组合多面体理论及几何构型设计

根据目前国内网壳形式的现状,提出了一种全部由五边形和六边形网格组成的网壳形式(以下简称组合多面体)。本文首先论述了组合多面体的几何性质,其几何性质的对称性和均匀性为它的实际应用提供了前提条件;然后又总结了这种组合多面体的面数计算公式,说明这样的组合多面体有无穷多个;之后根据节点突角和相等原理,分别算出了32面体,42面体,92面体,122面体的六边形构型,节点构型,杆长类型和突角和,又列出了162面体,252面体,272面体,482面体,752面体的这种性质,进而总结了这些特性间的关系,为组合多面体的建模提供了依据。

Effective grouting area of jointed slope and stress deformation responses by numerical analysis with FLAC^(3D)

To study the grouting reinforcement mechanism in jointed rock slope, first, the theoretical deduction was done to calculate the critical length of slipping if the slope angle is larger than that of joint inclination; Second, the numerical calculation model was founded by FLAG^3D, so as to find the stress and deformation responses of rock mass in the state before and after grouting, the analysis results show that the range between the boundary of critical slipping block and the joint plane that passes the slope toe is the effective grouting area （EGA）. After excavation, large deformation occurs along the joint plane. After grouting, the displacements of rock particles become uniform and continuous, and large deformations along the joint plane are controlled; the dynamic displacement can re- flect the deformation response of slope during excavation in the state before and after grouting, as well as the shear location of potential slip plane. After grouting, the dynamic displacement of each monitoring point reaches the peak value with very few time steps, which indicate that the parameters of the joint plane, such as strength and stiffness, are improved; the stress field becomes uniform. Tensile area reduces gradually; whole stability of the slope and its ability to resist tensile and shear stress are improved greatly.

Stability analysis unit and spatial distribution pattern of the terrain texture in the northern Shaanxi Loess Plateau

Terrain texture analysis is an important method of digital terrain analysis in quantitative geomorphological research and in the exploration of the spatial heterogeneity and autocorrelation of terrain features. However, a major issue often neglected in previous studies is the calculation unit of the terrain texture, that is, the stability analysis unit. As the test size increases, the derived terrain textures become increasingly similar so that their differences can be ignored. The test size of terrain texture is defined as the stability analysis unit. This study randomly selected 48 areas within the Loess Plateau in northern Shaanxi in China as the study sites and used the gray level co-occurrence matrix to calculate the terrain texture. The stability analysis unit of the terrain texture was then extracted, and its spatial distribution pattern in the Loess Plateau was studiedusing spatial interpolation method. Four terrain texture metrics, i.e., homogeneity, energy, correlation, and contrast, were extracted on the basis of the stability analysis unit, and the spatial variation patterns of these parameters were studied. Results showed that the spatial distribution pattern and the terrain texture metrics reflected a trend of high–low–high from north to south, which correlated with the spatial distribution of the landforms at the Loess Plateau. In addition, the terrain texture measures was significantly correlated with the terrain factors of gully density and slope, and this relationship showed that terrain texture measures based on the stability analysis unit could reflect the basic characteristics of terrain morphology. The stability analysis unit provided a reasonable analytical scale for terrain texture analysis and could be used as a measure of the regional topography to accurately describe basic terrain characteristics.

Relationship between oceanic heat content and sea surface height on interannual time scale

The relationship between heat content and the interannual time scale is examined with satellite sea surface height （SSH） in the global ocean on altimeter measurements, historical hydrography, and model assimilation outputs. Results show that correlation between altimetric SSH and heat content in the upper 700 m calculated from Ishii data is geographically nonuniform. In the tropical ocean, heat content and SSH are strongly correlated and exhibit nearly the same interannual variations. In the polar ocean, their correlation is relatively weak. Further analysis with Simple Ocean Data Assimilation outputs shows that such nonuniform distribution is not from dynamical origin but from the limited integral depth selected to calculate heat content. The integral depth of 700 m is inadequate to capture variation of the deep main thermocline in the polar region. The halosteric effect also contributes to the nonuniform pattern of correlation, because saline contraction becomes significant in the polar ocean owing to low temperature.

A modified model of a single rock joint's shear behavior in limestone specimens

The shear behavior of a single rock joint in limestone specimens,under a constant normal load(CNL),was analyzed in this study.Test specimens with different asperity roughness were prepared and tested.Goodman's model of a rock joint's shear behavior,under CNL,was modified to render a better representation of the data obtained.The model's applicability was validated.The proposed model showed better correlation with experimental data.It also,requires fewer variables.The steps to calculate all the necessary variables for the model are discussed.

