强冰雪灾害下大型薄壁圆柱钢壳结构稳定性研究

2008年我国南方地区发生强冰雪灾害,造成不少钢结构破坏。在化工、电力等工程中有很多作为整个系统关键设备的大型薄壁圆柱钢壳结构,柱壳内通常需设置一些横梁支承工艺设备,壳体既受到由上部壳体、顶盖和设备自重等荷载形成的沿环向均匀分布的整体轴向压力,又受到横梁支座传递来的局部轴向压力。在这些荷载作用下结构已经积累了一定的内力和变形,一旦再遭受强冰雪灾害,面积较大的顶盖和相连的其他管道上会快速积聚较大的雪荷载,导致结构发生失稳破坏。根据结构施工和使用过程,考虑加载路径的影响,先施加整体均布轴向压力,再施加局部轴向压力,然后施加模拟强积雪荷载的均布轴向压力,对112个带焊缝初始缺陷的薄壁圆柱壳结构进行了非线性稳定性数值分析。研究表明:随着初始整体荷载水平提高,柱壳承受积雪荷载的能力下降;随着缺陷幅值的增大,柱壳承受积雪荷载的稳定承载力与整体均布轴压下的稳定设计承载力的比值增大,其后屈曲承载能力也提高。柱壳下部储有浆液时;壳体承受积雪荷载的能力有小幅提高。根据大量计算结果,提出了考虑加载历史的遭受强冰雪荷载的圆柱壳稳定性设计建议。     

外压作用下偏心加劲功能梯度圆柱壳的非线性屈曲和后屈曲分析

通过解析法研究外压作用下功能梯度加劲薄圆柱壳的非线性屈曲和后屈曲性能。通过其在内部的偏心环和纵梁对壳体进行加固,假定壳体和加固件的材料性能在厚度方向为连续梯度。根据VonKarman理论中的刚度法和传统的壳理论推导出基本关系和平衡方程,可更准确地选择三种关于挠曲的近似公式,且使用盖勒金法得出的显式表达式可以推测出临界荷载和后屈曲压力-挠曲曲线。数值结果显示了加固件能有效地增强壳体稳定性。     

对称双圆弧柱壳的非线性屈曲

对于潜艇艇体耐压壳结构,屈曲特性在设计中被广泛关注。针对一种新型潜艇耐压艇体结构-对称双圆弧环肋柱壳,推导了相应的弹塑性失稳系数。采用非线性大挠度理论,给出了静水压力作用下含初始缺陷的对称双圆弧环肋柱壳大挠度弹塑性屈曲临界压力计算式。讨论了开口角、周向相当波数和初始几何缺陷对临界压力的影响。计算结果表明,开口角对结构弹塑性屈曲的临界压力影响很小,而周向相当波数是影响临界压力的主要因素。     

Y形柱稳定性分析研究

Y形柱是机场航站楼屋盖支承体系中常采用的一种构件形式,作为主要承重构件,其稳定性决定了屋盖结构的整体承载能力。利用荷载-位移全过程跟踪技术,考虑几何非线性、材料非线性和初始几何缺陷,研究了在竖向和水平风、地震作用下薄壁Y形柱的稳定性。研究表明:竖向荷载作用下Y形柱以分叉段平面外屈曲为主要失稳模式;Y形柱对初始几何缺陷不敏感;水平风荷载对Y形柱稳定性不起控制作用;竖向和水平荷载作用下,发生面外失稳前柱子分叉处已经进入塑性变形,柱子强度问题先于整体失稳。     

厚度阶梯式改变圆柱壳体在均匀外部压力作用下的屈曲分析

厚度呈阶梯式改变圆柱壳体结构在工程实践中有着广泛的应用,例如垂直安放的各种容器和筒仓结构。这类结构在空置或部分空置时,在外部压力的作用下易发生屈曲破坏。由于壳体复杂的厚度变化形式,屈曲模态可能有多种形式,如何准确地判断壳体的屈曲模态是此类结构设计时的一个难题。提出一种新的方法——"加权平均厚度方法",这种方法可以对任何厚度阶梯式改变的短、中等长度圆柱壳体结构进行稳定性分析。用此方法得到的结果与利用有限元软件ABAQUS得到的精确结果以及用当前欧洲规范得到的结果进行对比,结果表明,"加权平均厚度方法"可以对厚度阶梯式改变的短、中等长度圆柱壳体在外部均匀压力作用下的屈曲强度及屈曲模态进行非常准确的评估。     

均匀外压下的锥壳减速机试验

有关壳结构屈曲性能的研究日益增多,尤其是锥壳。然而,有关细长柱端壳体减速机的足尺模型和实际模型的屈曲性能试验研究还较缺乏。试验研究和分析3个锥壳减速机在均匀周边压力下的屈曲性能。进行有限元模拟和理论分析,比较屈曲荷载和变形模式。在研究范围内,收集足尺锥壳减速机的有关数据。     

