大气边界层中结构风载的计算方法比较

风载是大气边界层中露天结构的主要侧向载荷。针对目前工程中普遍采用的理论计算方法及计算流体动力学(Computational Fluid Dynamics,CFD)方法,分别论述利用CFD方法和理论计算方法计算结构风压及风载的原理。采用基于Reynolds时均N-S方程和标准k-ε湍流模型对一简单结构在不同高度的风压分布进行数值模拟,分析结构表面风压的分布特性,在此基础上比较两种计算方法的优劣。研究结果表明,由于未考虑结构脉动风载,数值计算结果较理论计算更小,但CFD方法可以获得风场中参数的更多信息,在对复杂结构的风载计算方面更方便有效。     

Modelling of wind load on single and staggered dual buildings

A method of modelling numerically the wind loads on single and staggered dual buildings using Computational Fluid Dynamics is presented in this paper. Simulation of a turbulent boundary layer over test models was carried out at the Supercomputing and Visualization Unit, the National University of Singapore, using FLUENT 6.1.18. Turbulence was introduced at the inlet through a parallel auxiliary simulation and the computation of the flow advanced in time using Large Eddy Simulation with a ReNormalization Group subgrid-scale viscosity model. Wind velocities at different locations and wind pressures on the building faces were recorded. Subsequently the flow characteristics were examined and the force and moment spectra deduced. The results were compared with data from earlier wind tunnel experiments carried out at Virginia Polytechnic Institute and State University. It can be concluded from the study that numerical wind modelling on tall structures is a promising alternative to conventional tests in atmospheric boundary layer wind tunnels.     

An automated,energy-based,finite-difference procedure for the elastic collapse of rectangular plates and panels

A FORTRAN IV, large capacity, computer program has been developed to determine collapse loads and bifurcation loads for linear and nonlinear prebuckling behavior for fiber-reinforced, laminated, rectangular plates and panels under general loading systems and boundary conditions. The program is based on the principle of total potential energy and uses finite-differences in the discretization process. Whole-station spacing has been used to calculate the strain energy associated with an area-element and an orthogonal finite-difference grid that provides for variable spacings in perpendicular directions is incorporated.Numerical results are presented that compare favorably with results obtained via the general computer program STAGS. Other numerical results are presented that illustrate the types of boundary conditions, applied loads, cut-outs and initial geometric imperfections that can be handled by the present program. A brief study of the effect of panel construction and initial geometric imperfections on the buckling behavior of fiber-reinforced panels is presented.     

Design program for multi-story structures

An efficient and short computer program, STFRD, has been developed to facilitate the structural engineer who is involved in multi-story building design. The program consists of three basic parts. The first part of the program performs a preliminary analysis of a frame section of a building using approximate methods to determine forces due to the loads. The loads will consist of uniform dead, live and wind loads. The second part of the program utilizes an iterative process, using the allowable stresses given by the AISC building specifications, to determine member sizes. The third part of the program consists of a matrix analysis of the frame section to determine actual forces on the members, due to the loads. This analysis is used in conjunction with the AISC building codes to verify the adequacy of the member sizes chosen. The program also has a redesign capability which is used if the preliminary member sizes are not adequate. The entire procedure has been programmed for use on a UNIVAC 1108 computer, FORTRAN IV language. The program may be obtained from the author.     

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.     

Computer method for analysis of multistory structures

A computer method for three dimensional analysis of multistory structures is presented. There are no restrictions referring to types of stiffening elements, their layout and changes in floor plane and variations in cross-sectional properties with height of the structure. The number of stiffening elements which may be included in analysis is practically unlimited. The loads may be vertical and lateral at arbitrary locations. Elastic warping of thin-walled members is included in analysis. The macro-flow-chart of the computer program and results of a numerical example is given.     

Rotational fluid flow using a least squares collocation technique

A potential theory approach for incompressible viscous flow which leads to the biharmonic equation is first developed. A numerical least squares collocation technique using fundamental singular solutions of the biharmonic equation is then applied to a rotational flow problem with moving boundaries that produce discontinuous boundary conditions associated with the biharmonic. It is shown that the least squares technique smoothes out local disturbances in boundary data of the type which are likely to present difficulties to the more commonly used boundary element method. A compact computer program for the method and the results for the problem of a rectangular channel with one moving boundary are included along with an experimental verification of the results using the thin plate bending analogy.     