Numerical Calculation of Channel Dredging Volume Using 3D Digital Stratum Model

Prediction of channel dredging volume is critical for project cost estimation. However, many proposed approximate methods are not accurate. This paper presents a novel numerical method to accurately calculate the dredg- ing volume using a 3D stratum model (DSM) and a channel surface model. First, the 3D DSM is constructed rapidly yet accurately from non-uniform rational B-splines (NURBS) surfaces through Boolean operation between a physical terrain model and a stratum surfaces model. Then, a parametric channel surface model is built from cross-section data and a channel center line using code implemented in the VC++ programming language. Finally, the volumes of different types of physical stratums can be calculated automatically and hierarchically to determine the dredging volume. Practical application shows that the DSM method is more precise and faster compared to the section method, and that the implementation of the developed software provides an interactive graphical user interface and visual presentation.

Quantitative analysis on influencing factors for interface propagation-based thermal conductivity measurement method during solid-liquid transition

The recently proposed interface propagation-based method has shown its advantages in obtaining the thermal conductivity of phase change materials during solid-liquid transition over conventional techniques. However, in previous investigation, the analysis on the measurement error was qualitative and only focused on the total effects on the measurement without decoupling the influencing factors. This paper discusses the effects of influencing factors on the measurement results for the interface propagation-based method. Numerical simulations were performed to explore the influencing factors, namely model simplification, subcooling and natural convection, along with their impact on the measurement process and corresponding measurement results. The numerical solutions were provided in terms of moving curves of the solid-liquid interface and the predicted values of thermal conductivity. Results indicated that the impact of simplified model was strongly dependent on Stefan number of the melting process. The degree of subcooling would lead to underestimated values for thermal conductivity prediction. The natural convection would intensify the heat transfer rate in the liquid region, thereby overestimating the obtained results of thermal conductivity. Correlations and experimental guidelines are provided. The relative errors are limited in ±1.5%,±3%and ±2% corresponding to the impact of simplified model, subcooling and natural convection, respectively.

Study of the features of outburst caused by rock cross-cut coal uncovering and the law of gas dilatation energy release

To study the law of gas dilatation energy release of rock cross-cut coal uncovering face, according to the analysis of the physical parameters distribution features of coal and rock mass in front of crosscut face,the equations of elastic potential of coal and gas dilatation energy theory were set up to process a contrast calculation of the sizes of two kinds of energy. The results show that gas dilatation energy is the uppermost energy source causing outburst occurrence. Furthermore, the mathematical model of spherical flow field gas dilatation energy release was established and MATLAB software was applied to make a numerical calculation analysis on the law of gas dilatation energy release. The results indicate that the gas dilatation energy is closely related to gas parameters and its energy index does reflect the possibility of coal seam outburst.

Study on How to Design Knitted Fabric Pattern with Mathematical Theory

To improve design capabilities for the knitted fabric pattern,a preliminary study is carried out for the design method.Based on mathematical theory,pattern could be created automatically by computer with inputting different parameters for mathematical functions.The knitted fabric simulation is realized by M1 CAD pattern preparation system of STOLL Company.In the pattern,different color unit is replaced by obverse stitch with different color,or by obverse stitch and reverse stitch with the same color separately,after that the effects of knitted fabrics could be simulated.Designing with this method,it would not only help to acquire a great of diversity patterns,but also improve design efficiency and save cost.

Computing the topology of an arrangement of implicitly defined real algebraic plane curves~§

We introduce a new algebraic approach dealing with the problem of computing the topology of an arrangement of a finite set of real algebraic plane curves presented implicitly. The main achievement of the presented method is a complete avoidance of irrational numbers that appear when using the sweeping method in the classical way for solving the problem at hand. Therefore, it is worth mentioning that the efficiency of the proposed method is only assured for low-degree curves.

Effect of flank angle and friction coefficient on contact stress of turbine rotor

In order to simulate the stress of turbine rotor in aeroengine, based on the ANSYS, the simplification model of the turbine rotor was built up. By applying the simplification model, the contact stress of turbine rotor was computed. The maximum contact stress appears at the chamfer below the flank, which agrees with experiment result. At the same time, the contact stress changing with the flank angle and friction coefficient was calculated, The results show that the contact stress in the flank increases slowly with the increase of flank angle; with the friction coefficient increasing, the contact stress in flank length decreases; the contact stress will not change when the friction coefficient is over 0.25.

NUMERICAL CALCULATION OF THREE-STREAM MIXING FLOW WITH WALL COOLING

The flow and the temperature in the threestream mixing flow of the lobed nozzle mixer-ejector with double-wall diffuser are numerically investigated. The domain of computation is divided into sub-domalns according to the shapes of the double-plate and lobed nozzle. The three-dimensional body-fitted coordinated grids are generated respectively in these sub-domains by solving Lapalace's equations. Grids are dense on the boundaries and orthogonal at the lobe. The grids of all sub-domains compose the whole grid of the domain. In order to avoid the divergence of the computation as the serious non-orthogonality of the grid from the lobe, the co-located grid, SIMPLEC and Chen-Kim modified k-εturbulence model are applied. The great viscosity, the linear and simultaneous cooperation under-relaxation factors are used to solve the coupling of the fluid and solid. Results show that the air is ejected into the double wall section to form the cooling flow. The wall temperature of the double-wall diffuser is lower than that of the single-wall diffuser. The average wall temperature goes down as the diffuser angle increases at the range of 0～5°,otherwise, the result at the range of 5～10°is opposite.

