Design charts for the general instability of ring-stiffened conical shells under external hydrostatic pressure

The paper describes experimental tests carried out on three ring-stiffened circular conical shells that suffered plastic general instability under uniform external hydrostatic pressure. In this mode of failure, the entire ring–shell combination buckles bodily in its flank. The cones were carefully machined from EN1A mild steel to a very high degree of precision.Using the results obtained from these three vessels, together with the results obtained from elsewhere, the paper also provides two-design charts, which are much easier to use than older design charts. The design charts allow the possibility of obtaining a plastic knockdown factor, so that the theoretical elastic buckling pressures for perfect vessels, can be divided by the plastic knockdown factor, to give the predicted buckling pressures. Although similar design charts have been produced in the past, the design charts presented here are based on using the simpler ring-stiffened circular cylinder, which has been made equivalent to the much more complex ring-stiffened circular conical shell. The advantage of using this method is that it is simpler and the design time is reduced by a factor of about 10 with little loss of precision. This method can also be used for the design of full-scale vessels.     

Buckling behaviour of ring-stiffned cylinders; experimental study

The effect of the number and size of rings on the buckling strength of ring-stiffened cylinders is studied experimentally. The results of ten machined ring-stiffened cylinders subjected to lateral pressure are presented. Five of the cylinders failed by the general instability mode and the rest failed by the shell instability mode. A sample of the experimental results which shows longitudinal and circumferential strains as well as the development of the circularity contours till collapse is presented. Buckling pressures obtained from the experiments are shown to be within ±30% of the corresponding value obtained from the theoretical analysis available in the literature.     

Vibration of circular cylinders containing water

A theoretical and an experimental investigation were carried out on three circular cylinders in air and also with the cylinders containing water. The investigations consisted of experimentally determining the circumferential eigenmodes and accompanying frequencies of these vessels, and then comparing the experimental results with the theoretical predictions.The theoretical analysis was based on the finite element method. Comparison between theory and experiment was found to be good for the higher eigenmodes, but less satisfactory for the lower eigenmodes.     

Buckling and vibration of ring-stiffened cones under uniform external pressure

Theoretical and experimental results are presented for the buckling and vibration of three ring-stiffened thin-walled cones constructed from mild steel. For vibration, the study consisted of exciting the cones in air and while partially and fully submerged in water. For the buckling study, the cones were subjected to a gradually applied uniform external pressure until instability occurred.     

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.     

薄壁圆管相贯加强环节点承载力性能研究

根据常用的薄壁钢管的相贯节点的特性，提出了在较大直径的钢管内部设置加强环的节点构造形式，建立了相应的有限元分析模型，运用ANSYS非线性有限元分析法，分别计算了在主支管相交区内不同方式设置不同数量和大小的加强环节点的各项指标，分析了加强环节点的受力特征与破坏模式，探讨了不同类型的加强环节点的承载力和变形性能，计算结果表明，在不同荷载组合下对节点进行局部加强环的构造形式对于提高节点承载力和减小局部变形是非常有效的措施。最后提出了相关的设计建议取值，避免了部分单纯由构造确定加强环节点的盲目性，具有重要的理论意义和工程意义。     

Experimental and numerical modelling of the three-dimensional incompressible flow behaviour in the near wake of circular cylinders

An experimental investigation was carried out to study the structure of the flow field around three-dimensional circular cylinders. The study of the flow field around an obstacle was performed in a wind tunnel using a particle image velocimetry (PIV) system. The flow of a fluid around an obstacle with a different velocity to the oncoming flow was examined. The results showed the dependence of the flow structure around the obstacle on its Reynolds number, and the spacing between a pair of obstacles. Detailed quantitative information of turbulence parameters in the vicinity of the obstacle was attained. Extensive wind tunnel experimental results are presented and compared with numerical simulation. A three-dimensional numerical model with Reynolds stress model (RSM) turbulence and a non-uniform grid system were used to examine the effects of a single cylinder and two cylinders in tandem on the flow. The principal objective was to analyse three-dimensional flow past a single cylinder and two circular cylinders placed in tandem by combining the application of a PIV experimental technique and an RSM turbulence model.For the case of two cylinders in tandem, the flow patterns are characterized in the gap region as a function of the distance between the cylinders. A good level of agreement was found between the experimental results of flow and numerical simulation.     

On interference between two circular cylinders in staggered arrangement at high subcritical Reynolds numbers

The results of a wind-tunnel investigation on the interference between two identical parallel circular cylinders arranged in staggered configurations, carried out in a uniform smooth flow at high subcritical Reynolds number, are presented. On the basis of the pressure measurements and the flow visualization, three main flow patterns are classified and discussed. Close attention is paid to the switching phenomenon of two different pressure patterns at critical angles. This switching creates discontinuity of large lift forces on cylinders. With measurements of velocity profiles and power spectral analysis in the gap between the two cylinders, the mechanism of the appearance of this extreme aerodynamic force is discussed.     

