Finite element techniques for the analysis of cooling tower shells with geometric imperfections

Two finite element methods for analysing geometrically imperfect cooling tower shells are presented. In the first the geometry of the imperfection is modelled by the elements; in the second the imperfection is represented by an equivalent load on the shell. Axisymmetric and general shell elements have been considered.Results are given which show that the first approximation to the equivalent load is sufficiently accurate and that it is possible to represent local imperfections by axisymmetric imperfections which require less computation. It is also shown that axisymmetric elements should be used wherever possible, because of their greater efficiency, following the geometry of an axisymmetric imperfection but representing local imperfections by equivalent loads.     

双层球面网壳的缺陷稳定分析

双层球面网壳是一种缺陷敏感型结构,影响结构稳定性的初始缺陷主要有杆件的初弯曲、杆件的残余应力和结构节点的初始安装偏差三种.本文首先利用有初始弯曲的杆件的平衡微分方程推导得到了杆单元的初始弯曲影响系数,利用CRC模型考虑了杆件残余应力的影响,并且利用有限元软件ANSYS的UPFs程序接口,开发了可以考虑残余应力和初始弯曲的杆单元;然后对原有仅能考虑节点安装偏差的随机缺陷模态法进行了改进和补充,最后提出了一种能够同时考虑三种缺陷的双层球面网壳的稳定分析方法.该法与一致缺陷模态法相比,具有更高的精度.     

Buckling modeling of reinforcing bars with imperfections

Reinforced concrete columns in seismic zones are subjected to combined actions, resulting in axial loads in longitudinal reinforcing bars. Thus, knowing the bar’s response, especially when it is subjected to important axial compressive forces that might lead to buckling, is important. A bar buckling model based on concentrated plasticity and with the capability of introducing an initial imperfection is described. The initial imperfection is imposed by bending the bar with a transversely applied nonpermanent force. Additionally, a comprehensive study of the monotonic tensile response beyond the peak stress point and a simple cyclic rule, complete the physical approach of the model. Comparisons of the model with experimental results reveal that peak capacity (average axial stress) is well captured, as well as the post-peak response shape (average axial stress versus strain), with differences observed basically in the peak capacity for specimens with high bar imperfection-to-diameter ratio, and in the shape of the post-peak response for specimens with low bar length-to-diameter ratio.     

A direct method for the stress analysis of the ring beam and shell of a cooling tower

A method for obtaining directly the stresses in the ring beam and shell of a cooling tower is presented. The stresses assuming a continuous base support are corrected by means of self-equilibrating base loads to give the actual discrete column support. The circumferential variation of the highly discontinuous base loads is represented by Fourier series. A careful study of the nature of the series involved leads to an explicit determination of significant terms and an assessment of accuracy when the series are truncated. The consequent savings in computation are shown to give the method practical viability.Examples of results for typical cooling towers are presented, together with typical computer times. It is shown that the method has clear advantages over present methods of determining ring beam stresses.     

闭式冷却塔直接供冷及其经济性分析

对过渡季或全年需要供冷的空调系统,提出了在室外环境湿球温度比系统要求的冷水温度低3～5℃时制冷机停止运行,利用蒸发冷却技术由闭式冷却塔直接为系统提供冷量的节能方案;采用对数平均温差法计算得到了系统转换为直接供冷模式的工况条件;实例分析表明,采用闭式冷却塔在主机不运行工况下直接供冷节能效果明显,增加的设备投资可在两年内收回,具有较好的经济效益.     

冷却塔处于系统下部时的水力分析

通过水力分析，指出系统高度是决定这种系统能否安全有效运行的关键因素，建议系统高度不宜超过12m。     

Buckling and dynamic instability analysis of stiffened shell panels

The static and dynamic instability characteristics of stiffened shell panels subjected to uniform in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effect of various parameters like shell geometry, stiffening scheme, static and dynamic load factors, stiffener size and position, and boundary conditions are considered in buckling and dynamic instability analysis of stiffened panels subjected to uniform in-plane harmonic loads along the boundaries.     

Analysis of hyperbolic cooling towers with local imperfections

Two methods to analyse hyperbolic cooling towers with local imperfections are presented. One method relies on the finite element technique. For this a specialized finite-element program, which can model any arbitrary imperfections while retaining the advantage offered by the basically axisymmetric nature of the shell, was developed. The other method is an approximate procedure, which may be implemented with a purely axisymmetric analysis capability. The two methods are compared through numerical studies. A cooling tower shell with a bulge-type imperfection is examined under dead load and wind load conditions. It is concluded that the finite-element model presented is effective for the analysis of such shells, while the equivalent-load method may be adequate for some cases. Also, it is shown that both meridional and circumferential stress resultants may be radically influenced by a small bulge imperfection.     

具有缺陷和应力限值的预应力钢支撑柱屈曲性能

通过预应力支撑加固的钢柱,一般增加了轴向抗压强度。过去,十分强调获得更高的临界屈曲荷载,然而,后屈曲性能是结构安全性和功能的重要保证。对具有几何缺陷和与可能的材料失效相关的应力极限的支撑柱的屈曲性能进行检验。考虑有几何缺陷支撑柱的屈曲性能,采用Rayleigh-Ritz方法对几何非线性模型公式化,并通过有限元方法进行验证。研究显示：对于承受最高临界荷载的预应力状态,系统对有几何缺陷的柱更为敏感。对某一给定形状结构,实际的最大荷载似乎随着预应力的增加而增加。研究建议：最佳的预应力取值应该大于基于传统方法的线性分析的结果。     

Buckling behaviour of prestressed steel stayed columns with imperfections and stress limitation

A steel column that is reinforced by prestressed stays, generally has an increased strength in axial compression. In the past, greater emphasis was placed on obtaining a higher critical buckling load. However, detailed knowledge of the post-buckling behaviour is important to ensure the safety and efficiency of the structure. The current work examines the buckling behaviour of a stayed column with geometrical imperfections, and stress limitation relating to possible material failure. A geometrically nonlinear model accounting for imperfect buckling behaviour of a stayed column was formulated using the Rayleigh–Ritz method, and then validated, using the finite element method. It is shown from these studies that the system tends to be most sensitive to imperfections at a prestress level that yields the highest critical load, and that the real maximum load capacity seems to increase as the prestress increases with a given configuration. The findings suggest that the optimal prestress should be greater than that found from using the previous convention that was based on linear analysis.     

