Elastic Buckling of Conical Shells under the Combined Loading of Axial Compression and External Pressure

2012 ◽  
Author(s):  
J. Blachut ◽  
D. Stanier
Keyword(s):  
Axial Compression ◽  
External Pressure ◽  
Combined Loading ◽  
Elastic Buckling ◽  
Conical Shells

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.

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.

Plastic General Instability of Ring—Reinforced Conical Shells Under Uniform External Pressure

2007 ◽  
Vol 44 (04) ◽  
pp. 268-277
Author(s):  
Carl T.F. Ross ◽  
Andrew P. F. Little ◽  
Robert Allsop ◽  
Charles Smith ◽  
Marcus Engelhardt
Keyword(s):  
Experimental Tests ◽  
External Pressure ◽  
Elastic Buckling ◽  
Conical Shells ◽  
Uniform External Pressure ◽  
Design Chart ◽  
Circular Conical Shells ◽  
High Degree ◽  
Very High ◽  
Ring Shell

The paper describes experimental tests carried out on three ring-reinforced circular conical shells that suffered plastic general instability under uniform external pressure. In this mode, the entire ring-shell combination buckles bodily in its flank. The cones were carefully machined from EN1A mild steel to a very high degree of precision. The paper also provides a design chart using the results obtained from these three vessels, together with the results of nine other vessels obtained from other tests. All 12 vessels failed by general instability. The design chart allows the possibility of obtaining a plastic knockdown factor, so that the theoretical elastic buckling pressures for perfect vessels can be divided by the plastic knockdown factor, to give the predicted buckling pressure. This method can also be used for the design of full-scale vessels.

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.

Elastic Stability of Cylindrical Shells under Axial and Lateral Loads

1964 ◽  
Vol 68 (647) ◽  
pp. 773-775 ◽  
Author(s):  
C. Lakshmikantham ◽  
George Gerard
Keyword(s):  
Axial Compression ◽  
Present Report ◽  
Compressive Loading ◽  
Elastic Stability ◽  
External Pressure ◽  
Point Of View ◽  
Combined Loading ◽  
External Loading ◽  
Lateral Loads ◽  
The Stability

In the stability analysis of cylinders under external loading, the axial compression and lateral pressure cases are relatively well established: see, for example, ref. 1. However, from a design point of view, a biaxial system of forces due to a combination of axial compression and external pressure is often encountered in launch vehicle structures. While many other combined loading cases have appeared in the literature, the case under present consideration has not; therefore, this note is devoted to a general treatment of this problem. It is to be noted that Radhakrishnan presented some specific results for this loading combination for elastic and plastic buckling.Using the Donnell equation for small deformations, the present report considers the effect of various compressive loading combinations on the stability problem of an un-stiffened circular cylinder.

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].

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