Näherungsweise Stabilitätsuntersuchung orthotroper Kreiszylinderschalen unter Manteldruck

Stability analysis of orthotropic circular cylinders under uniform external pressure by approximation. The design of orthotropic circular cylinders under uniform external pressure against buckling is neither in the national nor in the international standards and technical regulations sufficiently dealt with. To avoid large‐scale dimensional numerical analyses, a procedure for establishing the ideal external pressure p_ki, based on the investigation of the stability‐characteristics of orthotropic plates exposed to compression and/or shear along the edges, is developed by using some approximations. This solution allows the verification of the load‐bearing‐capacity of the structure under consideration by referring to the published standards and regulations for circular cylinders made out of isotropic material. It can be shown, that, depending on the geometry of the shell, the curvature and the degree of orthotropic stiffness distribution, these constructions can be described approximately either by an ideal shell comprising of adjusted isotropic material or by a circular ring with radial and tangential bedding. The strategy proposed in the following covers also the questions related to the adaption of the design concept based on buckling‐curves and in partial‐safety‐factors depending on the degree of imperfection‐sensibility to a large‐scale, three dimensional model using numeric solution procedures.     

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。     

恒高温后圆钢管混凝土轴压短柱弹塑性分析

在已有恒高温后混凝土单轴受压和钢材单轴拉伸力学性能研究的基础上,建立了恒高温后混凝土轴对称三轴受压应力-应变关系和复杂受力下的钢材多轴应力-应变关系。应用连续介质力学,建立了恒高温后钢管混凝土同时受压的同心圆柱体计算模型,采用弹塑性全过程分析理论,建立了恒高温后钢管混凝土轴压组合弹性模量理论计算公式和组合应力-应变关系全曲线的理论表达式,并编制相应的计算程序对恒高温后钢管混凝土轴压短柱受力性能进行弹塑性全过程分析,计算结果与试验结果吻合较好。     

Residual strength of damaged steel ships and offshore structures

A review is made of various forms of structural damage which may occur in ships and offshore steel structures, with particular reference to the influence of such damage on stiffness and ductile strength. Consideration is given to damage in a ship's bottom or side shell as may be caused by collisions, grounding, hydrodynamic impact or explosions and to the influence of such damage on hull-girder bending strength. Reference is made to the effects of bending and denting of tubular members in offshore platforms and of collision damage in externally pressurised ring-stiffened cylinders as may be employed in submersibles and large-diameter tubulars. Some methods are suggested for evaluation of residual stiffness and strength with emphasis on approximate analysis techniques which can be applied quickly and economically to obtain an early assessment of damage effects.     

Free vibrations of clamped-free circular cylinders

The problem of free vibrations of clamped-free circular cylinders has been analysed in detail using the first-order thin shell theory of Budiansky and Sanders. Two simple linear relationships for the frequency parameter are given by incorporating an interrelationship among displacement components in two different ways. For the variations in wave numbers, radius-to-thickness ratio and length-to-radius ratio the comparison with the exact frequencies and the frequencies due to various approximate formulae has been extensively studied. Strain and kinetic energy considerations are put forward to explain the apparent difference between linear and the cubic frequency approximations. In the case of two typical cylinders the theoretical results are shown to be in reasonable agreement with the observed frequencies and also with the results calculated by using Flügge shell theory equations.     

Flow-induced vibration of two circular cylinders in tandem arrangement. Part 2: Suppression of vibrations

This paper presents an experimental investigation on suppression of cross-flow vibrations of two circular cylinders in tandem arrangement, conducted at the fluid mechanics laboratory of Kitami Institute of Technology, Japan. To suppress the vibrations of the cylinders, tripping wires were deployed, attached symmetrically about the leading stagnation lines of the cylinders. Five spacing ratios were examined, i.e., L/D=0.1, 0.3, 0.8, 2.0 and 3.2 (L is the gap spacing between the two cylinders; D is the diameter of cylinder), which are representative for five Regimes I (0.1≤L/D<0.2), II (0.2≤L/D<0.6), III (0.6≤L/D<2), IV (2≤L/D<2.7) and V (L/D≥2.7), respectively, as classified in Part 1 [Kim et al., 2009. Flow-induced vibrations of two circular cylinders in tandem arrangement (part 1: characteristics of vibration). Journal of Wind Engineering and Industrial Aerodynamics, submitted together for publication]. Tripping wire position θ measured from the leading stagnation lines of the cylinders was changed from 20° to 60° to determine the optimum range of θ for suppressing structural vibrations. The shear layers separated from the two cylinders were investigated based on flow visualization. The main findings are: (i) the flow-induced vibration on the two cylinders depends strongly on θ, (ii) at θ=20–30° the vibrations on both cylinders are almost completely suppressed for all regimes except V, and (iii) for θ≥40° the vibration amplitudes of both cylinders are considerably larger than those of the plain cylinders, particularly at θ=40°, where the vibration of the upstream cylinder becomes divergent.     

