Torsional buckling behaviour of stiffened cylinders under combined loading

In this study cylindrical boundary conditions for finite element analysis are formulated that allow torsional displacement and buckling of a sector of a cylinder of half axial height, and of a circumferential arc angle that will divide into 360°. Finite element tests are carried out on un-stiffened elastic cylinders to verify the method of analysis against classical elastic torsional buckling theory.Elastic–plastic limit point finite element tests are carried out on ring and stringer stiffened and stringer stiffened cylinders to investigate the effects of stiffeners on post-buckling behaviour in torsion.A stringer stiffened cylinder is subjected to many combinations of axial force and surface pressure in the elastic range of response and then tested to failure in torsion to investigate the effects of axial and surface pressure loads on the resistance to plastic collapse in torsion.     

Elephant's foot buckling in pressurised cylindrical shells

Metal cylindrical bins, silos and tanks are thin shell structures subject to internal pressure from stored materials together with axial compression from the frictional drag of stored materials on the walls and horizontal loads. The governing failure mode is frequently buckling under axial compression. The internal pressure exerted by the stored fluids or solids can significantly enhance the buckling strength, but high internal pressures lead to severe local bending near the base. Local yielding then precipitates an early elastic‐plastic buckling failure. This failure mode, commonly known as “elephant's foot buckling”, has received relatively little attention to date and until recently was often ignored in tank and silo design. This problem is an unusual buckling condition, because it involves very high tensile stresses in one direction, coupled with rather small compressive stresses in the orthogonal direction. Thus, although it is a buckling failure involving considerable plasticity, it occurs at low buckling stresses and under conditions that appear to be classically “slender”. The normal concatenation of “slender” with “elastic” in buckling formulations does not apply at all here. This paper describes alternative approaches to the formulation of design rules for the elastic‐plastic instability and collapse of axially‐loaded internally‐pressurised thin cylindrical shells adjacent to the base support. The differences between the different approaches arise from different conceptual models for the manner in which an elastic‐plastic slender structure instability should be treated.     

Plastic buckling of complete toroidal shells of elliptical cross-section subjected to internal pressure

The plastic bifurcation buckling pressures of 60 internally-pressurised, perfect, complete toroidal shells of elliptical cross-section are given in the present paper, assuming elastic, perfectly plastic, material behaviour. The shell buckling programs employed in the computations were BOSOR 5 and INCA. Denoting the major-to-minor axis ratio by k, the numerical results show that the plastic buckling pressures are considerably lower than their elastic counterparts in the range 1.25≤k≤1.5 and are approximately equal to them for k=2.5. A limited study of the effects of non-axisymmetric initial geometric imperfections on the buckling pressures of the shells was also carried out using the INCA code. For the four cases studied the post-buckling behaviour was stable. This means that designers can use the buckling pressures given herein for perfect shells as a basis for their initial designs.     

有多条轴对称焊接凹陷的钢圆柱薄壳在内压力和轴压力共同作用下的强度

钢筒仓中圆柱薄壳承受内压力和轴压力共同作用:在轴压和低内压作用下,壳可发生弹性失稳;在轴压和高内压作用下,壳可发生塑性破坏.内压轴压共同作用下的圆柱薄壳对几何缺陷比较敏感:单条轴对称焊接凹陷可使壳的承载力降低;而多条轴对称凹陷由于相邻凹陷的相互作用,可使壳的强度进一步降低;对于小间距的凹陷,这种相互作用更为明显.本文首次对有多条小间距轴对称凹陷轴压圆柱薄壳的整体结构在不同水平内压作用下的强度进行了有限元分析,并将计算结果与欧洲规范EC3的设计曲线进行比较,对EC3的设计曲线提出了修改意见,从而达到安全设计的目的.     

Parametric study on buckling behaviour of dented short carbon steel cylindrical shell subjected to uniform axial compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings, etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (Lc/Rc∼1, Rc/t=117, 175, 280) cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination of dents do not have much effect on static buckling strength of thin cylindrical shells, whereas in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically. It is also found that the reduction in buckling strength of thin cylindrical shell with a dent of same size and orientation increases with increase in shell thickness.     