柱壳结构非线性稳定性分析

以薄壁柱壳为例，根据能量原理推导其线性屈曲荷载，并采用折减的方法近似地得出壳体非线性屈曲荷载的公式，最后采用有限元程序对公式进行验证，分析结果表明公式的正确性。     

卷边翼缘工形构件在压弯荷载作用下的稳定承载力设计理论

卷边工形截面构件作为一种高效型材,在弯矩与轴力共同作用下的破坏模型常常是伴随板件局部屈曲的整体失稳。利用板壳有限单元法,研究卷边工形截面构件在板件局部屈曲下的构件整体稳定承载力,建立其稳定承载力设计公式。首先,通过设计大量算例,研究了截面宽高比、腹板高厚比、翼缘宽厚比等截面参数对短柱承载性能的影响,其中考虑了板组之间屈曲的相关作用,获得了考虑板组局部屈曲特性的短柱稳定承载力相关公式。在短柱板件局部失稳承载力研究的基础上,计入构件长细比对长柱面内和面外稳定承载性能的影响,通过数值分析建立了卷边工形构件在压弯荷载作用下的稳定承载力设计公式。     

扭转作用下有缺陷柱形壳的屈曲和后屈曲性能

分析扭转作用下有缺陷柱形壳的屈曲和后屈曲性能。基于Karman-Donnell-Type非线性微分方程建立计算公式,采用壳屈曲的边界层理论进行分析,以获得能严格满足边界条件的解决方案。采用奇摄动技术,以确定屈曲载荷和后屈曲平衡路径。数值结果显示,目前的理论能对柱形壳的后屈曲性能进行较好评估。同时分析了几何参数对柱形壳的屈曲和后屈曲性能的影响。证实了扭转作用下柱形壳的后屈曲平衡路径并不稳定,并且相对更短的壳体具有更高的后屈曲平衡能力。最后,指出初始缺陷对柱形壳屈曲和后屈曲性能的影响。对具有初始横向挠曲的有缺陷壳体的分析结果显示：即便是非常小的缺陷,也确实会减少屈曲承载力,并使得后屈曲稳定性变差。扭转作用下柱形壳的屈曲和后屈曲性能显示出明显的缺陷敏感性。此外,如果缺陷更大,那么带来的影响也随之会变得更大。     

扭矩和轴压共同作用下各向异性薄壁和中厚壁圆筒的屈曲性能

采用基于考虑了各向异性和横向剪切刚度影响的厚壳理论的分析模型,研究各向异性、横向剪切刚度、长度和它们的相互作用对纯扭或者扭矩与轴压共同作用下圆筒屈曲性能的影响。由于该模型仅轴压下的屈曲性能得到验证,故将轴压下分析结果与扭转作用下作对比。结果表明,该模型对扭矩作用下屈曲性能亦有较好的适用性。研究表明,各向异性、横向剪切刚度及壳体长度均影响柱壳的临界力大小。这说明空心壳理论(Donnell理论)并不准确,应该采用考虑了各向异性和横向剪切刚度影响的厚壳理论。     

Effect of imperfections on wind-loaded cylindrical shells

The wind-induced buckling of thin-walled steel cylinders, such as silos and tanks, was investigated by wind-tunnel testing for a limited range of the parameters. While wind-buckling of short, stocky shells can be well represented by an equivalent uniform external pressure, long shells show quite a different behaviour, which is strongly influenced by the axial compression forces. This paper presents a study of this behaviour, based on numerical analyses and considering various types of imperfection shape. The effect of geometrical nonlinearity, as well as material plasticity, has also been included. A comparison with test results shows good agreement with the numerical results of imperfect shells, provided that special eigenmode-shaped modes of imperfections are excluded.     

Instability of cracked CFRP composite cylindrical shells under combined loading

Numerical analysis of cracked composite cylindrical shells under combined loading is carried out to study the effect of crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure are obtained, using the finite element method. In general, the internal pressure increases the critical buckling load of the CFRP cylindrical shells while torsion and external pressure decrease it. Numerical analyses show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell while for cylindrical shells under combined external pressure and axial load, the global buckling shape is insensitive to the crack length and crack orientation.     

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.     

真空引起的薄壁圆筒屈曲压力预测

研究均匀外压力下初始缺陷对圆柱形薄壳结构屈曲性能的影响。对缩尺薄壁圆筒的外形进行分析以测量壳体表面的几何缺陷。有限元分析时将这些初始缺陷考虑在内,并进行静态几何非线性分析。在实验室进行圆筒的倒塌试验,并将试验结果和有限元分析结果进行比较。结果表明,有限元分析能够准确预测圆筒的破坏坍塌压力和后屈曲模态。     

