Lateral–torsional buckling of cold-formed channel sections subject to combined compression and bending

This paper presents an analytical study of the flexural buckling and lateral–torsional buckling of cold-formed steel channel section beams subject to combined compression and bending about their major and minor axes. For channel section beams a bending about the minor axis creates a non-symmetric pre-buckling stress distribution, which has a significant influence on the lateral–torsional buckling of the beams. This kind of feature has not been discussed in the existing literature. The focus of this present study is the interaction between the compression load and the bending moments about the major and minor axes. It has been found that for a section subject to combined compression and the major-axis bending the bending moment will decrease the critical compression load, although the critical value of the largest compressive stress in the section actually increases with the applied bending moment. However, for a section subject to combined compression and the minor-axis bending the effect of the bending moment on the critical compression load depends on the direction of bending applied. For bending that creates a compressive stress in the lips the bending moment will reduce the critical compression load. However, for bending that creates a compressive stress in the web the bending moment has almost no influence on the critical compression load.     

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.     

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。     

Numerische Beulsicherheitsnachweise bei Schalenbeulfällen mit überkritischen Tragreserven

Numerical buckling strength verification of shell buckling cases with postcritical load carrying reserves. At many buckling endangered shell structures, the experimental data are not sufficient to assess the load carrying capacity. Therefore, the Eurocode EN 1993‐1‐6 provides the alternative of a numerical buckling strength verification. In this code, the first instability load is assumed to be decisive for the assessment of the load bearing capacity. The problem of local instabilities and postcritical load bearing reserves is only mentioned by the way but not sufficiently regulated for practice. The problems resulting from this restriction of the definition of failure are discussed in the contribution. Proposals for overcoming the deficiencies are submitted.     

Numerical study on lateral buckling of fully bonded sandwich pipes

Sandwich pipes (SP) are promising subsea pipelines for deep-water applications. Thus, their lateral buckling response is a significant design aspect. The temperature field of SP denotes the load in lateral buckling analysis, and it is calculated using the heat transfer differential equation in this study. A general temperature field formula is proposed for an arbitrary multilayer SP, and this formula is verified by finite element models. Another finite element model based on the fiber shell element is then constructed to investigate the lateral buckling response of SP. They are validated by existing experimental and numerical results. The evolution of the lateral buckling profiles and of stress distribution are studied in consideration of nonlinear pipe-soil interaction and nonlinear material constitutive law. Moreover, the influence of initial imperfections and pipe-soil interaction on lateral buckling response is examined. Finally, a formula is approximated for a SP with a half-wave sinusoidal imperfection profile on the basis of dimensionless analysis and numerical results. This formula is convenient for engineering applications.     

实腹圆弧钢拱的平面内稳定极限承载力设计理论及方法

拱的平面内稳定极限承载力设计一直没有成熟的规范指导。本文用有限壳单元模型先分析了工形截面两铰圆弧钢拱的平面内弹性屈曲性能,与拱的经典屈曲理论作了对比,指出了必须同时考虑长细比和矢跨比对屈曲荷载的影响。然后分析了两铰圆弧钢拱受静水压力和其它荷载作用下的弹塑性屈曲性能,指出了典型破坏机理为拱两侧1/4跨附近形成塑性铰导致结构失效。利用拱的弹性屈曲荷载定义了拱的正则化长细比,用Perry-Robertson公式的形式,建立了拱的稳定系数与正则化长细比的关系,提出了受静水压力的两铰圆弧钢拱的平面内稳定极限承载力设计方法,并用轴力和弯矩的两项相关公式提出了受其它荷载作用下的平面内稳定极限承载力设计方法。     

Buckling of compound hyperbolic paraboloidal shells

This paper presents the first elastic buckling analysis of a compound hyperbolic paraboloidal (hypar) shell under a uniformly distributed load. The compound shell is composed of four hypar panels of rectangular ground plan. A special feature of this analysis is the use of the pulse function to deal with the curvature discontinuities at the ridges. The stability-governing equations are derived from the general equations of Reissner for the linear elastic buckling of hypobolic paraboloidal shells, taking into account the curvature discontinuities at the ridges. These equations are then solved in an approximate manner by assuming trigonometric variations of the buckling deformations. Numerical results are presented, which show that the buckling modes of the shell are either symmetrical or antisymmetrical about both axes of symmetry. For antisymmetric buckling, the critical load of the compound shell is the same as that for a single hypar panel.     

四块组合型双曲抛物面扁扭壳的稳定分析

本文用脉冲函数处理四边简支四块组合型双曲抛物面扁扭壳脊线处的曲率不连续性,根据线性稳定理论导出了与单块四边简支双曲抛物面扁扭壳具有相同形式的临界荷载计算公式,并给出了有关参数的图表。研究表明,这种壳体可能有两种失稳模态,即关于两个对称轴对称或反对称失稳。反对称失稳时,其临界荷载与单壳相同。     

Robust design of composite cylindrical shells under axial compression — Simulation and validation

Thin-walled shell structures like circular cylindrical shells are prone to buckling. Imperfections, which are defined as deviations from perfect shape and perfect loading distributions, can reduce the buckling load drastically compared to that of the perfect shell. Design criteria monographs like NASA-SP 8007 recommend that the buckling load of the perfect shell shall be reduced by using a knock-down factor. The existing knock-down factors are very conservative and do not account for the structural behaviour of composite shells. To determine an improved knock-down factor, several authors consider realistic shapes of shells in numerical simulations using probabilistic methods. Each manufacturing process causes a specific imperfection pattern; hence for this probabilistic approach a large number of test data is needed, which is often not available. Motivated by this lack of data, a new deterministic approach is presented for determining the lower bound of the buckling load of thin-walled cylindrical composite shells, which is derived from phenomenological test data. For the present test series, a single pre-buckle is induced by a radial perturbation load, before the axial displacement controlled loading starts. The deformations are measured using the prototype of a high-speed optical measurement system with a frequency up to 3680 Hz. The observed structural behaviour leads to a new reasonable lower bound of the buckling load. Based on test results, the numerical model is validated and the shell design is optimized by virtual testing. The results of test and numerical analysis indicate that this new approach has the potential to provide an improved and less conservative shell design in order to reduce weight and cost of thin-walled shell structures made from composite material.     

