Buckling of thin-walled conical shells under uniform external pressure

Shells are for the most part the deep-seated structures in manufacturing submarines, missiles, tanks and their roofs, and fluid reservoirs; therefore it is a matter of concern to bring about some basic regulations associated with the existing codes. Above all, truncated conical shells (frusta) and shallow conical caps (SCC) subjected to external uniform pressure when discharging liquids or wind loads are discussed closely in this paper concerning and thrashing out their empirical nonlinear responses along with envisaging numerical methods in contrast. The buckling aptitude of shells is contingent upon two leading geometric ratios of “slant-length to radius” (L/R) and “radius to thickness” (R/t). In this paper, developing six frusta and four shallow cap specimens and their relevant FE models, use is made of laboratory modus operandi to enumerate buckling elastic and plastic responses and asymmetric imperfection sensitivity, whose adequacy has been reckoned through comparisons with arithmetical and numerical data correspondingly. These obtained upshots were aimed at validating and generalizing the data for unstiffened truncated cones and SCC in full scale.     

Short-term behaviour of shallow thin-walled concrete dome under uniform external pressure

Thin-walled spherical concrete shells or domes find widespread use in many applications, including in many iconic engineering structures of historical and religious significance. Despite this, very few experimental investigations have been reported in the open literature of shallow spherical concrete domes which allow for the effects of geometric and material non-linearities and of imperfections to be identified. This information is essential, however, in order to validate sophisticated numerical treatments, as well as to calibrate practical design and construction guidelines and is therefore much-needed. This paper reports an experimental study of a shallow thin-walled concrete dome under short-term loading, without the use of reinforcement in the concrete. The dome is 30 mm thick and has a base diameter of 3 m, being supported on a steel ring beam. The testing of the dome to failure under a uniform external pressure is described in the paper, and it is shown that it failed in a non-axisymmetric buckling mode well before the concrete reached its compressive strength. The failure pressure is compared with the ‘theoretical’ buckling results and the analytical results based on finite element analyses. In particular, this paper presents a comprehensive set of experimental data for the load–displacement and load–strain relationships and their distributions across the spherical dome throughout the loading regime.     

Vibration of a thin-walled carbon fibre corrugated circular cylinder under external water pressure

The paper reports on a theoretical and an experimental investigation carried out on a thin-walled corrugated carbon fibre circular cylinder in air and also under external water pressure. This corrugated circular cylinder was invented by Ross in 1987.The theoretical investigation was carried out using the finite element analysis to model both the structure and the fluid. The theoretical investigation used two different programs, one of which was the giant computer program ANSYS and the other was an in-house program developed by Ross and Little. For the shell structure, the ANSYS program used two different doubly curved thin-walled shell elements, while the in-house program used a simpler axisymmetric thin-walled shell element. This axisymmetric element allowed a sinusoidal variation of the displacements in the circumferential direction, thus, decreasing preparation and computational time. Agreement between the different finite elements was found to be quite good. The investigation also found that there was good correlation between experiment and theory for the in-house software, but was a little disappointing when using ANSYS. Errors may, however, have occurred with the experimental results, as the model was hand-made and neither its geometry nor its material properties were perfect. It was found particularly encouraging for the in-house software to give better results than ANSYS, as the in-house software only took a few hours to set up the computer model, and a few seconds to analyse the vessel, whereas the ANSYS software took several weeks to set up the computer model, and several minutes to analyse the shell. The ANSYS software, however, did have the advantage in producing excellent graphical displays in both the pre-processing and post-processing modes.     

Buckling of tube-stiffened prolate domes under external water pressure

The paper describes experimental tests carried out on three tube-stiffened prolate hemi-ellipsoidal domes under external water pressure.The tubes were stuck to the internal surfaces of these three domes, in their flanks, and the experimental tests showed that the tubes increased the buckling pressures of these domes, especially in one case, when the tube was subjected to an initial internal pressure.All three domes failed by lobar buckling, in their flanks, and showed buckling resistances much larger than similar unstiffened domes.     

