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.     

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.     

大矢跨比单层球面网壳动力试验模型弹塑性稳定分析

为了解水平地震作用下具有不同失效机制的单层球面网壳结构在静力荷载作用下的弹塑性稳定性能,利用有限元软件ANSYS,对两个矢跨比为1/2的单层球面网壳结构试验模型进行双重非线性全过程分析,获得结构的弹塑性极限承载力,比较二者的失稳模态,初步了解二者之间的差异。考察结构杆件屈曲、初始缺陷等因素对结构稳定性能的影响,并分析各因素对结构极限承载力的影响规律。结果表明,地震作用下,具有强度破坏特征的网壳结构在静力下的失稳模式表现为结构的整体失稳,而发生动力失稳破坏的结构则表现为局部失稳破坏。杆件失稳和初始缺陷使结构的临界荷载大幅度降低,且地震作用下属于强度破坏的单层球面网壳结构在静力下对初始缺陷的敏感性大于动力失稳破坏结构。     

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.     

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.     

Stability of circular cylindrical steel shells under combined loading

Circular cylindrical shells made of steel are used in a large variety of civil engineering structures, e.g. in off-shore platforms, chimneys, silos, tanks, pipelines, bridge arches or wind turbine towers. They are often subjected to combined loading inducing membrane compressive and/or shear stress states which endanger the local structural stability (shell buckling). A comprehensive experimental and numerical investigation of cylindrical shells under combined loading has been performed which yielded a deeper insight into the real buckling behaviour under combined loading . Beyond that, it provided rules how to simulate numerically the realistic buckling behaviour by means of substitute geometric imperfections. A comparison with existing design codes for interactive shell buckling reveals significant shortcomings. A proposal for improved design rules is put forward.     

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.     

Finite Element simulation of dynamic buckling of cylinders subjected to periodic shear

This paper deals with the buckling of cylindrical shells under a dynamic shear load. The aim of our study is to compare static buckling load and buckling load during a sweep frequency excitation. First, we describe the special experimental device and the two Finite Element codes used in this study. In a second part static tests and corresponding Finite Element calculations are presented in order to have a reference buckling load and to understand the effect of initial imperfections. Then, a vibration analysis is performed in order to investigate the effect of geometric imperfection and a preload. In the last part, we discuss dynamic results. When we reach the first eigen frequency, the buckling load drops and the buckling deformations increase due to a parametric resonance. There is a coupling between vibration and buckling modes.     

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.     

Buckling and strength characteristics of some CFRP stiffened curved panels

This paper describes the initial and post-buckling behaviour of CFRP stringer-stiffened curved panels. The panels are of 500-mm radius, 2-mm thickness and have either three or four blade stringers. Initial buckling loads were calculated using the finite strip code VIPASA within the design optimisation program PASCO. An unstiffened, externally supported panel is also considered.Stringer stiffening gave higher buckling loads than external supports. The initial buckling behaviour was influenced by geometric imperfections, and methods of modelling these with PASCO are discussed. The imperfections caused scatter in buckling load, but there was minimal scatter in failure load, despite the presence of impact damage in some cases. The failure loads were about 50% higher than the buckling loads.     

Buckling strength verification of cantilevered cylindrical shells subjected to transverse load using Eurocode 3

At present, there are only a few studies concerning the application of different types of buckling strength verification according to Eurocode 3 at combined loading. Besides the stress design as classical hand calculation method of checking cylindrical steel shells against buckling failure, the new Eurocode 3 also offers two global numerical analyses at different modelling levels. The linear buckling analysis (LBA) combined with a materially nonlinear but geometrically linear analysis (MNA) is the simpler concept from the perspective of the modelling and calculation effort. The more sophisticated method is a geometrically and materially nonlinear analysis of the imperfect structure (GMNIA). This paper presents the application of both numerical concepts to the cantilevered shell subject to a transverse load at the free edge. The results are compared to those from stress design. There are specific features at both types of numerical analysis: As the determination of the plastic reference resistance and the buckling parameters is the main focus at MNA/LBA, the choice of proper equivalent geometric imperfections demands special diligence at GMNIA. The presented analyses show that the GMNIA concept in connection with consistent equivalent geometric imperfections may lead to a safe and economic design of cylinders subject to combined loading. At the particular load case the MNA/LBA concept currently suffers from the lack of proper regulations concerning the determination of the overall buckling reduction factor.     

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.     

