfectly plastic. The FE results indicate that the static stability domains remain convex. The failure mechanisms, i.e., asymmetric bifurcation and axisymmetric collapse are discussed together with the spread of plastic strains through the wall thickness. Also, the combined stability domains are examined for regions of purely elastic behavior and for regions where plastic straining exists. The latter is not convex and repercussions of that are discussed. The spread of the latter is computed for a range of the (radius-to-wall-thickness)-ratios. Experimental results are based on laboratory scale models. Here, a single geometry was chosen for validation of numerically predicted static stability domain. Parameters of this geometry were assumed as follows: the ratio of bigger radius, r2, to smaller radius, r1, was taken as (r2/r1) = 2.02; the ratio of radius-to-wall-thickness, (r2/t), was 33.0, and the cone semi-angle was 26.56°, whilst the axial length-to-radius ratio was, (h/r2) = 1.01. Shells were CNC-machined from 252mm diameter solid steel billet. They had heavy integral flanges at both ends and models were not stress relieved prior to testing. Details about the test arrangements are provided in the paper. In particular, the development details and experience of the test rig for independent/combined loading of cones are given. The current contribution complements Ref. [1].

Plastic Buckling of Cones Subjected to Axial Compression and External Pressure

2011 ◽  
Author(s):  
J. Blachut ◽  
A. Muc ◽  
J. Rys´
Keyword(s):  
Axial Compression ◽  
Wall Thickness ◽  
Failure Load ◽  
Thickness Distribution ◽  
True Strain ◽  
Cone Angle ◽  
External Pressure ◽  
Large Radius ◽  
Perfectly Plastic ◽  
Failure Loads

The paper provides details about buckling tests on six steel cones and the corresponding numerical estimates of failure load (asymmetric bifurcation and/or collapse). Test models were machined from 250 mm billet. The wall thickness was 2 mm, small-end radius was 74.0 mm and the large radius end was 100 mm. The semi-cone angle was 14 deg. Cones had substantial, and integral top and bottom flanges. Experimental failure loads were obtained for: (i) the first two cones subjected to axial compression, (ii) subsequent two cones subjected to external pressure, and (iii) the remaining two models subjected to combined action of external pressure and axial compression. The magnitude of test pressure was about 5 MPa, and the axial failure load was approximately 230 kN. Good repeatability of experimental failure loads was obtained. Numerical estimates of failure loads were obtained for elastic perfectly plastic, engineering stress-strain, and true stress–true strain modelling of steel. Apart from axisymmetric modelling of shells, true geometry with true wall thickness distribution was adopted in calculations. Some of the numerical estimates of buckling loads are close to test data but other are not. The reasons for these discrepancies are highlighted in the paper.

Buckling of Composite and Homogeneous Isotropic Cylindrical Shells Under Axial and Radial Loading

1969 ◽  
Vol 36 (4) ◽  
pp. 791-798 ◽  
Author(s):  
M. M. Lei ◽  
Shun Cheng
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Circular Cylindrical Shell ◽  
Radial Pressure ◽  
Buckling Load ◽  
Simply Supported ◽  
Classical Boundary ◽  
Axial Compressive Stress ◽  
Radial Loading ◽  
Geometrical Dimensions

A theoretical analysis of the buckling of a multilayered thin orthotropic composite circular cylindrical shell of finite length, subjected to (a) uniform axial compression, and (b) axial compression combined with radial pressure, is presented. At each end of the shell, four boundary conditions are satisfied. Four combinations of boundary conditions for simply supported shells, and four combinations of boundary conditions for clamped shells, are treated. These boundary conditions are reduced to the vanishing of a fourth-order determinant. Buckling loads for boron-epoxy composite shells are determined and the results are shown in a series of diagrams. The effect of boundary conditions on the buckling load for various geometrical dimensions of composite cylinders is investigated. Details of the boundary conditions are shown to have strong influence on the buckling load of the shell. The minimum critical axial compression for a simply supported shell with boundary conditions SS1 is as low as 79 percent of the minimum critical axial compression for a shell with classical boundary conditions SS3. As a special case of a composite shell, the minimum critical axial compressive stress for a homogeneous, isotropic, simply supported shell with end conditions SS1 is found to be 43.7 percent of the classical critical stress.

Buckling of Cylinders With Imperfect Length

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
J. Błachut
Keyword(s):  
Mild Steel ◽  
Axial Compression ◽  
Wall Thickness ◽  
Axial Length ◽  
Small Amplitude ◽  
Thickness Ratio ◽  
Experimental Results ◽  
Dominant Factor ◽  
Buckling Strength ◽  
Perfect Model

Eighteen mild steel cylinders with the length-to-radius ratio, L/R ≈ 2.4 and with the radius-to-wall thickness ratio, R/t ≈ 185 were collapsed by axial compression. Cylinders had variable length at one end of sinusoidal profile. The magnitude of axial imperfection-to-wall thickness ratio, 2A/t, was varied between 0.05 and 1.0. Experimental results show that buckling strength strongly depends on the axial amplitude of imperfection. On average imperfect cylinders, with 2A/t = 1.0, are able to support 49% of experimental buckling load obtained for geometrically perfect model. The largest sensitivity of buckling strength was associated with small amplitude of imperfection in axial length. For example, for axial length imperfection amounting to 25% of wall thickness the buckling strength was reduced by 40%. It appears that the number of sinusoidal waves in the imperfection profile plays a secondary role, i.e., its role in reducing the buckling strength is not a dominant factor. The paper provides experimental details and comparisons with numerical results.

