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.     

Detuning of wind-induced vibrations of cooling tower shells

Detuning of wind-induced vibrations of cooling tower shells can be achieved through adequately stiff upper edge members. In this case and for double layer reinforcement bending resistance may be sufficient within the usual minimum reinforcement /5/. However, if the cornice stiffness is too weak the required bending reinforcement can exceed the prescribed minimum values by far (Fig. 8). Cracking and thus reduced durability of the cooling tower shell can not be excluded.     

Simulation of static and kinetic buckling of unstiffened and stiffened cooling tower shells

Natural draught cooling tower shells are loaded mainly by their dead weight and by the wind, which may both cause buckling failure. The present paper compares various numerical procedures to investigate the stability behaviour of cooling tower shells. These are a complete nonlinear analysis, a linear eigenvalue analysis for a stationary non-axisymmetric wind load, and a linear eigenvalue analysis for a wind load, approximated to be axisymmetric. The aim is to evaluate whether a geometrically nonlinear analysis can be replaced by a time-saving classical buckling analysis, probably even for an axisymmetric state of stress. The third procedure, as the most conservative, but a very effective one, will be applied to investigate the mechanical influence of ring stiffners on the buckling behaviour of cooling tower shells. Kinetic instability phenomena will also be examined. The structural improvement resulting from ring stiffeners will be quantified and summarized in design recommendations.     

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。     

A global plasticity formulation combined with a semi-analytical analysis of imperfect shells of revolution

A semi-analytical analysis of elastic plastic imperfect shells of revolution is presented. The Kirchhoff-Love hypothesis and moderate rotations of the normal are assumed. Inextensible imperfections are introduced as strain-free initial normal displacements. The material is assumed to be elastic-perfectly plastic. The small strain flow rule is associated with the Huber-Mises-Hencky yield condition approximated for generalized stresses. The Ivanov approximation, together with Crisfield's modification, is employed. The return mapping algorithm is used when integrating the physical relationships. Expansion of variables into truncated Fourier series with respect to the circumferential variable is used to reduce the problem to a one-dimensional one. Both plane-symmetric and plane-asymmetric terms are retained. The finite difference method based on a scheme with a middle point is applied for discretization.     

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。     

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.     

冷却塔供冷技术在我国应用的模拟与预测分析

认为冷却塔供冷 (又称免费供冷 )是一种节能降耗的系统形式。建立了冷却塔供冷系统在我国不同条件下的运行能耗模型 ,在模拟建筑上预测了全国 7个典型城市的应用情况 ,给出并分析了节能率、供冷温度等可用作设计参考的预测结果。     

A proposed stack configuration for dry cooling tower to improve cooling efficiency under crosswind

Cooling efficiency of a natural draft, dry cooling tower (NDDCT) is significantly affected under cross-wind condition and might decrease to 75 percent in the range of moderate to high wind-velocity condition. Separated flow occurring at the rear radiators, along with deflected plume exiting tower stack, reduces the cooling efficiency. Various researchers have recommended wind breakers to partially decrease the undesirable effect of the flow separation. But in the present research work, a new exit configuration has been proposed for tower stack, which could reduce the throttling effect of deflected plume. Numerical simulation of the proposed configuration showed improvement in the cooling efficiency up to 9 percent compared to the present, usual one at the generally investigated wind-velocity value of 10 m/s.     

A simplified approach to bridge deck flutter

Flutter instability of flexible bridge decks is investigated in the framework of the semi-empirical Scanlan's approach based on flutter derivatives. The equations of the eigenvalue problem of stability are manipulated and simplified thanks to the analysis of a large number of dynamic and aerodynamic data. Simple expressions for critical reduced wind speed and coupling frequency are obtained. The major interest of this approximate method is the fact that only three or even two flutter derivatives are required to calculate the flutter instability limit. In addition, these aerodynamic functions are known to be quite reliable and the easiest to be identified through wind-tunnel tests. The proposed formulas seem to give accurate results in a wide range of cases, unless the frequency ratio is very close to unity. The method is shown to apply also in case of cross sections prone to torsional flutter. Finally, the paper offers a valuable insight into the flutter behavior of several types of bridges and investigates the role in the instability onset played by various structural parameters, such as frequency ratio and structural damping.     

