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.

Buckling of Externally Pressurized Prolate Ellipsoidal Domes

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
P. Smith ◽  
J. Błachut
Keyword(s):  
New York ◽  
Test Procedure ◽  
External Pressure ◽  
Pressure Vessels ◽  
European Convention ◽  
Numerical Predictions ◽  
Current Design ◽  
Base Radius ◽  
Division 2 ◽  
Prolate Ellipsoidal

Details are given of a numerical and experimental study into buckling of steel ellipsoidal domes loaded by static external pressure. A range of geometries and thicknesses of domes is examined, as is the influence of different boundary conditions. Shells are examined on the basis of having the same mass. The main focus of the study is on prolate domes, i.e., those taller than a hemisphere of the same base radius. Numerical predictions are confirmed by pressurizing six laboratory scale prolate domes to destruction. Details are given of the manufacture and test procedure for the domes. The adverse effects of variations in shape and wall thickness are discussed, and finite element predictions are made for geometrically imperfect domes. Correlation between the two sets of results is good. Numerically and experimentally obtained results are related to the current design codes: ASME Boiler and Pressure Vessel Code, Sec. 8, Division 2 (described hereon as ASME VIII), PD5500, and ECCS recommendations (ASME B&PV Code, 2004 ed., Sec. 8, Division 2, New York, NY; BSI 2003 “Published Document PD5500: Specification for Unfired Pressure Vessels,” BSI London; European Convention for Constructional Steelwork Recommendations, 1988 “Buckling of Stell Shells-European Recommendations,” ECCS-TWG 8.4, 4th ed., Brussels), which at present make no provision for prolate domes. Suggestions are made for the possible inclusion of such domes into the standards.

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.

Optimal Design of Laminated Cylindrical Pressure Vessels for Maximum External Pressure

1997 ◽  
Vol 119 (4) ◽  
pp. 494-497 ◽  
Author(s):  
M. Walker ◽  
T. Reiss ◽  
S. Adali
Keyword(s):  
Finite Element ◽  
Optimal Design ◽  
Wall Thickness ◽  
Pressure Vessel ◽  
Golden Section ◽  
External Pressure ◽  
Pressure Vessels ◽  
Section Method ◽  
Vessel Length ◽  
Golden Section Method

Finite element solutions are presented for the optimal design of hemispherically and flat-capped symmetrically laminated pressure vessels subjected to external pressure. The effect of vessel length, radius, and wall thickness, as well as bending-twisting coupling and hybridization on the optimal ply angle and buckling pressure are numerically studied. Comparisons of the optimal fiber angles and maximum buckling pressures for various vessel geometries are made with those for a hybrid pressure vessel. The well-known golden section method is used to compute the optimum angle in each case.

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.

Strength, Stability, and Optimization of Pressure Vessels: Review of Selected Problems

2008 ◽  
Vol 61 (6) ◽  
Author(s):  
J. Błachut ◽  
K. Magnucki
Keyword(s):  
Research Effort ◽  
Static Stability ◽  
External Pressure ◽  
Pressure Vessels ◽  
Stress Concentrations ◽  
Work Related ◽  
Flexible Supports ◽  
Minimum Stress ◽  
The Stability ◽  
Ultimate Load Carrying Capacity

Recent research effort into some aspects of strength, static stability, and structural optimization of horizontal pressure vessels is reviewed in this paper. Stress concentrations at the junction of cylinder-ellipsoidal end closures are covered in detail. This in turn establishes efficient choices for wall thicknesses in the vessel. Detailed account of stresses for flexible supports of a horizontal cylindrical shell is provided. Dimensions of support components, which assure the minimum stress concentrations between a horizontal shell and its support, are calculated. In particular, the wall thickness is found for vessels being loaded by the weight of its content and placed on two supports. Stability issues are also reviewed in this paper. In particular, attention is paid to the stability of cylinder under external pressure and to the stability of end closures. The latter are loaded by internal or external pressure. Apart from buckling and plastic loads, the ultimate load carrying capacity, i.e., burst pressure, for internally pressurized heads is also examined. On a practical side, aboveground and underground cases are discussed. In the latter case of underground vessels the reinforcement by internal rings is assessed. The optimization part of this paper deals with the effective choice of the end closure depth and the shape of its meridian. The overriding aim here is to examine the stress concentrations and the ways in which they can be mitigated. The optimal shape of closures is also searched for, with respect to the maximum buckling pressure for a given mass of the head. In the case of internal pressure the maximum of plastic load is sought within a specified class of meridional profiles. Finally, optimal sizing of whole vessels is discussed for slender and compact geometries. Extensive references are made to relatively recent and ongoing work related to the above topics. This paper has 287 references and 50 figures.

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].

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.

scholarly journals Depressurization-Induced Nucleation in the “Polylactide-Carbon Dioxide” System: Self-Similarity of the Bubble Embryos Expansion

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1115
Author(s):  
Dmitry Zimnyakov ◽  
Marina Alonova ◽  
Ekaterina Ushakova
Keyword(s):  
Initial Rate ◽  
Initial Pressure ◽  
External Pressure ◽  
Self Similarity ◽  
Embryo Formation ◽  
Linear Behavior ◽  
Joint Influence ◽  
External Pressures ◽  
Adiabatic Cooling ◽  
Self Similar

Self-similar expansion of bubble embryos in a plasticized polymer under quasi-isothermal depressurization is examined using the experimental data on expansion rates of embryos in the CO2-plasticized d,l-polylactide and modeling the results. The CO2 initial pressure varied from 5 to 14 MPa, and the depressurization rate was 5 × 10−3 MPa/s. The constant temperature in experiments was in a range from 310 to 338 K. The initial rate of embryos expansion varied from ≈0.1 to ≈10 µm/s, with a decrease in the current external pressure. While modeling, a non-linear behavior of CO2 isotherms near the critical point was taken into account. The modeled data agree satisfactorily with the experimental results. The effect of a remarkable increase in the expansion rate at a decreasing external pressure is interpreted in terms of competing effects, including a decrease in the internal pressure, an increase in the polymer viscosity, and an increase in the embryo radius at the time of embryo formation. The vanishing probability of finding the steadily expanding embryos for external pressures around the CO2 critical pressure is interpreted in terms of a joint influence of the quasi-adiabatic cooling and high compressibility of CO2 in the embryos.

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