Full-Scale Wrinkling Tests and Analyses of Large Diameter Corroded Pipes

1998 ◽  
Author(s):  
Marina Q. Smith ◽  
Daniel P. Nicolella ◽  
Christopher J. Waldhart
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Axial Compression ◽  
Wall Thickness ◽  
Full Scale ◽  
Operating Conditions ◽  
Material Behavior ◽  
Combined Loading ◽  
Longitudinal Bending ◽  
Full Scale Tests

The aging of pipeline infrastructures has increased concern for the integrity of pipelines exhibiting non-perforating wall loss and settlement induced bending. While pressure based guidelines exist which allow pipeline operators to define operational margins of safety against rupture (e.g.; ANSI/ASME B31-G and RSTRENG (Battelle, 1989)), reliable procedures for the prediction of wrinkling in degraded pipes subjected to combined loading are virtually non-existent. This paper describes full-scale testing and finite element investigations performed in support of the development of accurate wrinkling prediction procedures for the Alyeska Pipeline Service Company. The procedures are applicable to corroded pipes subjected to combined loading such as longitudinal bending, internal pressure, and axial compression. During the test program, full-scale 48-inch diameter sections of the trans-Alaska pipeline were subjected to internal pressure and loads designed to simulate longitudinal bending from settlement, axial compression from the transport of hot oil, and the axial restraint present in buried pipe. Load magnitudes were designed based on normal and maximum operating conditions. Corrosion in the pipe section is simulated by mechanically reducing the wall thickness of the pipe. The size and depth of the thinned region is defined prior to each test, and attempts to bound the dimensions of depth, axial length, and hoop length for the general corrosion observed in-service. The analytical program utilizes finite element analyses that include the nonlinear anisotropic material behavior of the pipe steel through use of a multilinear kinematic hardening plasticity model. As in the tests, corrosion is simulated in the analyses by a section of reduced wall thickness, and loads and boundary constraints applied to the numerical model exactly emulate those applied in the full-scale tests. Verification of the model accuracy is established through a critical comparison of the simulated pipe structural behavior and the full-scale tests. Results of the comparisons show good correlation with measurements of the pipe curvature, deflections, and moment capacity at wrinkling. The validated analysis procedure is subsequently used to conduct parameter studies, the results of which complete a database of wrinkling conditions for a variety of corrosion sizes and loading conditions.

The buckling of truncated conical sandwich panels under axial compression and external pressure

2014 ◽  
Vol 229 (11) ◽  
pp. 1965-1978 ◽  
Author(s):  
Keramat M Fard ◽  
Mostafa Livani
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Sandwich Panel ◽  
Sandwich Panels ◽  
Shear Deformation Theory ◽  
External Pressure ◽  
Thickness Ratio ◽  
Composite Sandwich ◽  
The Core ◽  
Panel Thickness

Based on a new improved higher-order sandwich panel theory, the buckling analysis of a truncated conical composite sandwich panel with simply supported and fully clamped boundary conditions was performed for the first time. This panel was subjected to axial compression and external pressures. The governing equations were derived by using the principle of minimum potential energy. The first-order shear deformation theory was used for the composite face sheets, and for the core, a polynomial description of the displacement fields was assumed. Geometry was used for the consideration of different radii curvatures of the face sheets and the core was unique. The effects of types of boundary conditions, conical angles, length to smaller radius of core ratio, core to panel thickness ratio, and smaller radius of core to panel thickness ratio on the buckling response of truncated conical composite sandwich panels were also studied. The results were validated by the results published in the literature and the presented FE results were obtained by ABAQUS software.

Buckling of Cylinders With Imperfect Length

2013 ◽  
Author(s):  
J. Błachut
Keyword(s):  
Mild Steel ◽  
Axial Compression ◽  
Wall Thickness ◽  
Axial Length ◽  
Numerical Results ◽  
Thickness Ratio ◽  
Experimental Results ◽  
Dominant Factor ◽  
Buckling Strength ◽  
Perfect Model

Eighteen mild steel cylinders with the length-to-radius ratio, L/R ≈ 2.4 and with the radius-to-wall thickness ratio, R/t ≈ 185 were collapsed by axial compression. Cylinders had variable length at one end of sinusoidal profile. The magnitude-to-wall thickness ratio, 2A/t, was varied between 0.05 and 1.0. Experimental results show that buckling strength strongly depends on the axial amplitude of imperfection. On average imperfect cylinders, with 2A/t = 1.0, are able to support 49 % of experimental buckling load obtained for geometrically perfect model. The largest sensitivity of buckling strength was associated with small amplitudes of axial length. For example, for axial length imperfection amounting to 25 % of wall thickness the buckling strength was reduced by 40 %. It appears that the number of sinusoidal waves in the imperfection profile plays a secondary role, i.e., its role in reducing the buckling strength is not a dominant factor. The paper provides experimental details and comparisons with numerical results.

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