应用数学和力学

2002 Vol. 23, No. 4

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One-Dimensional Cellular Automaton Model of Traffic Flow Based on Car-Following Idea

DONG Li-yun, XUE Yu, DAI Shi-qiang

2002, 23(4): 331-337.

Abstract(2536) PDF(1075)

Abstract:
An improved one-dimensional CA traffic model was proposed to describe the highway traffic under the periodic boundary conditions. This model was based on the idea of the car-following model, which claims that the motion of a vehicle at one time step depends on both the its headway and the synchronous motion of the front vehicle, thus including indirectly the influence of its subneighboring vehicle. In addition, the so-called safety distance was introduced to consider the deceleration behavior of vehicles and the stochastic factor was taken into account by introducing the deceleration probability. Meanwhile, the conditional deceleration in the model gives a better description of the phenomena observed on highways. It is found that there exists the metastability and hysteresis effect of traffic flow in the neighborhood of critical density under different initial conditions. Since this model gives a reasonable depiction of the motion of a single vehicle, it is easy to be extended to the case of traffic flow under the control of traffic lights in cities.

The Interaction Problem Between the Elastic Line Inclusions

TAO Fang-ming, ZHANG Ming-huan, TANG Ren-ji

2002, 23(4): 338-346.

Abstract(2249) PDF(597)

Abstract:
Using the engineering model of elastic line-inclusion and the basic solutions of a single inclusion, the interaction problem between line inclusions in an elastic solid was investigated. A set of standard Cauchy-type singular equations of the problem was presented. The stress intensity factors at points of inclusions and the interface stresses of two sides of the inclusion were calculated. Several numerical examples were given. The results could be regarded as a reference to engineering.

XIE Fu-ding, YAN Zhen-ya, ZHANG Hong-qing

2002, 23(4): 347-352.

Abstract(2500) PDF(724)

Abstract:
Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou.

New Studying of Lattice Boltzmann Method for Two-Phase Driven in Porous Media

XU You-sheng, LIU Ci-qun, YU Hui-dan

2002, 23(4): 353-358.

Abstract(2364) PDF(656)

Abstract:
By using the interaction of particles, such as the physical principle of the same attractive each other and the different repulse each other, a new model of Lattice Boltzmann to simulate the two-phase driven in Porous Media was disscussed. The result shows effectively for the problem of two-phase driven in Porous Media. Furthermore, the method economizes on computer time, has less fluc tuation on boundary surface and takes no average measure.

Some Convergence Problem of Iterative Sequences for Accretive and Pseudo-Contractive Type Mappings in Banach Spaces

ZHANG Shi-sheng

2002, 23(4): 359-370.

Abstract(2063) PDF(729)

Abstract:
Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mappings in Banach spaces were obtained. The results improve, extend and include some recent results.

Kinematic Wave Properties of Anisotropic Dynamics Model for Traffic Flow

JIANG Rui, WU Qing-song, ZHU Zuo-jin

2002, 23(4): 371-375.

Abstract(2587) PDF(649)

Abstract:
The analyses of kinematic wave properties of a new dynamics model for traffic flow are carried out. The model does not exhibit the problem that one characteristic speed is always greater than macroscopic traffic speed, and therefore satisfies the requirement that traffic flow is anisotropic. Linear stability analysis shows that the model is stable under certain condition and the condition is obtained. The analyses also indicate that the model has a hierarchy of first and second order waves, and allows the existence of both smooth traveling wave and shock wave. However, the model has a distinctive criterion of shock wave compared with other dynamics models, and the distinction makes the model more realistic in dealing with some traffic problems such as wrong-way travel analysis.

A Mode Ⅱ Crack in a Two-Dimensional Octagonal Quasicrystals

YIN Shu-yuan, ZHOU Wang-min, FAN Tian-you

2002, 23(4): 376-380.