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.     

Dynamic torsional buckling of cylindrical shells in Hamiltonian system

By considering the effect of stress waves in a Hamiltonian system, this paper treats dynamic buckling of an elastic cylindrical shell which is subjected to an impact torsional load. A symplectic analytical approach is employed to convert the fundamental equations to the Hamiltonian canonical equations in dual variables. In a symplectic space, the critical torsion and buckling mode are reduced to solving the symplectic eigenvalue and eigensolution, respectively. The primary influence factors, such as the impact time, boundary conditions and thickness, are discussed in detail through some numerical examples. It is found that boundary conditions have limited influence except free boundary condition in the context of the scope in this paper. The localization of dynamic buckling patterns can be observed at the free end of the shell. The new analytical and numerical results serve as guidelines for safer designs of shell structures.     

利用Hamilton函数分析圆柱壳动态扭转屈曲

在Hamilton函数中考虑应力波的影响,研究冲击扭转载荷作用下弹性圆柱壳的动态屈曲。采用辛方法将基本方程转化为对偶变量的Hamilton典型方程。在辛空间将临界扭转和屈曲模式分别简化为求解辛本征值和本征解问题。主要影响因素有冲击时间、边界条件和厚度等,通过数值算例对这些因素进行了详细讨论。研究结果表明,边界条件的影响有限(自由边界条件除外)。在壳体自由端能够观察到局部动态屈曲模式。新的分析和数值模拟结果可作为壳结构的安全设计准则。     

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.     

双曲冷却塔下部子午线形对结构性能的影响

在不影响冷却塔冷却性能的前提下,对双曲冷却塔塔筒下部半径和下支柱斜率进行微调,并分析了其对结构动力特性、承载性能及稳定性的影响。研究表明,塔筒下部子午线形对结构的线性特征值屈曲分析结果影响甚微,下支柱斜率等于或略小于塔筒下缘斜率可以有效提高结构基频,提高其抗风性能。塔筒下部区域斜率的突然下降或持续快速下降均会使附近环向膜应力及环向位移发生突变,也因此可能使局部稳定无法满足要求。所以,在设计中应保证塔筒下部区域的子午向斜率与上部斜率一致缓慢下降,使应力分布连续平缓,同时又可在不增加壁厚的情况下满足局部稳定要求。     

Re-interpreting simultaneous buckling modes of axially compressed isotropic conical shells

Elastic stability of shell structures under certain loading conditions is characterized by a dramatically unstable postbuckling behavior. The presence of simultaneous ‘competing’ buckling modes (corresponding to the same critical buckling load) is understood to be largely responsible for such behavior. In this paper, within the framework of linear bifurcation eigenvalue analysis and Donnell shallow shell theory, the presence of simultaneous buckling modes in axially compressed isotropic cones is determined using the semi-analytical method of Galerkin. The results are presented in the plane of the dimensionless reciprocal meridional and circumferential buckling half wavelengths, and are compared with the locus of simultaneous buckling modes of axially compressed cylinders, described by the so-called Koiter circle. By using an optimizing procedure, it is shown that the cluster of simultaneous buckling modes in cones is well described by the Koiter circle of an equivalent cylinder with appropriate length and radius. Such optimizing values of length and radius allow us to gain some insight into the simplifying treatment of the buckling of cones through the concept of equivalent cylinder.     

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.     

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.     

Vibration, buckling and dynamic stability of cracked cylindrical shells

The presence of cracks in a structure can considerably affect its behaviour. This paper presents a finite element study on the vibration, buckling and dynamic stability behaviour of a cracked cylindrical shell with fixed supports and subject to an in plane compressive/tensile periodic edge load. The effects of crack length and orientation are analysed. Under tension load, the results show that the frequency of the shell initially increases with the load, but then decreases as the load further increases leading to buckling due to tension load. The size and the orientation of the crack and the loading parameter can all have a significant effect on the dynamic stability behaviour of the shell under both compressive and tensile loading. The effects of these parameters are discussed in detail.     

矩形开口对吸收塔结构非线性屈曲特性影响分析

为了分析矩形开口参数对于吸收塔结构稳定性的影响规律,以一实际在建吸收塔结构为研究背景,基于参数化模型的正交试验,采用有限元软件ANSYS对比分析了不同开口参数下吸收塔柱壳结构的非线性屈曲特性。结果表明:开口角度对于结构的影响较其他参数大,开口角度小于90°时,结构的非线性屈曲极限荷载下降趋势较为明显,超过120°后,降幅趋于缓和,壁厚25 mm工况下,90°开口时结构的非线性屈曲极限荷载较0°开口时下降91%,120°开口时较0°开口时下降95.2%;结构的非线性屈曲极限荷载随着矩形开口高度的增加而逐渐减小,但开口位置对于结构稳定性的影响在整个过程中近似呈线性变化。