Application of linear buckling sensitivity analysis to economic design of cylindrical steel silos composed of corrugated sheets and columns

The paper deals with global stability of steel cylindrical silos composed of corrugated walls and vertical columns with loads imposed by a bulk solid following Eurocode 1. The optimum silo design with respect to the steel weight was based on a sensitivity analysis method. The changes of silo column profiles at each design step were performed by means of influence lines for the buckling load factor due to the unit column bending stiffness variation. The corrugated walls were simulated as an equivalent orthotropic shell and vertical thin-walled columns as beam elements. The results were compared with the Eurocode 3 approach and verified by FE results of linear buckling and non-linear analyses with geometric non-linearity carried out with the commercial finite element code ABAQUS for a 3D shell model of a perfect silo. The proposed procedure allowed for a rational silo design with an economic material use. Some recommendations for the silo optimum design were elaborated.     

Stability of cylindrical steel silos composed of corrugated sheets and columns based on FE analyses versus Eurocode 3 approach

Comprehensive static and dynamic 3D stability finite element analyses of a cylindrical steel silo composed of corrugated sheets and open thin-walled vertical stiffener profiles were carried out by taking the geometric and material non-linearity into account. The silo was subjected to axisymmetric and non-axisymmetric loads imposed by a bulk solid following Eurocode 1. Theoretical and measured initial geometric imperfections were considered in calculations. The results of non-linear analyses were compared to those according to Eurocode 3. Modifications of the Eurocode formulae were proposed. Some recommendations for the silo engineering design were elaborated.     

Failure analysis of steel silos subject to wind load

Steel constructed are made of thin-walled cylindrical shells. They are widely used in various food and agriculture industries for storing granular solids, liquids, and bulk food. The present research study was completed to determine the structural behavior of thin-walled silo when subjected to wind load. The study included determination of deformational behavior of a large field silo and development of a finite element model. This experimental part of the study comprises a challenging full-scale test on 14.55 m diameter and 23.27 m high steel silo located in the open farm land near Bothwell in the province of Ontario, Canada. The finite element model was then developed for undertaking wind analysis to study the effect of different parameters such as different geometric dimensions, stiffener patterns, and wind girders on the wind-induced buckling strength of steel silos made of corrugated steel. Both linear and geometrically nonlinear buckling analyses were carried out to determine the critical wind speed for corrugated steel silos. The study found that the wind girders, also known as wind rings, significantly increase the buckling strength of the silo. This study found that the critical buckling wind speeds of the field silo specimen have increased by about 44%. Further, the optimum location for the addition of wind rings was found to be near the roof of the silo.     

仓壁柱承钢筒仓结构行为的研究

仓筒壁直接支承于支柱是小型钢筒仓一种简单、经济的支承方式。采用数值分析方法,包括线性应力分析、线性特征值屈曲分析及几何非线性分析,对这类仓壁柱承钢筒仓的结构行为、特别对其稳定性能进行了系统研究。分析了仓筒径厚比、支柱伸入仓筒的高度、支柱宽度等几何参数对结构性能的影响。研究表明,支柱伸入高度是影响仓壁柱承筒仓屈曲强度的主要因素,屈曲模态也与之密切相关。为提高仓壁柱承筒仓的承载能力,支柱应尽可能地延伸至仓筒的顶部,这种支柱伸至仓顶檐梁的构造可用于大中型筒仓结构。     

初始几何缺陷对仓壁柱承钢筒仓稳定性能的影响

仓筒壁直接支承于支柱是小型钢筒仓的一种简单、经济的支承方式。薄壳结构通常对初始几何缺陷十分敏感。引入周向轴对称焊缝凹陷和特征值屈曲模态两种缺陷形式,通过几何非线性分析,研究初始缺陷对轴压下仓壁柱承筒仓稳定性能的影响。研究表明,周向焊缝凹陷会显著降低结构的屈曲荷载,且与焊缝位置密切相关,而特征值模态缺陷只有在支柱接近仓顶时才会显著影响其屈曲强度。     

Nonlinear Dynamic Behavior of Granular Materials in Base Excited Silos

Nonlinear behavior of granular materials stored in steel silos subjected to dynamic base excitation due to earthquake is presented in the current article. Three-dimensional finite element (FE) modeling of the granular material silo is carried out under three-directional earthquake ground acceleration time histories. Granular material is modeled by adopting a continuum approach. The nonlinearity of the granular materials is represented by a hypoplastic material law in the FE approximation. The interface between the granular material and the silo wall is modeled by using surface-to-surface based contact formulation. The horizontal and vertical displacements of the granular material under earthquake ground acceleration at various depths of the silo are studied. Moreover, the stresses induced in the steel silo are also investigated. The static FE simulation and the analytical solution obtained by using Janssen's theory are observed to be in close agreement. Also, the dynamic FE simulations compare with the calculated results using Eurocode 8 part 4 with reasonable accuracy. The stresses in the steel silo wall are higher for loose packing of the granular material as compared to that for the dense packing.     

