Previous investigations have raised some doubts about the accuracy of flow theory predictions for a few plate and shell plastic buckling problems. The present series of buckling experiments on machined, mild steel, cylindrical shell models under non-proportional biaxial loading (axial tension plus external pressure) was designed to provide additional data for the evaluation of the J2 plasticity theories. Numerical calculations were carried out with the BOSOR 5 shell buckling program, using the J2 deformation and flow theories, and these were compared with the test results. Neither theory can be said to predict plastic buckling accurately. However, deformation theory predicted the bifurcation buckling loads reasonably well, whereas flow theory was often incorrect.
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.
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.
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.
In the first part of the paper a comparison of various theoretical methods for predicting the elastic buckling pressures of externally pressurized complete circular toroidal (that is doughnut shaped) shells is given. Calculations were also carried out using the BOSOR 5 shell buckling program. The accuracy of the latter was checked using two independent programs. The available experimental results on toroidal shells, from the United States and Russia, are summarized and their buckling pressures calculated using BOSOR 5. A simple equation for predicting the buckling pressures of these shells, due to Jordan, is also briefly reviewed. The buckling of externally pressurized complete elliptical toroidal shells is then discussed. Both buckling pressures and buckling modes for selected geometries are given. Depending on the major/minor axis ratio, the buckling pressures of the elliptical toroids can be larger or smaller than those of the corresponding circular toroids. Some part-cylindrical, part-spherical cross-sections were also explored. Buckling due to internal pressure is considered in the third part of the paper. It is predicted to occur for several complete toroids of elliptical cross-section. It is believed that this is a new result. It still has to be verified experimentally.
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