Buckling of thin-walled orthotropic cylindrical shells under uniform external pressure.: Application to corrugated tin cans

The general instability of thin-walled orthotropic circular cylindrical shells under external pressure is investigated. The buckling pressure can be predicted with the use of simple analytical formulae derived from an asymptotic analysis of the corresponding eigenvalue problems. The results predicted by these formulae are compared with finite element solutions and the four types of experimental models investigated by Ross (Thin Walled Structures 1996;26(3):179–93). The comparison proved to be accurate enough for practical purpose except for experimental model 1.     

Experiments on conical shell reducers under uniform external pressure

In previous studies, a proliferation of research work has been undertaken on the buckling behavior of shell structures particularly conical shells. Nonetheless, no experimental studies are found in the literature on the buckling of a full and real configured model of a slender shell reducer with two cylindrical end boundaries. To this end, buckling behavior of three conical shell reducers under uniform peripheral pressure was investigated and evaluated experimentally in this paper. In addition, relevant FE simulations as well as theoretical predictions were taken into account to compare buckling load and modes of deformation. Derived results were aimed at generalizing the data for conical reducers in full scale within the range of this study.     

The buckling of corrugated circular cylinders under uniform external pressure

Several partially corrugated circular cylinders were tested to destruction under uniform external pressure. Some of the vessels failed by inelastic general instability and some failed by a local buckling mode, which was neither the classical shell instability mode nor the classical general instability mode.

The experimentally obtained buckling pressures were found to be related to the magnitude of the initial out-of-roundness for the vessels that failed through inelastic general instability. The theoretical buckling pressures showed virtually no relationship with the experimentally observed buckling pressures, for the vessels that failed via the local buckling mode.     

Reduced stiffness buckling of sandwich cylindrical shells under uniform external pressure

A reduced stiffness lower bound method for the buckling of laterally pressure loaded sandwich cylindrical shell is proposed. Also, an attempt is made to assess the validity of the proposed reduced stiffness lower bound with FEM numerical examples. In addition, the proposed method is compared with classical and Plantema's approaches of the buckling of the laterally pressure loaded sandwich cylindrical shell. Comparison of the proposed reduced stiffness lower bound with that obtained from non-linear FEM analysis verifies that it indeed provides a safe lower bound to the buckling of laterally pressure loaded sandwich cylindrical shells. The attractive feature of the proposed reduced stiffness method is that it can be readily used in designing laterally pressure loaded sandwich cylindrical shells without being concerned about geometrical imperfections.     

Buckling of cylindrical shells with stepwise variable wall thickness under uniform external pressure

Cylindrical shells of stepwise variable wall thickness are widely used for cylindrical containment structures, such as vertical-axis tanks and silos. The thickness is changed because the stress resultants are much larger at lower levels. The increase of internal pressure and axial compression in the shell is addressed by increasing the wall thickness. Each shell is built up from a number of individual strakes of constant thickness. The thickness of the wall increases progressively from top to bottom.Whilst the buckling behaviour of a uniform thickness cylinder under external pressure is well defined, that of a stepped wall cylinder is difficult to determine. In the European standard EN 1993-1-6 (2007) and Recommendations ECCS EDR5 (2008), stepped wall cylinders under circumferential compression are transformed, first into a three-stage cylinder and thence into an equivalent uniform thickness cylinder. This two-stage process leads to a complicated calculation that depends on a chart that requires interpolation and is not easy to use, where the mechanics is somewhat hidden, which cannot be programmed into a spreadsheet leading to difficulties in the practical design of silos and tanks.This paper introduces a new “weighted smeared wall method”, which is proposed as a simpler method to deal with stepped-wall cylinders of short or medium length with any thickness variation. Buckling predictions are made for a wide range of geometries of silos and tanks (unanchored and anchored) using the new hand calculation method and compared both with accurate predictions from finite element calculations using ABAQUS and with the current Eurocode rules. The comparison shows that the weighted smeared wall method provides a close approximation to the external buckling strength of stepped wall cylinders for a wide range of short and medium-length shells, is easily programmed into a spreadsheet and is informative to the designer.     

