Influence of geometric imperfections on the load capacity of orthotropic stiffened and composite shells of revolution with arbitrary meridians and boundary conditions

A stiffness matrix for an element of a shell of revolution has been derived, considering arbitrary load distributions and initial geometric imperfections. This element-stiffness matrix is based on the transfer-matrix method and describes the whole section of a shell of revolution between two rings in modal coordinates (a so-called super-element). The modal coordinates here are circumferential Fourier members, thus reducing the partial differential equations to ordinary ones.

Several stability analyses investigating the sensitivity of composite shells to different geometric imperfection shapes were carried out. The influence of the load distribution and boundary conditions in combination with geometric imperfections was analysed by different modellings of a hypothetical Jupe Avant shell of the ARIANE 5 rocket.     

Reliable and accurate prediction of the experimental buckling of thin-walled cylindrical shell under an axial load

Reliable and accurate method of the experimental buckling prediction of thin-walled cylindrical shell under an eccentric load is presented. The experimental arrangement and specimens are discussed in detail, including the measurement of the geometric imperfections of the specimen's surface using a coordinate measuring machine. Different FE models, in terms of complexity, are used to simulate the experiment arrangement in an attempt to get a good agreement with the experimental buckling loads and study the effect of measured initial geometric imperfections, load eccentricity, load eccentricity position along the shell's circumferential direction and different experimental arrangement that influence the boundary conditions. It has been demonstrated that FE models with simplified rigid support conditions overestimate the prediction of the experimental buckling load even though these models included the effects of the measured initial geometric imperfections and load eccentricity. By contrast, FE models with realistically modeled support conditions achieved the best result. The average deviation −1.59% from the experimental buckling loads was achieved using the FE model simulating the mounting devices as elastic bodies and with surface-to-surface contact interaction behavior on the support. The presented work also demonstrated the strong influence of the eccentric load position along the imperfect shell's circumferential direction on the buckling of the thin-walled shell.     

单层组合加肋拱支网壳的稳定性

介绍了某相贯单层组合加肋拱支网壳结构在竖向荷载及风荷载作用下的整体稳定性。采用有限元软件MIDAS,在两种荷载工况下分别进行了此网壳结构的特征值屈曲、几何非线性屈曲分析,初始缺陷对网壳结构的整体稳定性影响分析。结果表明:网壳结构对初始缺陷较为敏感,初始缺陷会明显降低结构稳定性;不同的荷载工况下,失稳的情况亦不同且网壳结构稳定临界系数随着荷载的增大而降低。     

Influence of loading imperfections on the stability of an axially compressed cylindrical shell

An important phenomenon is presented which has not been given sufficient attention in the stability of shell structures: the buckling of a circular cylinder subjected to a set of equally distributed discrete axial concentrated loads is studied. It is shown that the critical load of a circular cylinder under axial compression is very sensitive to imperfection of the applied loads as well as to initial geometric imperfections and the boundary conditions.     

Dynamic buckling of fiber composite shells under impulsive axial compression

The paper deals with dynamic buckling due to impulsive loading of thin-walled carbon fiber reinforced plastics (CFRP) shell structures under axial compression. The approach adopted is based on the equations of motion, which are numerically solved using a finite element code (ABAQUS/Explicit) and using numerical models validated by experimental static buckling tests. To study the influence of the load duration, the time history of impulsive loading is varied and the corresponding dynamic buckling loads are related to the quasi-static buckling loads. To analyse the sensitivity to geometric imperfections, the initial geometric imperfections, measured experimentally on the internal surface of real shells, are introduced in the numerical models. It is shown numerically that the initial geometric imperfections as well as the duration of the loading period have a great influence on the dynamic buckling of the shells. For short time duration, the dynamic buckling loads are larger than the static ones. By increasing the load duration, the dynamic buckling loads decrease quickly and get significantly smaller than the static loads. Since the common practice is to assume that dynamic bucking loads are higher than the static ones, which means that static design is safe, careful design is recommended. Indeed, taking the static buckling load as the design point for dynamic problems might be misleading.     

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.     

