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

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
J. Błachut ◽  
O. Ifayefunmi
Keyword(s):  
Axial Compression ◽  
Wall Thickness ◽  
Degrees Of Freedom ◽  
Static Stability ◽  
Stability Domain ◽  
External Pressure ◽  
The Other ◽  
Elastic Behavior ◽  
Geometrical Parameters ◽  
Perfectly Plastic

This is the first study into elastic-plastic buckling of unstiffened truncated conical shells under simultaneously acting axial compression and an independent external pressure. This is both a numerical and experimental study. Domains of combined stability are 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 plastic strain 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 the bigger radius, r2, to the 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 semiangle was 26.56°, while the axial length-to-radius ratio was (h/r2) = 1.01. Shells were formed by computer numerically controlled machining from 252 mm 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.

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

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
J. Błachut ◽  
A. Muc ◽  
J. Ryś
Keyword(s):  
Axial Compression ◽  
Wall Thickness ◽  
True Strain ◽  
Safety Margin ◽  
External Pressure ◽  
Perfectly Plastic ◽  
Test Models ◽  
Failure Loads ◽  
Elastic Perfectly Plastic ◽  
Strain Modeling

The paper provides details about tests on six steel cones. Test models were machined from 250 mm diameter billet. All cones had substantial and integral top and bottom flanges in order to secure well defined boundary conditions. Experimental data were obtained for: (i) two cones subjected to axial compression, (ii) two cones subjected to external pressure, and (iii) the remaining two models subjected to combined action of external pressure and axial compression. Apart from axisymmetric modeling of tested cones, true geometry with true wall thickness was also used in calculations. Theoretical failure loads were obtained for: (i) elastic perfectly plastic, (ii) engineering stress–strain, and (iii) true stress–true strain modeling of steel. The latter approach coupled with measured geometry and wall thickness secured safe predictions of the collapse loads in all cases. Comparisons of experimental collapse loads with estimates given by ASME and ECCS design codes are included. It is seen here that the ASME and ECCS rules provide a safety margin of about 100% against the collapse (except 50% for axial compression in the case of the ECCS).

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.

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.

Experimental Perspective on the Buckling of Pressure Vessel Components

2013 ◽  
Vol 66 (1) ◽  
Author(s):  
J. Błachut
Keyword(s):  
New York ◽  
Wall Thickness ◽  
Glass Fibers ◽  
Static Stability ◽  
External Pressure ◽  
Pressure Vessels ◽  
Conical Shells ◽  
Thin Walled Structures ◽  
External Pressures ◽  
Spherical Caps

This review aims to complement a milestone monograph by Singer et al. (2002, Buckling Experiments—Experimental Methods in Buckling of Thin-Walled Structures, Wiley, New York). Practical aspects of load bearing capacity are discussed under the general umbrella of “buckling.” Plastic loads and burst pressures are included in addition to bifurcation and snap-through/collapse. The review concentrates on single and combined static stability of conical shells, cylinders, and their bowed out counterpart (axial compression and/or external pressure). Closed toroidal shells and domed ends onto pressure vessels subjected to internal and/or external pressures are also discussed. Domed ends include: torispheres, toricones, spherical caps, hemispheres, and ellipsoids. Most experiments have been carried in metals (mild steel, stainless steel, aluminum); however, details about hybrids (copper-steel-copper) and shells manufactured from carbon/glass fibers are included in the review. The existing concerns about geometric imperfections, uneven wall thickness, and influence of boundary conditions feature in reviewed research. They are supplemented by topics like imperfections in axial length of cylinders, imperfect load application, or erosion of the wall thickness. The latter topic tends to be more and more relevant due to ageing of vessels. While most experimentation has taken place on laboratory models, a small number of tests on full-scale models are also referenced.

Plastic Buckling of Conical Shells

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
J. Błachut ◽  
O. Ifayefunmi
Keyword(s):  
Axial Compression ◽  
Static Stability ◽  
External Pressure ◽  
Single Type ◽  
Simultaneous Action ◽  
External Hydrostatic Pressure ◽  
Conical Shells ◽  
Computer Numerically Controlled ◽  
Experimental Values ◽  
Yield Force

This paper studies the static stability of metal cones subjected to combined, simultaneous action of the external pressure and axial compression. Cones are relatively thick; hence, their buckling performance remains within the elastic-plastic range. The literature review shows that there are very few results within this range and none on combined stability. The current paper aims to fill this gap. Combined stability plot, sometimes called interactive stability plot, is obtained for mild steel models. Most attention is given to buckling caused by a single type of loading, i.e., by hydrostatic external pressure and by axial compression. Asymmetric bifurcation bucklings, collapse load in addition to the first yield pressure and first yield force, are computed using two independent proprietory codes in order to compare predictions given by them. Finally, selected cone configurations are used to verify numerical findings. To this end four cones were computer numerically controlled-machined from a solid steel billet of 252 mm in diameter. All cones had integral top and bottom flanges in order to mimic realistic boundary conditions. Computed predictions of buckling loads, caused by external hydrostatic pressure, were close to the experimental values. But similar comparisons for axially compressed cones are not so good. Possible reasons for this disparity are discussed in the paper.

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 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 Aerodynamics of inclined cylindrical bodies free-flying in a hypersonic flowfield

2021 ◽  
Vol 62 (9) ◽  
Author(s):  
Patrick M. Seltner ◽  
Sebastian Willems ◽  
Ali Gülhan ◽  
Eric C. Stern ◽  
Joseph M. Brock ◽  
...  
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Numerical Data ◽  
Static Stability ◽  
Free Flight ◽  
Aerodynamic Coefficients ◽  
Flow Topology ◽  
Motion Data ◽  
Continuous Rotation ◽  
German Aerospace

Abstract The influence of the flight attitude on aerodynamic coefficients and static stability of cylindrical bodies in hypersonic flows is of interest in understanding the re/entry of space debris, meteoroid fragments, launch-vehicle stages and other rotating objects. Experiments were therefore carried out in the hypersonic wind tunnel H2K at the German Aerospace Center (DLR) in Cologne. A free-flight technique was employed in H2K, which enables a continuous rotation of the cylinder without any sting interferences in a broad angular range from 0$$^{\circ }$$ ∘ to 90$$^{\circ }$$ ∘ . A high-speed stereo-tracking technique measured the model motion during free-flight and high-speed schlieren provided documentation of the flow topology. Aerodynamic coefficients were determined in careful post-processing, based on the measured 6-degrees-of-freedom (6DoF) motion data. Numerical simulations by NASA’s flow solvers Cart3D and US3D were performed for comparison purposes. As a result, the experimental and numerical data show a good agreement. The inclination of the cylinder strongly effects both the flowfield and aerodynamic loads. Experiments and simulations with concave cylinders showed marked difference in aerodynamic behavior due to the presence of a shock–shock interaction (SSI) near the middle of the model. Graphic abstract

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