初始缺陷对网壳结构动力稳定性能的影响

本文袭用静力稳定分析中的“一致缺陷模态法”,并将李雅普诺夫运动稳定理论引入结构分析,通过两个典型算例,检查了单层网壳结构在简谐荷载、阶跃荷载及三角形脉冲荷载作用下,初始缺陷对其动力稳定性能的影响.     

Dynamic buckling of thin-walled viscoplastic columns

The purpose of this paper is the analysis of strain-rate effect in dynamic stability of thin-walled orthotropic column of closed rectangular cross-section, subjected to in-plane pulse loading of finite duration. For the solution the first-order shear deformation theory displacement field is employed with the Green–Lagrange strain tensor application. The effect of strain rate sensitivity is included in the framework of the viscoplasticity constitutive Perzyna model for material behaviour under high strain rate loading. The numerical results are obtained with the finite element method application. In the performed analysis the strain-rate effect influence on the dynamic buckling load is examined as well as the initial imperfections of walls, pulse shape and the orthotropy ratio are considered. The results of dynamic criteria application are compared furthermore.     

Stochastic imperfection modelling in shell buckling studies

One possible avenue that may improve design against buckling is to recognise and account for the random nature of initial geometric imperfections introduced by manufacturing. This paper presents the application of a probabilistic methodology to the design and analysis of cylindrical shells under axial compression. Results from two cases are presented and compared: the first involves stringer-stiffened steel cylinders failing elastoplastically, whereas the second examines unstiffened composite cylinders buckling elastically. In both cases, the method is underpinned by statistical analysis of imperfections measured on nominally identical specimens. Nonlinear FE analysis is used for strength assessment and the results of the statistical analysis are introduced in the imperfection modelling. It is demonstrated that the method has advantages over code design based on ‘lower bound’ curves, in terms of the calculated buckling loads but also in offering a systematic and rational way by which randomness in imperfections can be assessed.     

On polymorphic uncertainty modeling in shell buckling

Buckling is typically the governing failure mode of thin-walled shells. In particular, geometric and material imperfections have a major influence on the buckling behavior. Small variations of imperfections have large effects on the load-bearing behavior. However, the design of shells is still characterized by a deterministic way of thinking, in which uncertainties have not yet been sufficiently considered. Even in probabilistic approaches, false assumptions are often generated due to the small amount of experimental data. The focus of this paper is an appropriate uncertainty quantification based on the available data. Therefore, the concept of polymorphic uncertainty modeling is presented on axially loaded shells with different types of imperfections. Finally, an idea for a novel design concept for shells based on a fuzzy-valued safety level is introduced. The paper is intended to initiate a rethinking of the methodology for the numerical design of shells with an appropriate uncertainty quantification.     

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.     

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.     

Shear resistance of longitudinally stiffened panels—Part 1: Tests and numerical analysis of imperfections

This paper deals with the results of four full-scale tests, numerical simulation of tests and initial geometric imperfection analysis for longitudinally stiffened panels in shear. The tests examine the influence of varying position and bending stiffness of one trapezoidal longitudinal stiffener on the panel shear resistance and its buckling behaviour. The stiffeners were designed such as to obtain both global and local buckling shapes. Numerical simulations (FEA), based on the test girder geometry, the measured initial geometric imperfections and elastic-plastic material characteristic from the tensile tests, demonstrate a very good agreement with the tests. The initial geometric imperfection study on different verified numerical models shows a limited sensitivity of the panel shear capacity to any kind of imperfection shape variation with amplitude at the allowable fabrication tolerances. Finally, the paper offers some ideas for modelling geometric imperfections with regard to the design or research demands.     

非对称荷载对大跨度非规则单层网壳结构性能的影响

以某大跨度非规则单层网壳为研究背景,应用ANSYS通用有限元分析软件对网壳结构进行了建模并重点模拟了风荷载、雪荷载、温度效应等多种非对称荷载作用,进行了静力分析、特征值屈曲分析以及非线性稳定分析。得到了网壳结构在15种典型荷载组合下的内力、位移结果,分析了非对称荷载对网壳结构静力性能的影响;考虑了几何非线性、材料非线性、初始缺陷,得到了网壳结构在非对称荷载作用下的稳定系数,分析了非对称荷载对网壳结构稳定性能的影响。强调指出非对称荷载作用在大跨度单层网壳结构设计中的重要性,为大跨度非规则单层网壳设计提供参考。