Elasto-plastic failure of locally supported silos with U-shaped longitudinal Stiffeners

Ranging from agriculture to food processing, from mining to industrial processing, all these sectors have a need for the temporary storage of (dry) powdered, granular, and bulk materials between different stages of all kinds of manufacturing processes and between manufacturing process and transportation, or vice versa. Silos are therefore the perfect solution to meet this need, because they can easily store large volumes on a relatively limited floor space. Frequently, silos have a circular platform and are placed in elevated position. The latter can be achieved by a limited number of discrete equidistant supports around the barrel circumference. However, in such cases, large loads have to be transferred to the limited number of supports, causing locally high axial compressive stress concentrations, and consequently premature failure due to plastic yielding and/or elastic buckling (depending on the thickness of the silo wall). A possible answer to avoid these problems is to provide a partial-height U-shaped longitudinal stiffener above each support. Such stiffeners allow for a more gradual load transfer to the supports, increasing the maximum failure load. This paper aims to map the influence of the dimensions of such longitudinal stiffeners (i.e. the parameters of the cross-section and the height) on the failure behaviour of thick-walled silos. All results and findings are based on geometrically and materially non-linear analyses or GMNA performed with finite element software. The simulations indicate that correctly, for thick-walled silos, failure will always occur by (elasto-)plastic yielding. Depending on the longitudinal stiffener cross-section, the location of failure will occur in the stiffened zone of the silo just above the supports for silos with stiffeners with a small cross-section, whereas for stiffeners with larger cross-sections, failure occurs in the unstiffened zone just above the terminations of the stiffeners. In addition, the stiffener width in circumferential and radial direction have respectively an advantageous and a disadvantageous influence on the failure load. Finally, the stiffener height only has a positive impact on the failure load when failure occurs in the unstiffened silo wall. This can be addressed to the distribution of the supporting force over the entire circumference with higher stiffeners.     

Application of inserts for suppression of coupled dynamic–acoustic effects during confined granular flow in silos

The paper discusses methods to prevent coupled dynamic–acoustic effects during silo flow by means of inserts. Laboratory tests were carried out with a perspex and steel model silo with different inserts along the wall. As bulk solids, sand, polymer granulate and PET flakes were used. An effective method for a reduction of dynamic–acoustic phenomena during silo flow was elaborated. It was verified in large metal silos.     

带仓顶室简承式筒仓的自振周期及地震作用计算

通过对筒承式筒仓的计算分析,带仓顶室筒承式筒仓的整体自振基本周期比筒仓主体的自振基本周期及仓顶室固定在地面的自振基本周期的大值要略大。采用基底剪力法计算筒仓水平地震作用时,计算仓顶室水平地震作用可采用筒仓的整体自振基本周期,其水平地震作用效应的增大系数一般取4.0,取振型指数大于1.0时,增大系数可取3.0;计算支承筒的水平地震作用应采用筒仓主体的自振基本周期。     

Experimental Investigation of Load Exerted on a Double-Cone Insert and Effect of the Insert on Pressure Along Walls of a Large-Scale Axisymmetrical Silo

Applications of flow aid devices such as inserts improve the silo discharging mode. Considerable effort has been made in finding the best configurations between inserts and silos to achieve optimal functional results. In the present investigation, experiments were carried out to measure the loads imposed on a double-cone insert by particulate solids (free-flowing sand) when it was fitted within an axisymmetrical large-scale silo. Concentric filling/discharging was implemented to carry out such measurements. Pressures along the walls of the silo were also measured. Analyses of the measurement results showed that: (1) the loads on the insert were rather stable in total, but appeared to be asymmetrical at the end of filling; (2) a sudden increase of the loads on the insert was observed at the transition from filling to discharging, but this increase lasted only for a short moment; and (3) the loads on the insert decreased slowly but remained rather high for a large part of the discharge. Effects of the double-cone insert on the pressures along the silo walls were discussed.     

