Comparison of numerical techniques for 3D flutter analysis of cable-stayed bridges

This paper presents the results of a comparison study of the numerical techniques of structural and aerodynamic force models developed based on the spline finite strip method with the conventional finite element approach in three-dimensional flutter analysis of cable-stayed bridges. In the new formulation, the bridge girder is modelled by spline finite strips. The mass and stiffness properties of the torsional behaviour of complex bridge girder, which have a significant influence on the wind stability of long-span bridges, are modelled accurately in the formulation. The effects of the spatial variation of the aerodynamic forces can be taken into account in the proposed numerical model by distributing the loads to the finite strips modelling the bridge deck. The numerical example of a 423 m long-span cable-stayed bridge is presented in the comparison study. The accuracy and effectiveness of the proposed finite strip model are compared to the results obtained from the equivalent beam finite element models. The advantages and disadvantages of these different modelling schemes are discussed.     

A numerical model for wind loads simulation on long-span bridges

A numerical model of the air flow problem around the girder of a long-span bridge is presented. The model is based on a finite volume formulation and it is able to simulate steady and non-steady wind loading conditions on the structure under the simplifying assumption, which is plausible for bridges with long spans, of a two-dimensional-like approaching flow. For a given bridge deck cross-section the proposed model allows the numerical evaluation of the flutter derivatives, which is useful to characterize in an analytical way the stability conditions of the overall wind-induced bridge response. In order to obtain satisfactory accuracy and stability of the numerical solution, a two-equation k–ϵ RNG turbulence model and special boundary conditions are employed. The accuracy and applicability of the model to wind engineering problems are successfully assessed by computing the aerodynamic behaviour of some simple cross-section shapes. Numerical results are also obtained for typical long-span bridge cross-sections and the comparison with the available wind tunnel measurements shows a good agreement.     

Numerical simulation for aerodynamic derivatives of bridge deck

An improved domain decomposition method is proposed to compute aerodynamic derivatives of bridge deck based on commercial Computational Fluid Dynamic (CFD) code FLUENT. In this method, the computational region is discretized into rigid boundary layer mesh region, dynamic mesh region and static mesh region. A simplified formula used to control the body-fitted grid height is deduced from the standard wall function. Aerodynamic derivatives of a flat plate and two long span bridge decks are computed and compared with the theoretical values and the wind tunnel tests results. Numerical results show that several aerodynamic derivatives are influenced by the accessory structures of the bridge deck such as guardrails and inspecting vehicle rails, etc.     

Computer simulation of buffeting actions of suspension bridges under turbulent wind

Suspension bridges are long-span flexible structures susceptible to various types of wind induced vibrations such as buffeting actions. In this paper, a three dimensional finite-element model formulated to deal with suspension bridges under turbulent wind is presented. In this model, all sources of geometric nonlinearity such as cable sag, force-bending moment interaction in the bridge deck and towers, and changes of bridge geometry due to large displacements, are fully considered. The wind loads, composed of steady-state wind loads, buffeting loads and self-excited loads, are converted into time domain by using the computer simulation technique. The Newmark-β step by step numerical integration algorithm is used to calculate the buffeting responses of bridges. Compared with the results obtained by classical buffeting theory, the validity of the simulation is proved.     

Support vector machine based aerodynamic analysis of cable stayed bridges

Flutter, a self-excited vibration resulting from the interaction between structural motion and aerodynamic force, is the major aspect in wind resistant design of cable stayed bridges. The critical speed for flutter of a deck section can be evaluated using the flutter derivatives obtained by sectional model testing of the bridge deck in a wind tunnel. Since it is very expensive, time consuming and laborious to conduct wind tunnel tests for all the practical dimensions of deck, the support vector machine (SVM) is applied for predicting the flutter derivatives for any deck size. The wind tunnel experimental data is collected from literature and SVM is trained. Thus predicted flutter derivatives are used for estimation of critical flutter velocity of cable stayed bridges. The effect of each aerodynamic derivative on flutter instability is investigated in this study.     