Mode interaction in thin-walled trapezoidal column under uniform compression

Interaction of nearly simultaneous buckling modes in the presence of imperfections is studied. The investigations is concerned with thin-walled trapezoidal columns under uniform compression. In these structures two modes are of particular interest, namely a local short-wave and an overall long-wave buckling mode of the whole structure, respectively. The asymptotic expansion established by Byskov and Hutchinson is also used here.The present paper is devoted to the study of equilibrium paths in the advanced post-buckled region of imperfect columns. The bifurcation stress is determined analytically and the asymptotically exact expansion is obtained for the initial post-bifurcation behaviour. The calculations are carried out for several types of rectangular and trapezoidal columns.     

Effect of local wavy imperfections on the elastic stability of cylindrical liners subjected to external uniform pressure

In engineering practice, the majority of the damaged utility or sewage pipelines are structurally safe, but due to the strict hydraulic requirements they require lining. For pipelines below groundwater table, liners should withstand safely the external groundwater pressure. Besides, liners are expected to carry external pressure associated with pumping of the grout around the liner to fill any gaps between the liner and its host pipeline.The critical external pressure at which the liner may buckle or become unstable has been the subject of many studies. Previous research work has always focused on the effect of global imperfections (such as ovality, loose-fit and wrinkle) on the stability of liners. Meanwhile, there is a lack of information regarding the influence of three-dimensional local imperfections on the stability of liners. The current paper reports on a numerical study that investigates the effect of various geometric parameters of local wavy imperfections on the elastic buckling pressure of cylindrical liners. New formulae based on the results of the study are suggested and may contribute to the update of current design specifications of cylindrical liners. The results are expected to help researchers to design for future experimental investigations to provide more insights into stability and behavior of locally imperfect liners.     

Design charts for the general instability of ring-stiffened conical shells under external hydrostatic pressure

The paper describes experimental tests carried out on three ring-stiffened circular conical shells that suffered plastic general instability under uniform external hydrostatic pressure. In this mode of failure, 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.Using the results obtained from these three vessels, together with the results obtained from elsewhere, the paper also provides two-design charts, which are much easier to use than older design charts. The design charts allow 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 pressures. Although similar design charts have been produced in the past, the design charts presented here are based on using the simpler ring-stiffened circular cylinder, which has been made equivalent to the much more complex ring-stiffened circular conical shell. The advantage of using this method is that it is simpler and the design time is reduced by a factor of about 10 with little loss of precision. This method can also be used for the design of full-scale vessels.     

Some thoughtd on mode interaction in thin-walled columns under uniform compression

Interaction of nearly simultaneous buckling modes in the presence of imperfections is studied. The investigation is concerned with thin-walled trapezoidal columns under uniform compression. The asymptotic expansion established by Byskov and Hutchinson is also used here. The present paper is devoted to an improved study of the equilibrium path in the initial post-buckling behaviour of imperfect structures. The results obtained include the effect of interaction of the ‘primary’ local mode and a ‘secondary’ local mode having the same wavelength as the primary. In this paper the analysis of a few buckling mode interactions is presented.     

Post-buckling of a non-uniform ring subjected to uniform external pressure

Rigid plastic analysis is used to find the post-buckling response of a non-uniform circular ring subjected to uniform external pressure. The non-uniform ring has a section of reduced thickness over part of its circumference. A five plastic hinge model is used to describe the non-axisymmetric post-buckling collapse. The principle of virtual work and upper bound theorem are applied to find the collapse pressure and mode of collapse. Depending on the non-uniformity, two modes of collapse can occur: global and snap-through buckling. Global buckling occurs when the angular extent is greater than 90 degrees. When the angular extent is less than 90 degrees and the thickness reduction is large, snap-through buckling takes place. Closed-form expressions for the variation of the collapse load with respect to non-uniformity of the ring are derived.     

Creep buckling of thin-walled polymeric pipe linings subject to external groundwater pressure

Repair of deteriorated sewer pipes is now often undertaken by installing a tight fitting thin-walled polymeric lining inside the cracked/deformed host pipe. It is demonstrated that structural design of these systems is most appropriately focused on proving a suitable factor of safety against long term creep buckling of the lining subject to external groundwater pressure within the confines of the host pipe. A programme of research identifying the appropriate performance criteria is then described. Firstly a suitable means of defining the required long term constitutive behaviour is considered. Secondly a series of laboratory tests which enable system behaviour to be defined is described. Finally a finite element model is developed, capable of predicting the required time dependent, highly nonlinear, long term system behaviour, and which therefore provides a suitable basis for the development of appropriate design guidelines.     