Numerical Simulation on CCOS Controllable Variable

On the basis of Preston hypothesis,the motion relationship between tool and workpiece upon the tools motion in planar model is analyzed.The effect on computer controlled optical surfacing (CCOS) caused by controllable variable is simulated except for the dwelling time,thus,some reference on theory is provided to optimize the former numerical control (NC) model,and fast manufacturing of large departure aspherics is realized.

Alternative Monte Carlo Approach for General Global Illumination

An alternative Monte Carlo strategy for the computation of global illumination problem was presented.The proposed approach provided a new and optimal way for solving Monte Carlo global illumination based on the zero variance importance sampling procedure. A new importance driven Monte Carlo global illumination algorithm in the framework of the new computing scheme was developed and implemented. Results, which were obtained by rendering test scenes, show that this new framework and the newly derived algorithm are effective and promising.

Crosswind stability of high-speed trains in special cuts

Analysis of the aerodynamic performance of high-speed trains in special cuts would provide references for the critical overturning velocity and complement the operation safety management under strong winds.This work was conducted to investigate the flow structure around trains under different cut depths,slope angles using computational fluid dynamics(CFD).The high-speed train was considered with bogies and inter-carriage gaps.And the accuracy of the numerical method was validated by combining with the experimental data of wind tunnel tests.Then,the variations of aerodynamic forces and surface pressure distribution of the train were mainly analyzed.The results show that the surroundings of cuts along the railway line have a great effect on the crosswind stability of trains.With the slope angle and depth of the cut increasing,the coefficients of aerodynamic forces tend to reduce.An angle of 75°is chosen as the optimum one for the follow-up research.Under different depth conditions,the reasonable cut depth for high-speed trains to run safely is 3 m lower than that of the conventional cut whose slope ratio is 1:1.5.Furthermore,the windward slope angle is more important than the leeward one for the train aerodynamic performance.Due to the shield of appropriate cuts,the train body is in a minor positive pressure environment.Thus,designing a suitable cut can contribute to improving the operation safety of high-speed trains.

Adaptive Surface Reconstruction Based on Tensor Product Algebraic Splines

Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput. Math., 17 （2002）, pp. 135-152） based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler＇s method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.

Analysis on Tectonic Movement of the Longmenshan Fault Zone before the Wenchuan M_S 8. 0 Great Earthquake

On the basis of elastic rebound theory,using the horizontal velocity field of the Chinese mainland calculated from GPS data during three observation periods from 1999 to 2007,the velocity components that are parallel and plumb to the fault zone are calculated respectively for different periods,and then relative ground movements of two sides of the fault zone are analyzed with power function fitting and graphics. The results show that the relative ground movement shows right-lateral shear deformation before the Wenchuan MS8. 0 earthquake,and at the same time the movement was hindered by the Longmenshan fault zone. Thus,this result has positive significance for distinguishing the elastic strain energy accumulation and deformation anomaly in an earthquake preparation process,and for conducting further research on earthquake prediction.

Technique Development and Application——Construction of a Beowulf Cluster for Parallel Computing

The large-scale computations are often performed in science and engineering areas such as numerical weather forecasting, astrophysics, energy resources exploration, nuclear weapon design, and plasma fusion research etc. Many applications in these areas need super computing power. The traditional mode of sequential processing cannot meet the demands of those computations, thus, parallel processing（PP） is the main way of high performance computing （HPC） now.

Research on the Causes and Coping Strategies of the Land Subsidence Caused by the Tunnel Construction Projects

In this paper, we conduct research on the causes and coping strategies of the land subsidence caused by the tunnel construction projects. We analyze the issues from the following of the perspectives. （1） Analysis method. To solve large scale system of the development of computer hardware and the numerical calculation method, we use the basic analysis to deal with it. （2） The empirical of methods. Ground motion is usually leads to the basic development of the inclined tunnel surface vertical displacement, the result of the movement process can turn to a settling tank. （3） Machine learning based approaches. In one of biggest difficulties when using neural network method is to obtain all possible parameters related to ground subsidence, we use the machine learning model to handle the challenge. In the final part, we show prospect for the future research, we will combine more numerical analysis tools to optimize the current methodology.

The Second-Order Imaginary Plane Method and Its Calculation Accuracy

In this paper, the basic principles and mathematical process of the Second-order Imaginary Plane Method (IPM) for modeling the radiative heat transfer are analysed and proved in detail. Through the numerical computation for the real process of the radiative heat transfer using the Second-order IPM,the previous IPM (the first-order), the Analytic Method and the Zone Method, it was shown that the calculation accuracy of the Secondr-order IPM is much higher than that of the first-order IPM, and its demand to computer capacity and time consuming is much lower than that of the Zone Method or the Analytic Method. It is verilied that the method is more effective and has a higher accuracy for modeling radiative heat transfer in engineering.