SPH-GPU并行计算在风沙流中的应用

为了实现小尺度范围风沙运动的真实感模拟,采用基于拉格朗日力学无网格形式的光滑粒子流体动力学（smooth particle hydrodynamics,SPH）方法解决了基于欧拉网格法因网格大变形或者变形边界等引起的各种问题,并克服了不能用固定欧拉网格追踪任意单颗粒子运动轨迹的困难,因此该方法在研究风沙运动方面有着独特的优势。然而,随着风沙流动中SPH粒子数目的增加,该方法计算效率低,计算规模大的缺陷在风沙模拟过程中尤为明显。为了提高其计算效率,在CUDA软硬件平台上,建立SPH-GPU并行加速的二维气沙两相耦合模型,对串行的热点程序进行分析,找出最耗时且适合并行的热点程序;其次对GPU并行计算模型进行验证,宏观上得到了沙粒群运动的时空变化规律,微观上得到了典型沙粒的跃移轨迹和变异的尖角轨迹;最后对比了三种不同粒子数下CPU与GPU的计算效率。模拟结果证明SPH-GPU并行计算方法能够进一步应用在风沙流的数值模拟研究中。     

Structural analysis of cable-reinforced inflatables

A computer simulation of behavior of cable-reinforced inflatable structures subjected to internal pressure, wind pressure, static concentrated and harmonic oscillating loads, and interacting with surrounding air is outlined. The simulation is based on a structure discretization approach with a cable under the constant pressure being used as a finite element. A numerical example given shows that the wind pressure and attached mass and damping significantly affect the dynamic response of the structure.     

Computer-aided optimum design of steel tubular telescopic pole structures

This paper presents a computer-aided approach for the optimum design of steel tubular telescopic pole structures. The author's experience in steel pole structure's design is implemented in a computer program called ODAPS (optimum design and analysis of pole structures). Although several other computer programs exist for the analysis and design of steel tubular pole structures, they are limited to cases where dimensions are pre-defined by the user. Different from these conventional programs, the developed program is able to automatically design the pole structure having the lightest weight that satisfies the limits states criteria within given geometrical boundary conditions. Simple equations and charts for the design of poles of different steel grade and having different length, subjected to various point loads at their top, are obtained using this program. It is possible to obtain economical designs for pole structures subjected to a specified loading using these equations or charts.     

Multirow joint fastener load investigation

A multirow joint subjected to the mechanical and thermal loadings was investigated to determine the loads taken by the fasteners in each row. The hole clearance was considered and its effect on the thermal expansion was defined. The friction in the interface between two plates in contact was analyzed and its effect on the distribution of fastener loads was determined. The primary joint design parameters, such as the material and size of the plates and of the fasteners and the patterns of fastener arrangement were considered. The principle of complementary virtual work was employed to derive the general equations involving these parameters, and the analytical solutions were obtained by solving the matrix equations. A computer program was developed to obtain the numerical solutions through the use of FORTRAN IV System 370/165 computer techniques. The application of the computer program to the practical joint design problems is discussed.     

Analysis of cable structures

A numerical procedure has been developed to analyze complex 3-dimensional assemblies of substructures and cables. The procedure is applicable to guyed towers, flexible transmission lines, cable roofs or mooring networks. The computer program, which has been developed to analyze these composite structures, accepts arbitrary loads on the substructures but restricts the loads on the cable elements to gravity, thermal, or fluid drag effects.The algorithm is built around an efficient cable element subprogram. From given loads and given positions of the ends of a cable, the subprogram determines the complete geometry of the cable, its end forces, and its tangent stiffness matrix. The cable elements are connected together or to substructures nodes.The equilibrium configuration of the assembly is approached by successive iterations which decrease the imbalance of forces which still exist at each node at the end of the previous iteration. Special numerical schemes, which insure rapid convergence of the analysis, are presented.The computer algorithm is discussed in detail, and the simplicity and efficiency of the formulation is demonstrated by several examples. Very large displacements of the nodes and associated second order effects on the substructures do not present any difficulty as the imbalances and stiffnesses at each iteration are based on the geometry of the system at the end of the previous iteration.     

Optimisation of tensile membrane structures under uncertain wind loads using PCE and kriging based metamodels

Tensile membrane structures (TMS) are light-weight flexible structures that are designed to span long distances with structural efficiency. The stability of a TMS is jeopardised under heavy wind forces due to its inherent flexibility and inability to carry out-of-plane moment and shear. A stable TMS under uncertain wind loads (without any tearing failure) can only be achieved by a proper choice of the initial prestress. In this work, a double-loop reliability-based design optimisation (RBDO) of TMS under uncertain wind load is proposed. Using a sequential polynomial chaos expansion (PCE) and kriging based metamodel, this RBDO reduces the cost of inner-loop reliability analysis involving an intensive finite element solver. The proposed general approach is applied to the RBDO of two benchmark TMS and its computational efficiency is demonstrated through these case studies. The method developed here is suggested for RBDO of large and complex engineering systems requiring costly numerical solution.     