Impact energy dissipation characteristics of thin-walled cylinders

Thin-walled, closed-end cylindrical specimens of both aluminium and steel alloys were tested under axial and diametrical compression loading in static as well as in impact conditions. The load-deflection behaviour of the specimens were recorded and the modes of collapse were observed. The two loading conditions were found to give the same pattern of buckling deformation, although the energy absorbed under impact loading was higher.The main purpose of results for circular cylinders under axial compression is to give a basis of comparison for the cylinders under diametrical compression and also for cylinders filled with liquid (soft drink) or sand under either longitudinal or lateral compression. In all these cases absorption was achieved.     

环向加劲钢筒仓在均匀内压作用下仓壁等效厚度研究

加劲肋通常作为增强筒仓仓壁强度和稳定性的措施,但目前对于如何确定筒仓加劲肋间距及尺寸的设计方法尚不明确。合理设置加劲肋,能起到提高筒仓强度承载力的作用,相当于增加了仓壁厚度。本文用数值方法研究了设置环向加劲肋的钢筒仓在均匀内压作用下的应力分布规律,提出环向加劲肋有效间距的概念,通过参数分析研究了加劲肋尺寸和筒仓几何特征对环向加劲肋有效间距的影响,提出有效间距的实用计算公式。在有效间距公式的基础上,推导出了更准确的均匀内压作用下环向加劲钢筒仓的仓壁等效厚度公式,对《粮食钢板筒仓设计规范》(GB50322-2011)中仓壁折算厚度的计算方法提出修正意见。     

Vibration of a thin-walled carbon fibre corrugated circular cylinder under external water pressure

The paper reports on a theoretical and an experimental investigation carried out on a thin-walled corrugated carbon fibre circular cylinder in air and also under external water pressure. This corrugated circular cylinder was invented by Ross in 1987.The theoretical investigation was carried out using the finite element analysis to model both the structure and the fluid. The theoretical investigation used two different programs, one of which was the giant computer program ANSYS and the other was an in-house program developed by Ross and Little. For the shell structure, the ANSYS program used two different doubly curved thin-walled shell elements, while the in-house program used a simpler axisymmetric thin-walled shell element. This axisymmetric element allowed a sinusoidal variation of the displacements in the circumferential direction, thus, decreasing preparation and computational time. Agreement between the different finite elements was found to be quite good. The investigation also found that there was good correlation between experiment and theory for the in-house software, but was a little disappointing when using ANSYS. Errors may, however, have occurred with the experimental results, as the model was hand-made and neither its geometry nor its material properties were perfect. It was found particularly encouraging for the in-house software to give better results than ANSYS, as the in-house software only took a few hours to set up the computer model, and a few seconds to analyse the vessel, whereas the ANSYS software took several weeks to set up the computer model, and several minutes to analyse the shell. The ANSYS software, however, did have the advantage in producing excellent graphical displays in both the pre-processing and post-processing modes.     

Stress concentration factors induced by out-of-plane bending loads in ring-stiffened tubular KT-joints of jacket structures

In the present paper, data extracted from the finite element analysis of 118 models, which were validated against the test results obtained from an experimental study, were used to investigate the geometrical effect on the weld-toe stress concentration factors (SCFs) in internally ring-stiffened tubular KT-joints subjected to four different types of out-of-plane bending (OPB) loads. Although the tubular KT-joints are commonly found in offshore jacket structures and despite the crucial role of SCFs in the evaluation of the tubular joint׳s fatigue performance, the SCFs in internally ring-stiffened KT-joints subjected to OPB loads have not been investigated so far and no design equation is available to determine the SCFs for OPB-loaded joints of this type. In the present research, geometrically parametric study was followed by the nonlinear regression analysis to develop a new set of SCF parametric formulas for the fatigue design of ring-stiffened KT-joints under the OPB loadings.     

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.     

Measurement of extreme aerodynamic interference forces acting on circular cylinders in turbulent boundary layers

Extreme interference wind loads on circular cylinders are investigated in wind tunnel simulations of atmospheric boundary layers with high turbulence levels. Since for circular cylinders interference effects caused by vortex shedding are pronounced, the present work tries to clarify to which extent turbulence effects are reducing the interference in this case. Aerodynamic forces and moments were measured with a piezoelectric six-component wind tunnel balance. The balance is distinguished by a large dynamic range, low interferences and a high natural frequency. The numerous results include comparisons of mean values, r.m.s. values and extreme values of force coefficients with and without interference with reference to the velocity profiles and the turbulence levels in two different boundary layer simulations. Conclusions are drawn with regard to the application of the results in estimating wind loads on cylindrical structures.