Buckling of cylindrical open-topped steel tanks under wind load

Vertical cylindrical welded steel tanks are typical thin-walled structures which are very susceptible to buckling under wind load. This paper investigates the buckling behavior of open-topped steel tanks under wind load by finite element simulation. The analyses cover six common practical tanks with volumes of 2×10³ m³ to 100×10³ m³ and height-to-diameter ratios H/D<1. The linear elastic bifurcation analyses are first carried out to examine the general buckling behavior of tanks under wind load, together with comparison to that of tanks under uniform pressure and windward positive pressure (only loaded by positive wind pressure in the windward region). The results show that for larger tanks in practical engineering, the stability carrying capacity of wind load is relatively lower. It is also indicated that the buckling behavior of tanks under wind load is governed by the windward positive pressure while wind pressure in other region of tank essentially has no influence on the buckling performance. The geometrically nonlinear analyses are then conducted to investigate the more realistic buckling behavior of tanks under wind load. It is found that the buckling behaviors of perfect tanks and imperfect tanks are much different. The weld induced imperfection only has little influence on the wind buckling behavior while the classical buckling mode imperfection has significant influence, leading to a considerable reduction of wind buckling resistance. The influences of thickness reduction of cylindrical wall, liquid stored in the tank and wind girder on the buckling behavior are also examined. It shows that the thickness reduction of cylindrical wall considerably reduces the wind buckling resistance while sufficient liquid stored in the tank and wind girder significantly increase the wind buckling resistance.     

Form of circumferential weld-induced imperfections for tapered-wall cylindrical shell structures

Initial geometric imperfections have a great effect on the buckling strength of thin-walled cylindrical shells under axial compression, and the circumferential weld-induced imperfection is usually the most deleterious imperfection form. Two axisymmetric imperfection forms proposed by Rotter and Teng have widely been employed in the buckling analysis of cylindrical shells. However, the applicability of the two forms for tapered-wall cylinders needs further study, since they are derived from the elastic bending theory for long thin-walled cylinders with a constant wall thickness. This paper presents a modified form of circumferential imperfection for tapered-wall cylinders. Finite element analyses are carried out by employing the trapezoidal strain field approach to model the welding process, and the obtained circumferential depression shapes are used to evaluate the availability of the modified imperfection form. It is shown that the modified imperfection form is reasonable for any wall thickness ratio between two adjacent strakes, and the most suitable shape function, which is very close to the FE results, can be obtained by giving suitable values of the roundness in the modified form.     

Plastic Axisymmetric Collapse of Thin-Walled Circular Cylinders and Cones Under Uniform External Pressure

This paper reports on two theoretical investigations and an experimental investigation into the plastic axisymmetric buckling of two thin-walled conical shells and several thin-walled circular cylindrical shells, under uniform external pressure.

One of the theoretical investigations was a non-linear finite element solution for plastic axisymmetric buckling, which gave good results.

The other theoretical solution was for the plastic non-symmetric bifurcation buckling of thin-walled circular cylinders. This second solution was a very simple one and, although it was based on plastic lobar buckling, it gave very good predictions for plastic axisymmetric collapse. This latter observation prompted the conclusion that there may be a link between plastic lobar buckling and plastic axisymmetric buckling.     

Buckling of circular cylindrical shells partially subjected to external liquid pressure

Theoretical analyses are presented for the buckling of circular cylindrical shells partially subjected to external liquid pressure. The shells are assumed to stand vertically with the lower end clamped, and the upper end clamped or free. In the analyses, the Donnell equations are used for the basic equation, and prebuckling deformation as well as the membrane state of stress of the shell are taken into account. The Galerkin method is used, and the critical pressures at various liquid heights as well as the wave numbers, are obtained for a wide range of the geometrical parameters of the shell Z. A convenient chart which indicates the buckling liquid height for a given shell and liquid are presented. Experimental studies are also conducted by using test cylinders made of polyester film, and water. The theoretical and experimental results for the buckling liquid height, are in excellent agreement.     

Buckling and post-buckling behaviour of elastic seven-layered cylindrical shells – FEM study

The paper is devoted to buckling and post-buckling problems of an elastic seven-layered cylindrical shell under uniformly distributed pressure. The shell is an untypical sandwich structure composed of main corrugated core and two three-layer faces. Numerical FEM model for the shell has been elaborated. The calculations have been performed with the use of the ANSYS code for elastic shells of different dimensions. The linear and non-linear analyses of the shells have been performed with the use of the finite elements method. Critical pressure and equilibrium paths for the family of seven-layered shells subjected to uniformly distributed external pressure are calculated. The influence of corrugation pitch of main core and the length of the shell on the critical pressure has been determined. The results of these investigations are presented on the graphs.     

Hydrostatic, wind and non-uniform lateral pressure solutions for containment vessels

The governing Flügge stability equations in coupled form are used for cylinders subjected to external pressure that varies circumferentially. Three cases are considered: fluid (hydrostatic) pressure, wind pressure and partial (patch) circumferential pressure. The wind load follows the Australian Standard AS 1170.2 (1989). Longitudinal variation of the load is not considered. The numerical process gives the stagnation buckling pressure for different shell geometry and simple support conditions at each end. The Galerkin method is employed to orthogonalize the error made with the introduction of the finite series into the governing equations. The solutions are compared with a few published solutions in the literature.