Buckling analysis of a cooling tower shell with measured and theoretically-modelled imperfections

Geometrical imperfections were measured using photogrammetric techniques on an existing reinforced concrete cooling tower shell. The imperfections, related to the radii of such a real shell, were used as input data to create a real shape of the cooling tower. Numerical analysis was carried out for three models: (P) perfect shell of revolution, (M) shell with measured imperfections, (T) shell with a theoretical imperfection corresponding to the primary buckling mode under dead load. The buckling analysis was related to the linearized eigenvalue problem of elastic shells. The shell midsurface was approximated by eight-node quadrilateral isoparametric finite elements. Computations were carried out using the ANKA computer code. Critical values of the load parameter enable confirmation of a partial correlation between existing imperfections and buckling modes under dead load. The most disadvantageous direction of the wind load application on the real shell was found, in order to evaluate the decrease in the load-carrying capacity of the cooling tower shell against buckling. Theoretically modelled imperfections give rather unrealistic values of buckling loads of the real shell.     

Creep buckling of cylindrical shells under external lateral pressure

In this paper, the authors present the results of an analysis of creep buckling of cylindrical shells under external lateral pressure. The nature of the material, the dimensions of the specimens and the type of boundary permit an elastic analysis of this phenomenon. The results of tests and calculations show on the one hand that this phenomenon is very sensitive to the presence of initial geometric imperfections; and on the other hand that it is possible to establish a monograph giving the critical time of an electroplated nickel shell as a function of its initial imperfections and of the nominal applied load. In this manner, the same reasoning can be applied to other shells made up of other materials that are sensitive to creep (resins, concretes, wood, metals at high temperatures, etc.).     

金寨影剧院网壳屋盖结构的分析与设计

金寨影剧院屋盖采用了椭圆抛物面网壳结构.文章对网壳结构进行了结构的动力分析,计算了结构在风荷载作用下的响应,并对网壳结构进行了考虑初始几何缺陷的屈曲分析,得到了结构的极限承载力.     

Experimental investigation of buckling of wind turbine tower cylindrical shells with opening and stiffening under bending

An experimental and numerical study of the buckling behavior of cantilevered shells with opening and stiffening is presented in this paper. Unlike previous experimental studies, the present work focuses on shell slenderness as well as opening and stiffening reflecting the main geometric characteristics of wind turbine towers. The specimens can be classified as medium slenderness shells affected mainly by inelastic effects and secondarily by geometric imperfections. Both load–displacement curves as well as strain measurements are presented and compared with numerical predictions by finite element analyses, accounting for both inelastic effects and geometrical nonlinearity as well as for contact interaction between the various parts of the specimens. A good agreement between numerical and experimental results was found in terms of load–displacement curves and ultimate load. Due to the influence of the shape and size of geometric imperfections, a complete match of the numerically obtained strains to the corresponding experimental ones was not possible. The provided stiffening was found to be able to compensate the strength loss due to the presence of the cut-out.     

轴压下薄壁圆柱形壳屈曲试验承载力的准确可靠预测方法

论述了一种能可靠并准确预测偏心荷载下薄壁圆柱形壳屈曲试验的方法。详细描述了试验装置和试件,包括用配套的设备测量试件表面的几何缺陷。为了精确地预测屈曲试验的荷载,根据不同的复杂度建立了不同的有限元模型模拟试验装置,并研究了初始几何缺陷、荷载偏心、沿柱圆周方向的荷载偏心位置和影响边界条件的不同试验装置对屈曲承载力的影响。解释了具有简单刚性支座的有限元模型会过高估计屈曲试验承载力的原因。尽管这些模型均考虑了初始几何缺陷和荷载偏心的影响。作为对比,计算了考虑实际支座条件有限元模型的结果。在有限元模型中,用弹性实体单元模拟固定装置,用面—面接触单元模拟试件与支座间的接触面,计算出的屈曲承载力与试验有着平均约-1.59%的偏离。沿有缺陷薄壁圆柱形柱圆周方向的荷载偏心位置对屈曲承载力有显著影响。     

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.     

Konsistente geometrische Ersatzimperfektionen für den numerisch gestützten Beulsicherheitsnachweis axial gedrückter Schalen

Consistent equivalent geometric imperfections for the numerical buckling strength verification of axially compressed shells. A geometrically and materially nonlinear analysis with imperfections included (GMNIA) is the most sophisticated and perspective the most accurate method of a numerical buckling strength verification of steel shell structures. By this way, equivalent geometric imperfections, which have to cover the influence of all deviations from the nominal dates of the resistance parameters, are fundamental. The problems resulting from this aim are discussed in the paper. The Eurocode gives hints regarding the application of equivalent imperfections and makes statements about their amplitudes, which are to be adopted. It is shown, that the current regulation doesn't cover all relevant parameters with respect to the load bearing capacity. This way, inconsistencies between numerically and experimentally determined buckling resistances arise for several geometries. Modifications are suggested for the basic buckling case of the axially compressed shell to succeed in consistent equivalent geometric imperfections.     