Static buckling analysis of thin cylindrical shell with centrally located dent under uniform lateral pressure

One of the common failure modes of thin cylindrical shell subjected to external pressure is buckling. The buckling pressure of these shell structures are dominantly affected by the geometrical imperfections present in the cylindrical shell which are very difficult to alleviate during manufacturing process. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the critical buckling pressure of thin cylindrical shells with a centrally located dent is studied using non-linear static finite-element analysis of ANSYS under external pressure with simply supported boundary conditions at the top and bottom edges of the thin cylindrical shell.     

高架式钢筒仓中转折连接的试验研究

用于散料储存的大型高架式钢筒仓结构通常由仓筒、锥形漏斗以及支承裙筒组成。在漏斗壁拉力水平分力的作用下 ,漏斗 -仓筒 -裙筒连接处产生相当大的周向压力 ,通常通过设置环梁以增加其强度。转折连接的主要破坏模式包括塑性破坏及环梁的弹性或塑性屈曲。国际上对这类连接的屈曲及破坏强度已有了大量的理论研究 ,并建立了基于理论的设计建议 ,但其试验研究尚属空白。本文总结了作者针对钢筒仓转折连接的稳定与强度问题近期在香港理工大学进行的一项大型试验研究项目。首先简单介绍该项目所建立的一套用于薄壳结构屈曲试验的试验装置 ,然后给出三个系列试验 (内压下的圆锥 -圆柱筒连接、散料荷载下的漏斗 -仓筒 -裙筒连接及散料荷载下的漏斗 -仓筒 -裙筒 -环梁连接 )的主要试验结果     

Elastic buckling of cylindrical pipe linings with variable thickness encased in rigid host pipes

Cured-in-place plastic pipe linings are widely used in the rehabilitation of deteriorated rigid pipelines. Generally, the thickness of the pipe lining is assumed to be constant for simplification during the previous analysis. However, the thickness of the pipe lining may be a variable due to corrosive liquids or gases in service. This paper develops an analytical solution for the elastic buckling of cylindrical pipe linings with variable thickness subjected to external hydrostatic pressure. In addition to the analytical solution based on the minimum potential energy theory, a numerical analysis using the finite element method (FEM) is also performed for comparison. The FEM results agree well with the analytical solutions. Both the FEM results and the analytical solutions are discussed and compared with the models presented by other authors. When the thickness of pipe lining is constant, our analytical solutions can be simplified to Glock's typical solutions.     

Experimental collapse of thin cylindrical shells submitted to internal pressure and pure bending

A thin-walled pressurised cylindrical shell is sensitive to buckling phenomena when it experiences locally a compressive stress. It is often considered that its behaviour under bending is rather similar to pure compression, but very few are the experimental investigations that precise the real behaviour of a thin pressurised cylinder submitted to a bending load. A large amount of experimental results is presented here, obtained on thin shells (550<R/t<1450) of moderate length (L/R≈2). The evolution of the cylinders' behaviour that has been recorded when internal pressure increases is outlined. It is shown that one must distinguish between local buckling and global collapse of the structure. A comparison of our experimental data to design recommendations given by two standards (NASA SP8007 and Eurocode 3) is finally achieved, putting in advance safety margins provided by these codes.     

Design by analysis of ductile failure and buckling in torispherical pressure vessel heads

Thin shell torispherical pressure vessel heads are known to exhibit complex elastic–plastic deformation and buckling behaviour under static pressure. In pressure vessel Design by Analysis, the designer is required to assess both of these behaviour modes when specifying the allowable static load. The EN and ASME boiler and pressure vessel codes permit the use of inelastic analysis in design by analysis, known as the direct route in the EN Code. In this paper, plastic collapse or gross plastic deformation loads are evaluated for two sample torispherical heads by 2D and 3D FEA based on an elastic-perfectly plastic material model. Small and large deformation effects are considered in the 2D analyses and the effect of geometry and load perturbation are considered in the 3D analysis. The plastic load is determined by applying the ASME twice elastic slope criterion of plastic collapse and an alternative plastic criterion, the Plastic Work Curvature criterion. The formation of the gross plastic deformation mechanism in the models is considered in relation to the elastic–plastic buckling response of the vessels. It is concluded that in both cases, design is limited by formation of an axisymmetric gross plastic deformation in the knuckle of the vessels prior to formation of non-axisymmetric buckling modes.     