A simplified approach for the wind response analysis of cable-stayed masts

The standard approach for the equivalent static analysis of line-like structures, based on the gust factor, is reviewed, with special reference to the case of systems with intermediate elastic supports, like cable-stayed masts. For this class of structures the first modal shape exhibits an inversion point and the effect of the upper modes cannot be neglected. A new analysis method, based on the definition of a gust function variable along the height is proposed and applied to a case study. The results are compared with those obtained using the patch load method and the direct integration of the equations of motion which accounts for geometric nonlinearity.     

塔式起重机在电厂特大型冷却塔中的应用

随着我国电力工业的迅速发展 ,大容量的发电机组逐渐取代中、小型机组 ,电厂的标志性建筑———双曲线冷却塔的淋水面积越来越大、高度越来越高 ,传统的井架吊桥施工运输方法已经不能满足特大型冷却塔的施工需要。井架吊桥施工的缺点如下 :①缆绳对井架的稳定和安全使用极为重要 ,缆绳与地面的夹角有一定要求 ,随着井架的升高 ,缆绳锚固定点距离就越大 ,需要跨越原有建筑物和高压电线 ,给井架搭设和使用增加了难度 ;②井架上料速度慢 ;③为保持井架的稳定性 ,随井架使用高度的增加要加大井架的断面 ,组装井架的工作量和劳动强度加大 ,成本也…     

Shallow shell finite element for the large deflection geometrically nonlinear analysis of shells and plates

An investigation into the large deflection, geometrically nonlinear behaviour of shells is carried out in the present paper. The finite element method is used in conjunction with linearised incrementation and the Newton-Raphson iterative technique.The finite element used is based on independent strain assumptions insofar as it is allowed by the compatibility equations. Strain-displacement relationships based on shallow shell formulation are used and applied to an element having three principal curvatures. The resulting element has the only essential external degrees of freedom, satisfies the exact requirement of strain free rigid body modes of displacements and can be used for the representation of cylindrical, spherical and hyperbolic paraboloid shells.Complex load-deflection curves are obtained for cylindrical and spherical shells by incrementing loads as well as deflections. The relative behaviour of cylindrical and spherical panels having the same overall dimensions are also discussed in terms of stiffness, instability and snap-through phenomena.     

Full-scale and model tests on wind-induced,static and dynamic stresses in cooling tower shells

The response of the shell of concrete cooling towers to turbulent wind is investigated by experimental methods. Calculations based on membrane theory are used to verify the reliability of the test results with respect to the membrane forces. The tests include measurements of wind load and shell response in model and full-scale conditions. For the model tests, dynamic similarity of the model was observed, and the atmospheric boundary layer was simulated. The Schmehausen cooling tower was equipped with special strain and pressure pick-ups for the full-scale observations. The results suggest that there is considerable bending in circumferential stresses, and that dynamic stresses are not always correctly calculated by assuming a static design wind load, affecting in particular the buckling safety of the shell.     

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.     

Buckling behaviour of imperfect spherical shells subjected to different load conditions

The paper deals with an analysis of the bifurcation and initial post-buckling behaviour of highly imperfection-sensitive large spherical .shells, such as cargo tanks for ship transportation of liquefied natural gas and large spherical containment shells for nuclear power plants. The numerical analysis procedure has sufficient generality to treat shells of revolution with arbitrary curved generators and with arbitrary variation of the thickness. The shells can be subjected to non-axisymmetric time-varying loadings. The purpose of the paper is to present simple procedures for scantling selections in the initial design phase and to propose an analysis procedure for verification of the final design of optimized thin-walled spherical shells.     

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。     

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.