Postbuckling analysis of stiffened cylindrical shells under combined external pressure and axial compression

A new approach is extended to investigate the buckling and postbuckling behaviour of perfect and imperfect, stringer and ring stiffened cylindrical shells of finite length subject to combined loading of external pressure and axial compression. The formulations are based on a boundary layer theory which includes the edge effect in the postbuckling analysis of a thin shell. The analysis uses a singular perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Some interaction curves for perfect and imperfect stiffened cylindrical shells are given and compared well with experimental data. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of stiffened cylindrical shells have also been discussed.     

Effects of imperfections of the buckling response of composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different shell-wall laminates two different shell-radius-to-thickness ratios. The shell-wall laminates include four different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios includes shell-radius-to-thickness ratios equal to 100 and 200. The numerical results include the effects of traditional and nontraditional initial imperfections and selected shell parameter uncertainties. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. The cylinder parameter uncertainties considered include uncertainties in geometric imperfection measurements, lamina fiber volume fraction, fiber and matrix properties, boundary conditions, and applied end load distribution. Results that include the effects of these traditional and nontraditional imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure of the shells are presented. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. In addition, a common failure analysis is used to predict material failures in the shells.     

Postbuckling analysis of cylindrical shells under combined external liquid pressure and axial compression

A postbuckling analysis is presented for a circular cylindrical shell of finite length which is subjected to combined loading of external liquid pressure and axial compression. The formulations are based on a boundary layer theory which includes effects of the nonlinear prebuckling deformation, the nonlinear large deflection in the postbuckling range and the initial geometrical imperfection of shells. The analysis uses a singular perturbation technique to determine interactive buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect cylindrical shells. Typical results are presented in dimensionless graphical form.     

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。     

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.     

Pressure buckling of end supported shells of revolution

A reduced stiffness theoretical analysis of imperfection sensitive elastic buckling for end supported cooling tower-type shells, provides lower bounds of experimentally recorded buckling pressures. Classical analysis of these shells with the same empirically realistic boundary support conditions, in contrast, provides unreliable upper bounds of test buckling pressures. By attempting to attribute this imperfection sensitivity to notionally weakened boundary conditions, past interpretations may have provided non-conservative advice for the estimation of design buckling pressures. The reduced stiffness method provides a simple, alternative basis for designing against imperfection sensitive buckling.     

Wind pressures and buckling of cylindrical steel tanks with a dome roof

An experimental/computational strategy is used in this paper to evaluate the buckling behavior of steel tanks with a dome roof under exposure to wind. First, wind tunnel experiments using small scale rigid models were carried out, from which pressure distributions due to wind on the cylindrical part and on the roof were obtained. Second, a computational model of the structure (using the pressures obtained in the experiments) was used to evaluate buckling loads and modes and to study the imperfection sensitivity of the tanks. The computational tools used were bifurcation buckling analysis (eigenvalue analysis) and geometrical nonlinear analysis (step-by-step incremental analysis). Geometric imperfections and changes in the buckling results due to reductions in the thickness were also included in the study to investigate reductions in the buckling strength of the shell. For the geometries considered, the results show low imperfection sensitivity of the tanks and buckling loads associated with wind speeds 45% higher than those specified by the ASCE 7-02 standard.     

Wind pressures and buckling of cylindrical steel tanks with a conical roof

Tanks with a conical roof are studied in this paper under wind load, for a roof which is supported by rafters and columns. Buckling occurs in the form of deflections in the cylindrical shell and the buckling mode is localized in the windward region. Both bifurcation analysis and geometrically nonlinear analysis have been performed using finite element discretizations of the structure. The wind pressures have been obtained from wind tunnel experiments performed as part of the research, and have been obtained for tank geometries for which information was not previously available. The results show high imperfection sensitivity of tanks with a conical roof, and buckling loads for wind velocities in the same order as those expected to occur in the Caribbean region.     

Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads

Free and forced vibration of composite circular cylindrical shells are investigated based on the first love's approximation theory using the first-order shear deformation shell theory. The boundary conditions (BCs) are considered as clamped-free edges. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The axial compressive load was less than critical buckling loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. The effect of fiber orientation, axial load, and some of the geometric parameters on the time response of the shells has been shown. The results show that dynamic responses are governed primarily by natural period of the structure. The accuracy of the analysis has been examined by comparing results with those available in the literature and experiments.     