刚性外筒内不同厚度圆柱形内筒的弹性屈曲分析

塑性管道内管被广泛应用于修复损坏的刚性管道。在之前的分析中,一般简化地认为内管是等厚度的。然而,在正常使用中,由于腐蚀性液体或气体的腐蚀,会造成内管厚度不均。论述了在外部流体压力作用下不同厚度圆柱体形管道内管的弹性屈曲的分析结果。根据最小势能理论得出了分析结果,并与有限元数值分析结果进行了对比。结果显示,有限元的分析结果与最小势能理论分析结果较好地吻合。分别对最小势能理论分析结果和有限元分析结果进行了讨论,并与其他理论得出的结果进行了对比。当内管厚度是常数时,本分析结果就简化为Glock的经典结论。     

Buckling and postbuckling of cylindrical shells with one end pinned and the other end free

Using finite element analysis, this paper examines the linear bifurcation buckling loads, and nonlinear collapse loads, of cylindrical shells with one end pinned and the other end free, under a variety of axial and pressure load combinations. The pinned end is formulated so as to provide no axial restraint. For the bifurcation analysis, loads are related back to the classical solutions for cylinder buckling loads, to explain the very low values found for this set of boundary conditions.The nonlinear analysis includes both imperfections and material plasticity. In this analysis, it is found that cylindrical shells with pinned-free boundary conditions are notably imperfection insensitive, and for a range of geometries are able to reach collapse loads significantly greater than their bifurcation load. For other geometries, collapse loads very close to the bifurcation load are found. This unusual imperfection insensitivity for a cylindrical shell is explained in terms of the large flexibility engendered by the pinned-free boundary conditions and the oval buckling mode.     

Deflection and buckling behavior of thin,circular cylindrical shells under wind loads

Some wind-tunnel tests have been conducted on the buckling behavior of closed-ended, thin cylindrical shells such as silos. Detailed measurements of the prebuckling deflections as well as of the buckling pressures were made with a variety of elastic cylinders in both smooth and turbulent flows.The results indicate that the prebuckling deflection is extremely sensitive to the wind pressure distribution, while the buckling pressure is less sensitive to it. It was also found that the pressure—deflection relationship exhibits a marked nonlinearity as the wind pressure approaches the buckling pressure. The experimental results were compared with the results of a stability analysis based on Donnell's theory, and a relatively good agreement was derived with respect to the buckling pressure.Furthermore, on the basis of the experimental results, an empirical formula for the buckling pressure was proposed as function of the height/radius ratio and the radius/ thickness ratio of the cylindrical shell.     

Research on stability of single-layer inverted catenary cylindrical reticulated shells

The structural configuration and method of analysis of the single-layer inverted catenary cylindrical reticulated shell are introduced in this paper, and the elastic as well as elastic–plastic stability of this kind of reticulated shell is then investigated. The stability of the structures with different types of grid patterns is compared, and the reasonable grid pattern is hence recommended. The structural buckling mode and ultimate load-carrying capacity are studied in detail by parametric analysis. Influence of various factors on structural ultimate load is investigated, and the fitting formula of ultimate load is thus presented. Comparison analysis between the inverted catenary and circular cylindrical reticulated shells is also carried out. The work will provide guidance in theory for practical applications of this kind of structure.     

Local buckling in infinitely,long cylindrical shells subjected uniform external pressure

This paper presents a unique approach to analyze the buckling of an infinitely long cylindrical shell subjected to the external pressure. Buckling is considered to occur locally in the shell, spreading over a certain length along the longitudinal axis of the shell. A plausible function of the flexural displacement is created according to Timonshenko's ring solution of the transverse collapse mode. The governing equations based on Donnell–МУШТАРИ's shell theory are solved using Ritz method and the equilibrium conditions are educed. Numerical computations are performed for cases when shell thickness/radius ratios are 0.1, 0.05 and 0.03. In general, the pressure decreases sharply with a very slight increase of the normalized radial deflection just at the beginning of the initiation, then falls quite slowly till the two opposite points on the inner surface of the shell contact each other. It is found that the buckling pressure of the shell converges to the critical value given by Donnell–МУШТАРИ's shell theory and the span of the buckling mode in the longitudinal axis of the shell is independent of material properties. Solutions given in this paper can be used to address the problem of steady-state buckle propagation in the shells.     

