The shape of circumferential weld-induced imperfections in thin-walled steel silos and tanks

The strength of thin-walled cylindrical shell structures is highly dependent on the nature and magnitude of imperfections. Most importantly, circumferential imperfections have been reported to have an especially detrimental effect on the buckling resistance of these shells under axial load. Due to the manufacturing techniques commonly used during the erection of steel silos and tanks, specific types of imperfections are introduced into these structures, among them circumferential weld-induced imperfections between strakes of steel plates. The shape of such a localised circumferential imperfection has been shown to have a great influence on the degree of strength loss of thin-walled cylindrical shell structures. The results of a survey of imperfections in an existing silo at a location in Port Kembla, Australia in combination with linear elastic shell bending theory was used to develop and calibrate a shape function which accurately describes the geometric features of circumferential weld imperfections. The proposed shape function is the first function to combine shell theory with actual field imperfection measurements. It is a continuous function and incorporates all the necessary features to represent the geometry of a circumferential weld-induced imperfection. It was found that after filtering out the effects of overall imperfections three parameters governed the shape of the surveyed imperfections: the depth, the wavelength and the roundness.     

风荷载下均匀厚度的锚固柱状壳体的屈曲

与承受均匀外部压力作用下的柱状壳体相比,承受不均匀风压的柱状壳体表现出不同的屈曲性能。不同的长宽比下,会出现相当复杂多样的屈曲模式;线性和非线性屈曲分析的结果也会有很大的不同。相比之下,除了较短的柱体或边界条件发生变化外,在均匀外压力作用下,柱体常出现环向失稳,且受几何变化的影响很小。对风压力下厚度均匀的锚固短柱壳和长度适中的柱壳进行了广泛的研究,旨在获得筒仓和锚固贮水池设计的有用信息,以防止其在风载作用下发生屈曲。线性和非线性有限元分析结果表明,短圆筒中出现环向受压失稳模式。对长度适中的柱,截面出现呈椭圆状的前屈曲对屈曲强度有重要的影响。参考均匀外压下的传统临界值,得到风荷载下线性和非线性临界滞止压力的经验公式。简要探讨了屈服和缺陷敏感性的影响。     

Vibration correlation technique for the estimation of real boundary conditions and buckling load of unstiffened plates and cylindrical shells

Nondestructive experimental methods to calculate the buckling load of imperfection sensitive thin-walled structures are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. Vibration correlation technique (VCT) allows determining equivalent boundary conditions and buckling load for several types of structures without reaching the instability point. VCT is already widely used for beam structures, but the technique is still under development for thin-walled plates and shells. This paper intends to explain the capabilities and current limitations of this technique applied to two types of structures under buckling conditions: flat plates and cylindrical shells prone to buckling. Experimental results for a flat plate and a cylindrical shell are presented together with reliable finite element models for both cases. Preliminary results showed that the VCT can be used to determine the realistic boundary conditions of a given test setup, providing valuable data for the estimation of the buckling load by finite element models. Also numerical results herein presented show that VCT can be used as a nondestructive tool to estimate the buckling load of unstiffened cylindrical shells. Experimental tests are currently under development to further validate the approach proposed herein.     

基于改进一致缺陷模态法的轴压圆柱薄壳极限承载力分析

对结构进行缺陷稳定分析的主要方法是一致缺陷模态法和随机缺陷模态法,一致缺陷模态法对薄壁圆柱壳结构进行非线性分析得到的极限承载力与其实际承载能力有一定差距,随机缺陷模态法则工作量很大。基于圆柱薄壳轴压失稳呈现出多模态屈曲的特点,本文提出改进一致缺陷模态法,通过对圆柱壳分别施加不同屈曲模态找到最不利缺陷分布形式。文中通过有限元法验证了改进一致缺陷模态法的可靠性,同时指出按照某一类高阶屈曲模态施加初始缺陷能得到薄壳的最不利极限承载力。     

Coupled dynamic instability of thin-walled structural systems

The dynamics of thin-walled structural systems are presented for both the pre- and the post-buckling states. The influence of the coupling effect of axial compression and initial imperfection on the dynamical response of columns, plates and cylindrical shells is discussed. The theoretical procedure used to study the subject is presented, together with illustrative examples. The use of the results obtained for the prediction of buckling loads of cylindrical shells by means of nondestructive vibration tests is also presented. The implications of the results on the design of thin-walled systems is discussed. The work is done in the scope of the elastic stability, and damping is not included in the analysis.     