复合圆柱形壳在径向冲击荷载和轴压荷载作用下的瞬时动力响应

基于首次逼近理论,利用第一阶剪切变形理论对圆柱形壳的自由和强迫振动进行分析。边界条件（BCs）考虑为悬臂状态。分析复合壳体在横向冲击和轴向压力作用下的动力响应（轴压荷载小于临界屈曲荷载）,同时对复合柱形壳进行了建模分析。利用卷积积分对给定荷载状况下的壳体进行分析。揭示纤维方向、轴向荷载及一些几何参数对壳体时间响应的影响。结果表明：动力响应主要由结构的自振周期所控制。     

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。     

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

Linear eigenvalue analysis of cracked cylindrical shells under combined internal pressure and axial compression is carried out to study the effect of crack type, size and orientation on the buckling behavior of cylindrical thin shells. Two types of crack are considered; through crack and thumbnail crack. Our calculations indicate that depending on the crack type, length, orientation and the internal pressure, local buckling may precede the global buckling of the cylindrical shell. The internal pressure, in general, increases the buckling load associated with the global buckling mode of the cylindrical shells. In contrast, the effect of internal pressure on buckling loads associated with the local buckling modes of the cylindrical shell depends mainly on the crack orientation. For cylindrical shells with relatively long axial crack, buckling loads associated with local buckling modes of the cylindrical shell reduce drastically on increasing the shell internal pressure. In contrast, the internal pressure has the stabilizing effect against the local buckling for circumferentially cracked cylindrical shells. A critical crack length for each crack orientation and loading condition is defined as the shortest crack causing the local buckling to precede the global buckling of the cylindrical shell. Some insight into the effect of internal pressure on this critical crack length is provided.     

Finite element based coupled mode initial post-buckling analysis of a composite cylindrical shell

This paper presents a finite element formulation of Koiter's initial post-buckling theory using a multi-mode approach. Initial post-buckling theory provides direct information about the imperfection sensitivity of a structure under compressive loading, and is also the basis of a nonlinear reduced order model. The objective of the present work is to illustrate the capability of the implementation for buckling analysis of shell structures including modal interaction. A coupled mode initial post-buckling analysis for a composite cylindrical shell under axial compression, including the effect of a nonlinear pre-buckling state, has been carried out using a small number of representative modes. For small imperfection amplitudes the limit-point buckling loads obtained with the reduced order model compare reasonably well with full model nonlinear analysis, illustrating that a fast prediction of the coupled mode response of imperfect shells is possible using the approach proposed.     

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.     

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.     

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.     

Combined axial and pressure buckling of end supported shells of revolution

A reduced stiffness theoretical analysis of the imperfection sensitive elastic buckling for end supported shells of revolution is extended to the case of arbitrary combinations of axial and radial pressure loading. Depending upon the shell and loading parameters, the potential reductions in load capacity due to imperfections are shown to involve two distinct forms of post-buckling loss of stiffness. Lower bounds in each of these regimes are provided by appropriate reduced stiffness models, and shown by comparisons with available test data to be reliable even for relatively perfect test models. By attributing reductions in load carrying capacity to weakened end support conditions, it is suggested that past interpretations of these tests may have underestimated the deleterious effects of initial imperfections.     

Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion

Buckling and postbuckling behaviors of imperfect cylindrical shell subjected to torsion are investigated. The governing equations are based on the Karman–Donnell-type nonlinear differential equations. A boundary layer theory of shell buckling is applied to obtain the analytic solutions that meet the boundary conditions strictly. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the current theory gives quite good estimates of the postbuckling paths of cylindrical shells. The effects of the geometric parameters on the buckling and postbuckling behaviors of the cylindrical shells are analyzed. It is confirmed that the postbuckling equilibrium paths of cylindrical shells subjected to torsion are unstable and the relatively shorter shells have higher postbuckling equilibrium paths. Finally, the effects of the initial imperfections on the buckling and postbuckling behaviors of the cylindrical shells are clarified. The illustrated results of the imperfect shells with different initial transverse deflections show that extremely small imperfections do indeed reduce the buckling loads and make the postbuckling equilibrium paths be lower. The buckling and postbuckling of cylindrical shells under torsion exhibit obvious imperfect sensitivity. Furthermore, the effects become greater following with the larger imperfections.     

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。     

单层柱面网壳抗连续倒塌性能

研究了不同荷载布置形式、支承方式条件下,单层柱面网壳的抗连续倒塌性能和倒塌破坏模式,采用基于构件承载能力的敏感性评价指标,分析了初始缺陷、压杆失稳等因素对杆件、节点敏感性指标的影响。结果表明,当采用四边支承时,满跨均布荷载起控制作用,跨中节点为敏感构件,与之相邻斜杆为关键构件;当采用纵向两边支承时,半跨均布荷载起控制作用,杆件和节点的敏感性指标在1/3跨处最大,支座处最小。当考虑初始缺陷时,杆件、节点重要性系数分别增大了41%和53%;当考虑压杆失稳时,杆件和节点重要性系数分别增大了45%和62%。通过对关键构件进行加强,可以优化该类结构的抗连续倒塌性能。