Flexural-torsional buckling of shallow arches with open thin-walled section under uniform radial loads

An arch with an open thin-walled section that is subjected to a radial load uniformly distributed around the arch axis may suddenly buckle out of its plane of loading and fail in a flexural-torsional buckling mode. The classical flexural-torsional buckling load for an arch with an open thin-walled section under a uniform radial load has been obtained by a number of researchers, based on the consideration that the uniform radial load produces a uniform axial compressive force without in-plane bending prior to the occurrence of flexural-torsional buckling. This assumption is correct for deep arches. However, the uniform radial load may produce substantial bending actions in shallow arches prior to flexural-torsional buckling, and so the classical buckling analysis based on the assumption of uniform axial compression may produce incorrect flexural-torsional buckling loads for shallow arches. This paper investigates the flexural-torsional buckling of shallow arches with an open thin-walled section that are subjected to a radial load uniformly distributed around the arch axis. It is found that shallow arches under a uniform radial load are subjected to combined in-plane compressive and bending actions prior to flexural-torsional buckling, and that using the classical buckling solution for circular arches under uniform compression produces incorrect buckling loads for shallow arches. A rational finite element model is developed for the flexural-torsional buckling and postbuckling analysis of shallow arches with an open thin-walled section, which allows the buckling loads to be obtained correctly.     

基于IDA的网壳结构动力失稳分析

地震作用下网壳结构的倒塌本质上属于动力失稳问题,如何确定网壳结构倒塌的极限状态点,是网壳结构倒塌分析中一个非常重要的问题。采用近年来发展起来的一种用于评价结构抗震性能的动力参数分析方法,即增量动力分析(IDA)方法,作为分析结构整体倒塌能力的新方法,为网壳结构的动力失稳分析和倒塌分析提供了一个新的分析途径,并据此可以找到网壳结构倒塌的极限状态点。最后,指出该方法的优点和有待改进之处。     

Buckling of super ellipsoidal shells under uniform pressure

This article is concerned with the elastic buckling of super ellipsoidal shells under external uniform pressure. The middle surface of a super ellipsoidal shell is defined by the following equation: (x/a)²ⁿ +(y/b)²ⁿ + (z/c)²ⁿ  = 1 where n is an integer varying from unity to infinity. It is clear from the equation that the range of shell shapes covered sphere (n = 1, a = b = c) to cube (n = ∞, a = b = c) and ellipsoid (n = 1) to cuboid (n = ∞). By adopting a recently proposed solid shell element for the buckling analysis, the critical buckling pressures of thin to thick super ellipsoidal shells are obtained and tabulated for engineers. The shell element allows for the effect of transverse shear deformation, which becomes significant in thick shells. Their buckling shapes are also examined. In addition, a simple approximate formula for predicting the critical buckling pressure of thick spherical shells is proposed.     

Elastic-plastic collapse of non-uniform cylindrical shells subjected to uniform external pressure

The objective of this paper is to derive analytical solutions for the elastic buckling and plastic collapse pressures of a cylindrical shell with reduced thickness over part of its circumference. The section of reduced thickness is used to represent a corroded region in a pipe. The proposed solutions are extensions of Timoshenko's solutions for the elastic-plastic collapse of a linear elastic, perfectly plastic cylindrical shell subjected to uniform external pressure. A modified interaction formula for the fully plastic membrane forces and bending moments in the non-uniform cylinder has been proposed for plastic collapse. A parametric study shows that the elastic buckling pressure decreases smoothly with corrosion angle when the corrosion depth is less than 0.5t. When the corrosion depth is greater than 0.5t, the elastic buckling strength first decreases very rapidly with corrosion angle. Furthermore, the elastic buckling pressure decreases uniformly with corrosion depth when the corrosion angles are greater than 30°, while the elastic buckling strength decreases more rapidly at higher corrosion depths when corrosion angles are less than 30°. Another parametric study on a steel pipe shows that the initial and fully plastic yield pressures both decrease monotonically with corrosion depth for a given corrosion angle and imperfection.