Buckling failure analysis of all-terrain crane telescopic boom section

In this research work, a nonlinear structure analysis by the finite element analysis (FEA) was carried out to investigate the failure reason of an all-terrain crane telescopic boom. An overall simplified model consisting of telescopic boom and luffing jib was established by beam element, and analyzed using geometric nonlinear static method. A local detailed model consisting of the 4th and 5th telescopic boom section (TBS) was established by shell and solid element, and analyzed using geometric nonlinear and contact nonlinear static method. The result of the overall simplified model FEA indicated that the boom strength met the design criteria, and the 5th TBS of local detailed model occurred stress wrinkle.Structure experiment was designed based on the boom load characteristics in accident and analyzed using nonlinear static method and explicit dynamic method; the connection of load, boom buckling failure and stress wrinkle was studied. The result indicated that the accident was caused by elastic buckling. When the telescopic boom stress state changed from continuous state to wrinkle state, the buckling occurred. So the critical buckling state characteristic was stress wrinkle.     

热贮料作用下浅圆筒仓温度效应研究

为了研究热贮料对筒仓位移及内力的影响并方便设计时计算由热贮料产生的温度效应,本文推导了热贮料作用下仓壁位移和内力的计算公式,并通过数值模拟验证了公式的准确性。利用所推导公式分析了竖向温差对钢筒仓和内外、竖向温差对混凝土筒仓的影响。结果表明竖向温差使钢筒仓在冷热贮料交界面附近的仓壁出现较大的径向位移差;并导致温度应力显著增大;该温度应力随着径厚比的减小而增大。内外温差使混凝土筒仓上端产生较大的周向拉力;竖向温差也使筒仓中部的周向力增大;且径厚比对周向力的影响与钢筒仓相似。     

Buckling of thin‐walled cylindrical shells under axial compression

Lightweight thin‐walled cylindrical shells subjected to external loads are prone to buckling rather than strength failure. The buckling of an axially compressed shell is studied using analytical, numerical and semi‐empirical models. An analytical model is developed using the classical shell small deflection theory. A semi‐empirical model is obtained by employing experimental correction factors based on the available test data in the theoretical model. Numerical model is built using ANSYS finite element analysis code for the same shell. The comparison reveals that the analytical and numerical linear model results match closely with each other but are higher than the empirical values. To investigate this discrepancy, non‐linear buckling analyses with large deflection effect and geometric imperfections are carried out. These analyses show that the effects of non‐linearity and geometric imperfections are responsible for the mismatch between theoretical and experimental results. The effect of shell thickness, radius and length variation on buckling load and buckling mode has also been studied. Copyright © 2009 John Wiley & Sons, Ltd.     

复合材料层合板剪切稳定性试验及强度预测

对无损伤及含冲击损伤的复合材料层合板进行了剪切稳定性试验,基于数字图像相关方法 (Digital image correlation,DIC)对层合板屈曲后屈曲行为进行了实时测量。试验结果表明：引入冲击损伤后,复合材料层合板剪切屈曲波形、屈曲载荷无明显变化,失效模式转变,承载能力下降了9.69%。随后,基于断裂面失效理论,建立了考虑剪切非线性效应的复合材料渐进损伤失效模型,并对复合材料层合板剪切失效过程进行了模拟。模型采用软化夹杂法将冲击损伤等效简化,直接将损伤区的几何边界信息写入材料模型中,不需要对冲击损伤区进行切割,从而保证了整体网格质量。与试验结果对比发现：模型考虑剪切非线性对屈曲载荷预测无明显影响,对后屈曲承载能力的预测精度影响较大,不考虑剪切非线性效应时的误差可达20%以上;软化夹杂法可以有效地模拟冲击损伤,预测的含冲击损伤的复合材料层合板的屈曲载荷、破坏载荷误差分别为-3.17%、-1.27%。     

Multi-scale study of particle flow in silos

The flow characteristics of solid particles in a silo were studied experimentally and theoretically. A multi-scale study of the particles flow was performed by means of discrete element method (DEM). The dependence of flow behaviors on the particles diameter distribution and silo geometry was analyzed to establish the spatial and statistical distributions of microdynamic variables related to flow and silo structures such as velocity, porosity, coordination number, and interaction forces between particles. The results show that the distribution of particle diameter has great effects on particles flow, and the mixing of multi-sized particles is propitious to granular flow. The geometry of silos has greater effects on granular flow than particle size distribution, and inserts can improve the flow behaviors of “funnel flow” type to “mass flow”. Linear equations can be used to describe the relationship between discharge rate and orifice size by G^2/5 vs. D_o for the same distribution of particles diameter. The flow structure of particles in the silos is spatially non-uniform, which is illustrated by spatial and statistical distributions of porosity and coordination number. Both porosity and coordination number are affected by the mode of particles packed, which is affected by the geometry of silos and particle size distribution. The distribution of contact forces between particles is spatially non-uniform too. In flat-bottomed silo, there are arched stress chains in the vicinity of the orifice under the “bridging action”, which disappeared in wedge-shaped hopper silo.     