Vibration, buckling and collapse of ovaloid toroidal tanks

A shell-theory finite element analysis is carried out for toroidal tanks with ovaloid cross-section. The analysis serves to determine the natural frequencies, and the buckling and collapse pressures. A variety of support conditions are considered, including lines of support at the inner and outer equator of the tank. For validation, comparison is made with previously published results for stress, vibration, and buckling of elliptical toroidal shells. Finally, a parametric study is carried out to determine the influence on the natural frequency, and buckling and collapse pressures, of shell size, shell thickness, material properties, and support conditions.     

Buckling behaviour of ring-stiffned cylinders; experimental study

The effect of the number and size of rings on the buckling strength of ring-stiffened cylinders is studied experimentally. The results of ten machined ring-stiffened cylinders subjected to lateral pressure are presented. Five of the cylinders failed by the general instability mode and the rest failed by the shell instability mode. A sample of the experimental results which shows longitudinal and circumferential strains as well as the development of the circularity contours till collapse is presented. Buckling pressures obtained from the experiments are shown to be within ±30% of the corresponding value obtained from the theoretical analysis available in the literature.     

Stability loss of thin-walled cylindrical tubes, subjected to longitudinal compressive forces and external corrosion

The paper is devoted to investigation of stability loss of thin-walled elastic circular cylindrical pipes subjected to simultaneous action of longitudinal compressive forces and uniform corrosion from outside. The pipe is treated as a thin closed elastic circular cylindrical shell which can be described within Kirchhoff–Love approximation. The critical time of stability loss of the pipe is found, using the upper critical load value for static stability loss of the pipe, not subjected to corrosion, and the law of corrosion rate. Numerical results were obtained for pipes, made from steel and aluminum with different initial wall thickness.     

Buckling of intermediate ring supported cylindrical shells under axial compression

This paper is concerned with the elastic buckling of axially compressed, circular cylindrical shells with intermediate ring supports. The simple Timoshenko thin shell theory and the more sophisticated Flügge thin shell theory have been adopted in the modeling of the cylindrical shells. We used these two representative theories to examine the sensitivity of the buckling solutions to the different degree of approximations made in shell theories. By dividing the shell into segments at the locations of the ring supports, the state-space technique is employed to derive the solutions for each shell segment and the domain decomposition method utilized to impose the equilibrium and compatibility conditions at the interfaces of the shell segments. First-known exact buckling factors are obtained for cylindrical shells of one and multiple intermediate ring supports and various combinations of boundary conditions. Comparison studies are carried out against benchmark solutions and independent numerical results from ANSYS and p-Ritz analyses. The influence of the locations of the ring supports on the buckling behaviour of the shells is examined.     

Plastic buckling of thin hemispherical shell subjected to concentrated load at the apex

This study presents the analytical, numerical, and experimental results of thin hemispherical metal shells into the plastic buckling range illustrating the importance of geometry changes on the buckling load. The hemispherical shell is rigidly supported around the base circumference against horizontal and vertical translation and the load is vertically applied by a rigid cylindrical boss at the apex. Kinematics stages of initial buckling and subsequent propagation of plastic deformation for rigid-perfectly plastic shells are formulated on the basis of Drucker–Shield's limited interaction yield condition. The effect of the radius of the boss, used to apply the loading, on the initial and subsequent collapse load is studied. In the numerical model, the material is assumed to be isotropic and linear elastic perfectly plastic without strain hardening obeying the Tresca or Von Mises yield criterion. Both axisymmmetric and 3D models are implemented in the numerical work to verify the presence of non-symmetric deformation modes in the case of thin shells. In the end, the results of the analytical solution are compared and verified with the numerical results using ABAQUS software and experimental findings. Good agreement is observed between the load–deflection curves obtained using three different approaches. A secondary bifurcation point is detected in thin shells in which the deformation degenerates from symmetric to non-symmetric behavior. The bifurcation point depends on the (R/t₀) ratio and the material parameters.