基于数值计算的高速列车气动阻力风洞试验缩比模型选取方法

为给高速列车气动阻力风洞试验模型选取提供更多的参考依据,通过计算流体力学(Computational Fluid Dynamics,CFD)方法,研究不同比例的高速列车缩比模型对气动阻力风洞试验结果的影响.首先,计算得到开口式风洞测试段的静压系数分布曲线,为高速列车气动阻力测量试验模型的长度选择以及摆放位置提供依据;其次,通过数值计算得到全尺寸模型列车在明线运行时,以及不同比例的模型列车在风洞中运行工况下的气动阻力信息,并从阻塞效应和雷诺数的变化,以及风洞试验段内静压分布的影响这3个方面对列车模型的气动阻力结果进行分析,得到在所研究风洞中较合理的列车缩比模型比例选取范围.这种以CFD为基础进行数值仿真,选取风洞试验中列车模型比例及试验测试位置的方法,为在地面交通工具风洞中进行高速列车模型气动阻力试验的缩比模型选取提供一定依据.     

Buffet suppression in long-span suspension bridges

We study the aerodynamic control of long-span suspension bridges and seek to raise the critical flutter wind speeds, while simultaneously suppressing buffeting. The control system design study is based on a simple flexible bridge section model that interacts with a constant-velocity air stream. A streamlined bridge deck is assumed and non-steady thin aerofoil theory is used to describe the interactions between the bridge deck and the air stream. Classical turbulence models, first developed in the aircraft industry, are used to model the buffet forces acting on the deck. While a wide variety of control systems is possible, we focus on a compensation scheme that can be implemented using passive mechanical components such as springs, dampers and a rack and pinion mechanism. A single-loop control system is investigated that controls a trailing-edge flap by sensing movements of the bridge deck; several such mechanisms are contemplated. The first finding is that the critical wind speed for flutter can be greatly increased, with good robustness characteristics, through passive feedback control. It is also possible simultaneously to suppress flutter using the same passive mechanical controller by solving a passive mixed H₂/H_∞ control problem. The effect of flexible controller mounting arrangements are considered briefly.     

Automation of bridge deck graphical representations based on a shape geometric model

The construction of a new bridge interferes with the existent environment. A careful aesthetic study must be made at an early stage in the design and the visualisation of a three-dimensional (3D) model of the structure is the best way to analyse it. As the bridges deck presents a complex shape it is difficult to execute a 3D deck model as well as the specific drawings or a 3D finite elements mesh of the deck.The modelling scheme proposed here allows the automation of the geometric design phases related to the deck element using as a means of integration a geometric database representative of the real deck shape. This concept was implemented in a computer programme. This application is an important support in a bridge design namely at the conceptual, analytical and final stages.     

Sensitivity analysis of bridge flutter with respect to mechanical parameters of the deck

A methodology for carrying out an analytical sensitivity analysis of the flutter phenomenon in long-span bridges is developed. Decks of bridges are generally bluff bodies and therefore the aeroelastic forces under wind action have to be experimentally evaluated in wind tunnels. Such forces depend on the response frequency of the bridge, which is not known until the problem is solved. Consequently, the calculus of the critical wind speed that initiates the flutter instability comprises a complex nonlinear eigenvalue problem. During the design phase, the sensitivity analysis gives very interesting information about the gradient of the flutter speed with respect to the key chosen design variables, moments of inertia of the bridge deck. The presented method is applied to the Great Belt and Vasco da Gama Bridges, as well as to the old Tacoma Bridge.     

The impact of supercomputers on CFD

The application of computational fluid dynamics (CFD) to the design of commercial transport aircraft has revolutionized the process of aerodynamic design. Today, CFD stands alongside the wind tunnel in terms of importance. The wind tunnel and CFD each have strengths and limitations, and when used together in complementary roles they enable the achievement of aerodynamic design objectives that previously were not achievable. Today's role of CFD in airplane design is described and a number of specific examples that illustrate the contribution of CFD are given. The limitations of CFD are summarized and the challenges of the future described.     

Dynamic instability of suspension bridges

Suspension bridges are long, slender flexible structures which have the potential to be susceptible to a variety of types of wind-induced instabilities, the most serious of which are divergence (due to stationary wind forces) and flutter (due to aerodynamic forces). Flutter occurs at certain wind speeds where aerodynamic forces acting on the deck feed energy into an oscillating structure, so increasing the vibration amplitudes. If this situation is approached the basic safety of the bridge is threatened. This paper describes a computational method for predicting flutter speed based on a modal technique. A selection of the lowest vertical and torsional natural mode shapes is included with the aerodynamic forces in an interaction analysis which yields an unsymmetric matrix eigenvalue problem, the roots of which indicate if flutter is possible. The paper addresses the question of how the degree of refinement of the basic structural model and the number of natural modes included in the interaction analysis affect the flutter speed predictions.     