Buckling of cylindrical shells under transverse shear

This work concerns with experimental studies on buckling of thin-walled circular cylindrical shells under transverse shear. The buckling loads are also obtained from finite element models, empirical formulae and codes and are compared. Experiments are conducted on 12 models made of stainless steel by rolling and longitudinal seam welding. In situ initial geometric imperfection surveys are carried out. The tests are conducted with and without axial constraint at the point diametrically opposite the loading. Theoretical analyses are carried out using ABAQUS finite element code. Two finite element models considered are: (i) geometry with real imperfection (FES-I) and (ii) critical mode imperfect geometry (FES-II). In the former, the imperfections are imposed at all nodes and in the latter, the imperfection is imposed by renormalizing the eigen mode, using the maximum measured imperfection. General nonlinear option is employed in both the cases for estimating the buckling load. Galletly and Blachut’s expressions, design guidelines of Japan for LMFBR main vessel expressions (empirical formulae), ASME and aerospace structural design codes are used for comparing with experimental loads.The comparisons of experimental, numerical and analytical buckling loads reveal the following. The numerical results are always higher than the experimental values; the percentage difference depends on the wall thickness. FES-II predicts somewhat a lower load than that of the FES-I. The Japanese guidelines predict the lowest load, which is conservative. Experimental loads are lower than that predicted by both ASME and aerospace structural design codes.     

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。     

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.     

The study of ultimate strength in notched cylinders subjected to axial compression

Inclusion of various defects, e.g. imperfection or notches, in cylinders during their service life is expected and identifying of the load bearing capacity of the structure in the presence of those imperfection and damages are necessary. In the present paper, the plastic buckling of notched cylinders is studied experimentally and numerically for various groups of the cylinder dimensions. The study focuses on influences of various characteristics of notches, such as orientation, position and notch length on the buckling capacity of the cylindrical shells. In this direction, the amount of absorbed internal strain energy affected by inserting notch is calculated and compared with intact ones.     

An analytical method for the buckling analysis of cylindrical shells with non-axisymmetric thickness variations under external pressure

This article presents an analytical method for the buckling analysis of laterally pressured cylindrical shells with non-axisymmetric thickness variations. The previous results for thickness variations under external pressure are reviewed firstly. Then, a general analytical method that combines the perturbation method and Fourier series expansion is developed to derive buckling load formulas, which is in terms of thickness variation parameter up to arbitrary order. A classical non-axisymmetric thickness variation is discussed in detail by the presented analytical method. When non-axisymmetric modal thickness variation becomes axisymmetric, the buckling loads degenerate to the known results. Furthermore, the influence of circumferential modal thickness variation with mode corresponding to twice the circumferential buckling mode on the buckling of laterally pressured cylindrical shells is analytically investigated and the results show a great agreement with previous numerical ones by Gusic et al. Thus we confirm the presented method. In addition to theoretical analysis, calculations and comparisons are also performed. The general analytical method presented in the article can be utilized to determine the buckling loads of shells with general thickness variations.     

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.     

残余应力对局部轴压焊接圆柱壳承载力的影响

焊接钢圆柱薄壳广泛应用于钢筒仓和钢油罐结构中,屈曲通常是该结构的设计控制条件,圆柱薄壳的屈曲在大多数荷载工况下对焊接几何缺陷十分敏感.现有研究标明,焊接残余应力可少量提高均匀轴压圆柱壳的稳定承载力,但对于局部轴压荷载下圆柱薄壳中残余应力的效应,相关的研究很少.采用施加收缩应变法,建立了分别考虑焊接几何缺陷以及考虑或不考虑焊接残余应力焊接圆柱薄壳的数值分析模型,研究了含有周向焊缝、竖向焊缝以及砌砖式焊缝(patterned welds)的局部轴压焊接圆柱壳屈曲行为,通过比较考虑/不考虑残余应力圆柱薄壳的计算结果,得到残余应力对局部轴压圆柱壳承载力的影响.     