An assessment of the role of geometric imperfections in the collapse of the fiddlers ferry cooling tower

The B2 cooling tower at Fiddlers Ferry Power Station collapsed during a gale in January 1984. It was known that this tower contained a roughly axisymmetric bulge just above the ring beam which had been present since the time of construction. This paper describes various finite element analysis that were carried out to assess the effect of this geometrical imperfection on the stresses in the tower. It is shown that the bulge would have caused vertical cracks to develop and the subsequent propagation of both horizontal and vertical cracks would have ultimately lead to the collapse of the tower.     

冷却塔不均匀沉陷的应力分析

用一般的薄壳有限元分析方法 ,对某冷却塔由于地基下沉而引起塔应力的重新分布作了计算分析 ,提出了不均匀沉陷对塔应力分布规律的影响     

ANSYS在双曲线冷却塔中的静力分析

分析了某工程中双曲线冷却塔的几何结构及荷载作用,运用ANSYS软件建立计算模型,考虑自重和风荷载两种工况,对双曲线冷却塔进行了静力分析,得到了一些有参考价值的结论。     

考虑初始几何缺陷的网壳结构整体稳定性可靠度分析

网壳结构的设计由重力荷载和初始几何缺陷共同作用下的整体稳定性控制,而结构的初始几何缺陷形状和最大值是未知的。采用联立自回归模型分别对球面网壳和柱面网壳结构的初始几何缺陷进行建模,研究空间相关初始几何缺陷对结构整体稳定极限承载力概率分布和可靠度的影响。评估杨氏模量对不同荷载工况作用下极限承载力概率分布和可靠度的影响。在永久荷载与雪荷载作用下,杨氏模量的影响可以忽略不计;如果各节点初始几何缺陷标准差的最大值等于1/2或1/3规范推荐的初始几何缺陷最大值,按规范中安全系数满足2的规定进行设计,结构的失效概率约小于6.5×10^-5;若安全系数取1.5,结构失效概率约小于5.1×10^-4。考虑永久荷载与活荷载的组合时,如果各节点初始几何缺陷标准差的最大值等于1/2或1/3规范推荐的初始几何缺陷最大值,安全系数取2时,网壳结构的失效概率均可忽略不计;若安全系数取1.5,球面网壳及柱面网壳的失效概率分别小于10^-7和10^-6。即若达到规范采用的可靠度,规范中的安全系数也许可降低至1.5且可针对不同地区确定不同安全...     

塔机软附着在双曲线冷却塔施工中的应用

以一实际工程为背景,介绍双曲线冷地塔施工的一项新工艺－软附着塔式起重机运输方案,供广大工程技术人员借鉴和参考。     

基于ANSYS的网壳结构屈曲数值分析

介绍了网壳结构的发展和特点,分析了网壳结构的计算方法,基于大型有限元软件ANSYS对单层网壳进行了屈曲分析,给出了具体结论,为工程结构设计与监测提供了理论依据。     

冷却塔结构强度及稳定性三维有限元计算分析

通过工程实例介绍了大型通用有限元软件ANSYS在双曲线冷却塔结构设计中的应用,计算分析表明：风荷载是冷却塔结构设计中的控制荷载;设计地震6度时冷却塔可以不作抗震验算仅采取抗震构造措施。     

Wind pressure fluctuations on a cooling tower

The results of model and in situ measurements of the fluctuating wind pressures over a cooling tower are presented. On the model, wind pressures were detected by means of two Brüel-Kjaer microphones at Re = 5.04 × 10⁵; the pressure transducers used in situ were identical to those used in measurements on the Post Office Tower, London (Gt. Britain), at Re = 3.48–5.22 × 10⁷. The power spectral densities obtained from the model and in situ measurements are in good agreement. Great attention was given to the decay of the coherence function above a certain reduced frequency the value of coherence ceases to diminish. Values of normalised spectral densities and coherence functions are recommended for theoretical calculations of the dynamic response of a cooling tower.     

Buckling of a thin-walled cylindrical shell with foam core under axial compression

This paper investigates the effect of partially filled foam core on the behavior of buckling in a thin-walled cylindrical shell. Previous studies have focused on 100% infill or simply used a fixed thickness of foam core. However, this may not be the optimum arrangement in terms of design. To further investigate this, a theoretical analysis is carried out using the Rayleigh–Ritz approximation, and a new formula is proposed to predict the critical buckling stress of an infill ranging from 0% up to 100% rigid. The proposed formula agrees well with works reported in the literature. It also shows that filling a foam core in a thin-walled cylindrical shell can enhance its resistance to buckling failure. Meanwhile, a simplified formula is provided to the practicing engineer. The paper concludes that an excessive increase in foam core thickness beyond 10% of outer radius is inefficient due to extra cost and weight.     

组合载荷作用下冷却塔的应力分析

针对某工程组合荷载对冷却塔应力分布的影响问题，用一般的薄壳有限元分析方法，计算了某冷却塔在风载和温度载荷作用下冷却塔应力的分布，对塔的安全性进行了评估。