Virtual wind tunnel: An alternative approach for the analysis of bridge behaviour under wind effects

The study of bridge responses under wind-induced loads is based upon full aeroelastic model testing or hybrid methods which use section model tests and subsequent computer analysis. Both methodologies present several strong points and some shortcomings, specially related with the visualization of the bridge dynamic behaviour. Nowadays, advances and improvements in computational power and computer aided design technologies make possible a new way towards the feasible design of long span bridges considering its aerodynamic and aeroelastic behaviour. The virtual wind tunnel (VWT) technique developed by the authors joins together accurate section model testing with computer aided design in order to obtain a detailed computer visualization of the complete bridge behaviour under wind flow. The results obtained for the Tacoma Narrows Bridge and the Messina Strait Bridge are presented.     

Computational analysis of the performance of a venturi-shaped roof for natural ventilation: Venturi-effect versus wind-blocking effect

Computational Fluid Dynamics (CFD) is used to gain insight in the aerodynamic performance of a venturi-shaped roof (called VENTEC roof). The simulations are performed with the 3D steady Reynolds-averaged Navier–Stokes (RANS) equations and the Renormalisation Group k–ε model. A detailed analysis is conducted of the influence of the so-called venturi-effect and the wind-blocking effect on the aerodynamic performance of the VENTEC roof. The specific roof configuration is intended to create a negative pressure in the narrowest roof section (contraction) which can be used to partly or completely drive the natural ventilation of the building zones. The CFD simulations are based on a detailed grid-sensitivity analysis and on successful validation of the grid-independent results by comparison with experiments in an atmospheric boundary layer wind tunnel. The simulations show that the aerodynamic performance of the roof is governed by the balance between the so-called venturi-effect on the one hand and the wind-blocking effect on the other hand. The venturi-effect cannot act to its full extent because the flow is non-confined. The wind-blocking effect refers to the effect of the resistance exerted by the roof contraction on the air flow and the resulting tendency of the approaching wind to flow around and over the roof, rather than only being forced through the roof contraction. The results indicate that because of the wind-blocking effect, the highest contraction ratio does not provide the best aerodynamic performance and the largest negative pressure, which is a counter-intuitive result. The paper also provides a parametric analysis to optimise the roof contraction height and contraction ratio. The study in this paper illustrates the use of CFD to increase insight in building aerodynamics and to support sustainable building design.     

CFD modeling of scale effects on turbulence flow and scour around bridge piers

Sediment scour near bridge piers is a problem of nationwide concern because it has resulted in more bridge failures than all other causes in recent years. The existing bridge scour equation from HEC-18 was developed from laboratory experiments in relatively small scale. Field studies by Mueller [Mueller D, Wagner Chad R. Analysis of pier scour predictions and real-time field measurements. In: Proceedings of ICSF-1 first international conference on scour of foundations, Texas A&M University, College Station, Texas, USA; 2002] indicate that it is difficult to verify the scour equation with field data obtained from large bridge piers. In this study, computational model simulations using a 3D CFD model were conducted to examine scale effects on turbulent flow and sediment scour. For the large-scale model, the physical scale and boundary velocity were set up from the small scale model based on the Froude similarity law. Results of flow and sediment scour were obtained from two different approaches: (a) Froude similarity which is commonly used in physical modeling and (b) full scale 3D CFD modeling. Unlike physical modeling in which the effect of turbulent Reynolds number is ignored, the CFD model employs a 2nd order turbulent model to calculate turbulent velocity and sediment scour. Effects of scale on turbulence flow and sediment scour were investigated by comparing different results obtained from a full scale numerical model to those derived from the Froude similarity method.     

Dynamic response of trussed bridges for moving loads

A continuum approach is presented to obtain the transverse vibration of trussed bridges traversed by a single moving load. The efficiency and the accuracy of the method are determined by comparing its results with those obtained by the dynamic analysis of the bridge as a discrete lumped mass system, which can account for both truss action and flexural action of the deck in the response. Using the proposed method, a parametric study is performed to show the influence of some important parameters on the dynamic response of the bridge. The parameters include relative stiffness of the bridge deck and truss, number of panels, type of truss and speed parameter.     