Direct solution of the Helmholtz equation using fourier analysis on the cyber 205

This paper deals with a fast direct method for the efficient numerical solution of the three-dimensional Helmholtz equation for various boundary conditions on both scalar and vector computers. The numerical algorithm is based on Fourier analysis in two directions. Fast-Fourier-transformation (FFT) is applied if appropriate pre- and postprocessing is available (depending on the boundary conditions). The code achieves full vectorization on computers like the CYBER 205. A version coded exclusively in FORTRAN 77 is also available for use on scalar computers. The performance of the presented program package is illustrated in terms of the computer time required on several computers.     

The use of computational fluid dynamics in TsAGI experimental works

The paper describes methods to calculate the flow around an aircraft model in a wind tunnel. It formulates special boundary conditions to achieve the necessary flow parameters in the control section, as well as to simulate some features of wind tunnel walls, for example, perforation. In order to accelerate the numerical solution convergence, a method for implicit smoothing is suggested allowing the calculation duration to be reduced several times. The cases of practical use of this methodology are given. It is shown that in the conditions of the TsAGI subsonic wind tunnel, it is possible to simulate the effect on the model from the elements of the structure that are missing in this tunnel, for example, the running track. A mathematical model of the European Transonic Windtunnel (ETW) with slotted walls is presented. It is shown that the flow in the reentry affects the main flow in the test section of this tunnel. Data on the effect of the model support in the TsAGI wind tunnel T-128 are given. The peniche height used in the half-model tests has been justified. The conclusion is made that the mathematical model of the wind tunnel is an obligatory part in experimental studies.     

Numerical computation of wind pressures on buildings

This paper discusses the computer simulation of wind pressures on buildings. The control volume technique is used to discretize the three-dimensional differential equations of the flow and the standard k-ε turbulence model is incorporated in the numerical modelling for closure. A modular-structure, computational tool named TWIST (Turbulent WInd Simulation Technique), has been developed and implemented in various computer systems including, for the first time, microcomputers. Computed mean values of wind-induced pressures on buildings agree well with experimental data obtained from boundary layer wind tunnels. The influence of various computational parameters such as the number of grid nodes on the time of computation and the computed results is also discussed.     

Bifurcation, pre- and post-buckling analysis of frame structures

A procedure is developed for investigating the stability of complex structures that consist of an assembly of stiffened rectangular panels and three-dimensional beam elements. Such panels often form one of the basic structural components of an aircraft or ship structure. In the present study, the stiffeners are treated as beam elements, and the panels between them as thin rectangular plate elements, which may be subject to membrane and/or bending and twisting actions.

The main objective of the study is the determination of the critical buckling loads and the generation of the complete force-deformation behavior of such structures within a specified load range, based on the use of a computer program developed for this purpose. The present formulation can trace through the postbuckling or post limit behavior whether it is of an ascending or descending type. A limit load extrapolation technique is automatically initiated within the computer program, when the stability analysis of an imperfect or laterally loaded structure is being carried out.

The general approach to the solution of the problem is based on the finite element method and incremental numerical solution techniques. Initially, nonlinear strain-displacement relations together with the assumed displacement functions are utilized to generate the geometric stiffness matrices for the beam and plate elements. Based on energy methods and variational principles, the basic expressions governing the behavior of the structure are then obtained. In the incremental solution process, the stiffness properties of the structure are continuously updated in order to properly account for large changes in the geometry of the structure.

The computer program developed during the course of this study is referred at as GWU-SAP, or the George Washington University Stability Analysis Program.     

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.     

CONFAP—a computer program for inelastic analysis of reinforced concrete framed structures

This paper presents a computer program CONFAP for the inelastic analysis of reinforced concrete framed structures. A unified formulation of the inelastic analysis as a Linear Complementarity Problem is explained. The computer program is described with the aid of a flow chart and significant computational steps involved in the program are given. The computational efficiency of CONFAP and its applicability to large structures is demonstrated through three selected examples.     

Numerical yield line analysis

A numerical method based on the virtual work approach of the yield line theory is presented. The method consists of computing the yield load of a plate based on the geometry of an assumed collapse mechanism defined by means of nodes, planes and lines. Since the method is numerical, it allows the yield line analysis of plates with complex shapes, assumed mechanisms and loadings. Algorithms for the calculations of the work done by the external loads on the plate and the internal work dissipated by the yield lines in the assumed mechanism are described. The features of a computer program are outlined, and a numerical example of the numerical yield line analysis of a reinforced concrete slab is given.