华能大厦单层柱面网壳的设计及分析

以某低矢跨比的单层柱面网壳分析与设计为例,分析该网壳在各种荷载作用下的受力特点;讨论网壳支承刚度对网壳的受力影响;介绍网壳的设计和节点构造方法;并着重研究网壳的整体稳定性。得出：低矢跨比单层柱面网壳的整体稳定对支承刚度和初始几何缺陷较敏感;考虑塑性影响后,低矢跨比柱面网壳的稳定承载力相对弹性稳定承载力有大幅度降低;不同...     

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 of elastic cylindrical shells considering the effect of localized axisymmetric imperfections

The effect of localized axisymmetric initial imperfections on the critical load of elastic cylindrical shells subjected to axial compression is studied through analytical modeling. Some classical results regarding sensitivity of shell buckling strength with respect to distributed defects having axisymmetric or asymmetric forms are recalled. Special emphasis is placed after that on the more severe case of localized defects satisfying axial symmetry by displaying an analytical solution to the Von Kármán–Donnell shell equations under specific boundary conditions. The obtained results show that the critical load varies very much with the geometrical parameters of the localized defect. These variations are not monotonic in general. They indicate, however, a clear reduction of the shell critical load for some defects recognized as the most hazardous isolated ones. Reduction of the critical load is found to reach a level which is up to two times lower than that predicted by general distributed defects.     

Plastic buckling of axially compressed circular cylindrical shells

For elastic-plastic cylindrical shells with initial axisymmetric imperfections bifurcation into a non-axisymmetric shape is analysed. The shell material is represented by a phenomenological plasticity theory that accounts for the formation of a vertex on subsequent yield surfaces. The influence of various geometric and material parameters is investigated for a wide range of radius-to-thickness ratios. It is shown that for the thicker shells bifurcation generally occurs beyond the maximum axial compressive load. A few analyses for shells with additional non-axisymmetric imperfections show the unstable post-bifurcation behaviour and the sensitivity to imperfections of more general shapes.     

常州市体育馆椭圆抛物面弦支穹顶稳定性研究

常州市体育馆椭圆抛物面钢屋盖采用由Levy索杆系和单层网壳构成的弦支穹顶结构,与已研究的常规弦支穹顶相比,其具有体量大,矢跨比高和外形为椭圆抛物面的特点。将弦支穹顶与单层网壳进行稳定性对比研究,包括构件屈曲、线性屈曲和几何非线性屈曲等,分析了高矢跨比弦支穹顶中索杆系的作用以及对结构设计起控制作用的破坏形式。研究结果表明,索杆系增加了弦支穹顶的整体性,降低了其对初始几何缺陷的敏感性,但对结构刚度、基本自振周期和模态、构件屈曲荷载、线性屈曲荷载、无初始缺陷的非线性屈曲荷载、屈曲模态等影响不大。高矢跨比弦支穹顶仍对初始缺陷较为敏感,稳定性仍是结构设计控制因素之一。此外,由于椭圆抛物面外形,活荷载布置形式对结构屈曲模态影响较大,且满跨活荷载并不一定是最不利的活荷载布置形式。     

Understanding imperfection-sensitivity in the buckling of thin-walled shells

The buckling of thin-walled shell structures under load is still imperfectly understood, in spite of much research over the past 50 years. In this paper the author traces the history of the ideas which have been deployed in order to shed light on what is often referred to as ‘imperfection-sensitive’ buckling behaviour of shells. The ideas, which recur in various combinations, involve interaction of competing buckling modes, nonlinear behaviour, the growth of initial geometric imperfections under load and the alteration of the distribution of membrane stress as imperfections grow. The author claims that there are strong grounds for supposing that ‘locked in’ initial stresses on account of imperfect initial geometry and the static indeterminacy of boundary conditions of real shells have a pronounced effect on the buckling performance. This effect has been ignored in the past, and is the subject of a current experimental study.     

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.