Measuring and computational system of TsAGI T-128 transonic wind tunnel

Having been developed at TsAGI, measuring and computational system of T-128 transonic wind tunnel is presented. Structure of the system, as well as basic characteristics of the subsystems used for measuring the aerodynamic loads, pressure distribution and flow parameters are described. Specific features of the system’s software for the given wind tunnel are discussed. Application of the system enables to improve the accuracy of evaluating the aerodynamic characteristics of aircraft models by ten times.     

Computer aided design of prestressed concrete highway bridges

The paper presents a computer aided design system for prestressed concrete highway bridges which, starting from few geometrical data, provides the complete geometry, prestressing steel, reinforcing steel, amount of materials and cost of all the bridge elements: deck, bearings, piers, abutments and foundations. Different configurations are devised, from short and medium to long-span bridges, accounting for different deck super-structures and erection methods. All the results are displayed on the computer screen and can be printed. The system provides also DXF files containing the general layout, cross-sections and prestressing arrangement of box girder bridges. This system allows, in a short time, an accurate design and an economical estimation of a particular bridge, taking into account the most important technical requirements. It is a useful decision-making tool for both design and administration engineers.     

改进的桥梁三维重构及裂缝检测系统

针对桥梁病害检测问题, 尤其是损害程度较高的裂缝检测, 结合已有的桥梁检测系统, 本文提出一种改进的桥梁检测系统, 改进后的系统硬件是大疆M210-RTK无人机, 软件由图像数据获取模块、裂缝检测模块、3D模型构建模块构成. 其中, 裂缝检测模块增加了裂缝长宽计算功能, 对裂缝分段迭代后进行曲线拟合求取长度, 骨架法计算宽度. 在实验中设置无人机的飞行轨迹、扫描间距, 拍摄距离以及对待检测桥梁桥墩分区域编号, 最终拍摄了200张桥墩桥面图片和采集了桥梁视频数据. 通过对桥墩桥面裂缝种类的识别和裂缝长宽计算, 更全面的了解了裂缝信息及危害程度, 减少了后期人工测量, 并结合Ubuntu 16.04系统, 使用直接稀疏里程计法(DSO)进行桥梁3D建模, 3D模型能够方便直观的展示桥梁概况. 改进后的系统稳定, 方法省时省力, 适用性广, 特别是对一些跨海大桥及周边环境复杂的桥梁检测具有重要意义.     

分布抽吸率对整车风洞试验段流场影响的数值模拟

为探讨适用于整车风洞的分布抽吸率,采用计算流体力学（Computational Fluid Dynamics,CFD）方法研究经边界层控制后的试验段流场．针对不同分布抽吸率下的试验段,利用FLUENT对流场进行模拟,然后计算边界层位移厚度、静压因数和气流偏角．二维和三维的数值模拟结果均表明,试验段边界层的位移厚度随分布抽吸率的增加而减小;当分布抽吸率达到某一数值后,若继续增大,那么边界层的位移厚度将基本保持不变．研究结果对风洞建设及试验时分布抽吸率的选取有参考意义．     

Multiobjective backtracking search algorithm: application to FSI

Fluid-structure interaction (FSI) problems play an important role in many technical applications, for instance, wind turbines, aircraft, injection systems, or pumps. Thus, the optimization of such kind of problems is of high practical importance. Optimization algorithms aim to find the best values for a system’s parameters under various conditions. In this paper, we present a new Backtracking Search Optimization Algorithm for multiobjective optimization, named BSAMO, a new evolutionary algorithm (EA) for solving real-valued numerical optimization problems. EAs are popular stochastic search algorithms that are widely used to solve nonlinear, nondifferentiable and complex numerical optimization problems. In order to test the performance of this algorithm, a well known benchmark multiobjective problem has been chosen from the literature, and for FSI optimization, using a partitioned coupling procedure. The method has been tested through a 2D plate and a 3D wing subjected to aerodynamic loads. The obtained Pareto solutions are then presented and compared to those of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The numerical results demonstrate the efficiency of BSAMO and also its best performance in tackling real-world multiphysics problems.