Experimental investigations on buckling of cylindrical shells under axial compression and transverse shear

This paper presents experimental studies on buckling of cylindrical shell models under axial and transverse shear loads. Tests are carried out using an experimental facility specially designed, fabricated and installed, with provision forin-situ measurement of the initial geometric imperfections. The shell models are made by rolling and seam welding process and hence are expected to have imperfections more or less of a kind similar to that of real shell structures. The present work thus differs from most of the earlier investigations. The measured maximum imperfections δ_max are of the order of ±3t (t = thickness). The buckling loads obtained experimentally are compared with the numerical buckling values obtained through finite element method (FEM). In the case of axial buckling, the imperfect geometry is obtained in four ways and in the case of transverse shear buckling, the FE modelling of imperfect geometry is done in two ways. The initial geometric imperfections affect the load carrying capacity. The load reduction is considerable in the case of axial compression and is marginal in the case of transverse shear buckling. Comparisons between experimental buckling loads under axial compression, reveal that the extent of imperfection, rather than its maximum value, in a specimen influences the failure load. Buckling tests under transverse shear are conducted with and without axial constraints. While differences in experimental loads are seen to exist between the two conditions, the numerical values are almost equal. The buckling modes are different, and the experimentally observed and numerically predicted values are in complete disagreement.     

航空复合材料加筋板剪切稳定性及后屈曲承载性能

开展了复合材料加筋板剪切稳定性试验,研究了加筋板在承剪状态下的屈曲载荷、屈曲模态、后屈曲承载性能及破坏模式。试验结果表明,加筋板在剪切屈曲载荷下形成的屈曲波长轴线与加强件轴线夹角约45°,当屈曲比达到1.2时,存在二次屈曲行为,最终破坏载荷约为屈曲载荷的1.28倍;加筋板在二次屈曲失稳前,加强件几乎保持直线,起"屈曲分隔"的作用。结合试验现象,进行了加筋板剪切屈曲及后屈曲性能理论分析,得出的理论屈曲载荷与试验屈曲载荷的相对误差为7.2%,后屈曲阶段的理论载荷-应变曲线与试验结果的相对误差在10%以内,并确定了后屈曲角随屈曲比的变化规律。     

轴心受压等边角钢构件局部稳定受力性能随钢材强度变化规律的研究

随着钢结构的发展,高强度热轧等边角钢在钢结构中的应用越来越广泛,如输电铁塔和大跨度桁架等.而高强度钢材在材料性能方面与普通强度钢材有明显的区别,使得钢材强度不同时轴心受压等边角钢构件的局部稳定受力性能存在较大差异.目前国内外关于这方面的研究成果较少.笔者利用通用有限元分析软件ANSYS 建立有限元模型,考虑了构件的残余应力和几何初始缺陷,对轴心受压等边角钢构件的局部稳定受力性能进行了有限元分析,研究其随钢材强度和宽厚比变化的影响规律,并与美国规范(AISC 360-05)和欧洲规范(Eurocode 3)的设计方法进行了比较,提出了设计建议,为相关设计提供了参考.     

基于非线性屈曲材料模型的张弦桁架连续倒塌分析

在拉索失效等工况下,张弦桁架连续倒塌时主要破坏形式为压杆的受压屈曲和拉杆的受拉屈服。为考虑受压杆件的屈曲效应,目前分析研究一般采用将每根杆件划分为多个单元并施加初始几何缺陷的方法,分析效率低、耗时长。针对这一问题,在梁柱单元修正混合强化本构模型的基础上,结合梁柱单元非线性屈曲材料模型,提出了张弦桁架连续倒塌快速分析方法,并通过算例验证了材料模型的正确性。利用ANSYS/LS-DYNA编制了所提出材料模型的子程序,基于增量动力分析法,开展了张弦桁架在拉索失效工况下的连续倒塌分析。在此基础上,对三种加强方式的结构进行增量动力分析,研究了加强部分重要杆件对张弦桁架在拉索失效工况下抗连续倒塌能力的影响。开展了张弦桁架连续倒塌易损性研究,综合评估了张弦桁架抗连续倒塌能力。结果表明:快速分析方法比传统分析方法缩短计算耗时39.89%;在加强了部分跨中上弦杆、跨中下弦杆后,张弦桁架的极限承载力最多提高16.67%,达到两种形态所对应的荷载值也均有所提高;基于快速分析方法可有效评估张弦桁架的综合抗连续倒塌能力。