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.     

Numerical evaluation on shell buckling of empty thin-walled steel tanks under wind load according to current American and European design codes

Liquid storage steel tanks are vertical above-ground cylindrical shells and as typical thin-walled structures, they are very sensitive to buckling under wind loads, especially when they are empty or at low liquid level. Previous studies revealed discrepancies in buckling resistance of empty tanks between the design method proposed by the American Standard API 650 and the analytical formulas recommended by the European Standard EN1993-1-6 and EN1993-4-2. This study presents a comparison between the provisions of current design codes by performing all types of numerical buckling analyses recommended by Eurocodes (i.e. LBA-linear elastic bifurcation analysis, GNA-geometrically nonlinear elastic analysis of the perfect tank and GNIA-geometrically nonlinear elastic analysis of the imperfect tank). Such analyses are performed in order to evaluate the buckling resistance of two existing thin-walled steel tanks, with large diameters and variable wall thickness. In addition, a discussion is unfolded about the differences between computational and analytical methods and the conservatism that the latter method imposes. An influence study on the geometric imperfections and the boundary conditions is also conducted. Investigation on the boundary conditions at the foot of the tank highlights the sensitivity to the fixation of the vertical translational degree of freedom. Further, it is indicated that the imperfection magnitude recommended by the EN1993-1-6 is extremely unfavorable when applied to large diameter tanks. Comments and conclusions achieved could be helpful in order to evaluate the safety of the current design codes and shed more light towards the most accurate one.     

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.     

Dynamic FE simulations of buckling process in thin-walled cylindrical metal silos

The buckling of cylindrical steel silos is caused by the wall friction force due to shearing between the silo fill and silo wall. The aim of this paper is to investigate the stability process in a silo composed of thin-walled isotropic plain rolled sheets using a static and dynamic finite element analysis by taking both the geometric and material non-linearity into account during eccentric discharge. Silo shells were subjected to axisymmetric and non-axisymmetric loads imposed by a bulk solid following Eurocode 1. The differences between the results of static and dynamic analyses were comprehensively discussed. The advantages of a dynamic approach were outlined.     

Quasi-static axial buckling behavior of NiTi thin-walled cylindrical shells

The quasi-static axial buckling response of super-elastic NiTi thin-walled cylindrical shells has been investigated. The results show that the main buckling pattern is the non-axisymmetric mode with various circumferential patterns depending on the geometry of a specimen. The specific energy is strongly related to the geometry and the buckling mode of a specimen. The austenite–martenite phase transition is concentrated in the buckling area to form so-called phase transition hinges. The buckling behavior of a specimen is significantly related to the phase transition and phase transition hinges. After unloading a NiTi specimen can recover to its initial shape, which differs from an elastic–plastic specimen.     

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。     

Buckling and postbuckling behaviour of cylindrical shells under combined external pressure and axial compression

Buckling and postbuckling behaviour of perfect and imperfect cylindrical shells of finite length subject to combined loading of external pressure and axial compression are considered. Based on the boundary layer theory which includes the edge effect in the buckling of shells, a theoretical analysis for the buckling and postbuckling of circular cylindrical shells under combined loading is presented using a singular perturbation technique. Some interaction curves for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, and it is shown that both agree well. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of cylindrical shells have also been discussed.     

关于圆柱壳几何缺陷分析中傅立叶级数选取的探讨

圆柱壳屈曲一般对壳壁上微小几何缺陷的型式和幅值均十分敏感.为了能将缺陷的不同分量和圆柱壳的结构特征联系起来以及研究缺陷各分量对壳屈曲强度的影响,缺陷通常采用傅立叶级数分解.然而,大多数先前的研究选取不适当的傅立叶级数得到不正确的结果.本文首先考察傅立叶级数的数学描述基础,进而讨论不同傅立叶级数在描述不同型式几何缺陷的表现,从而得出如何选取适当的傅立叶级数用来描述圆柱壳几何缺陷的结论.采用这些适当的傅立叶级数,能更好地了解圆柱壳几何缺陷的特征分量以及这些分量对壳体屈曲强度的影响.