Abstract(2547) PDF(604)

Abstract:
The present study develops the fracture theory for a two-dimensional octagonal quasicrystals. The exact analytic solution of a Mode Ⅱ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate were determined, the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystal and quasicrystal were figured out. These provide important information for studying the deformation and fracture of the new solid phase.

Statistic Modeling of the Creep Behavior of Metal Matrix Composites Based on Finite Element Analysis

YUE Zhu-feng

2002, 23(4): 381-390.

Abstract(2404) PDF(570)

Abstract:
The aim of the paper is to discover the general creep mechanisms for the short fiber reinforcement matrix composites (MMCs) under uniaxial stress states and to build a relationship between the macroscopic steady creep behavior and the material micro geometric parameters. The unit cell models were used to calculate the macroscopic creep behavior with different micro geometric parameters of fibers on different loading directions. The influence of the geometric parameters of the fibers and loading directions on the macroscopic creep behavior had been obtained, and described quantitatively. The matrix/fiber interface had been considered by a third layer, matrix/fiber interlayer, in the unit cells with different creep properties and thickness. Based on the numerical results of the unit cell models, a statistic model had been presented for the plane randomly-distributed-fiber MMCs. The fiber breakage had been taken into account in the statistic model for it starts experimentally early in the creep life. With the distribution of the geometric parameters of the fibers, the results of the statistic model agree well with the experiments. With the statistic model, the influence of the geometric parameters and the breakage of the fibers as well as the properties and thickness of the interlayer on the macroscopic steady creep rate have been discussed.

A New High-Order Multi-Joint Finite Element for Thin-Walled Bar

LI Zheng-liang, BAI Shao-liang, XIE Wei

2002, 23(4): 391-399.

Abstract(2342) PDF(514)

Abstract:
A new high-order multi-joint finite element for thin-walled bar was derived from the Hermite interpolation polynomial and minimum potential energy principle. This element's characteristics are that it is of high accuracy and can be used in finite method analysis of bridge, tall mega-structure building.

Elastic Analysis of Orthotropic Plane Problems by the Spline Fictitious Boundary Element Method

SU Cheng, HAN Da-jian

2002, 23(4): 400-406.

Abstract(2834) PDF(1326)

Abstract:
Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.

On Some Properties of Lienard Systems

HAN Mao-an

2002, 23(4): 407-414.

Abstract(1987) PDF(637)

Abstract:
Some sharp sufficient conditions for generalized Lienard systems to have positive or negative semi-orbits which do not cross the vertical isocline are given. Applications of the main results to some polynomial systems are also presented.

Analytical Solution of Radiation Sound Pressure of Double Cylindrical Shells in Fluid Medium

CHEN Mei-xia, LUO Dong-ping, CHEN Xiao-ning, SHEN Rui-xi

2002, 23(4): 415-421.

Abstract(2143) PDF(668)

Abstract:
The Donnell theory of shell was applied to describe shell motion. The inner and outer shells were stiffened by transverse components. Using deformation harmonious conditions of the interface, the effects of stiffeners were treated as reverse forces and moments on the double cylindrical shell. In the acoustic field produced by vibration and sound radiation of the double shell, the structure dynamic equation, Helmholtz equation in the fluid field and the continuity conditions of the surface of fluid-structure compose the vibration equation coupled by the sound-fluid-structure. The extract of acoustic pressure comes down to the extract of coupling vibration equation. The near field acoustic pressure can be solved directly by complicated calculational methods.

On the Continuity and Differentiability of a Kind of Fractal Interpolation Function

LI Hong-da, YE Zheng-lin, GAO Hang-shan

2002, 23(4): 422-428.

Abstract(2458) PDF(613)

Abstract:
The sufficient conditions of Helder continuity of two kinds of fractal interpolation functions defined by IFS were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable.

A Computational Method for the Navier-Stokes Equations at All Speeds

ZHAO Xing-yan, SU Mo-ming, MIAO Yong-miao

2002, 23(4): 429-435.

Abstract(2576) PDF(1031)

Abstract:
A PLU-SGS method based on a time-derivative preconditioning algorithm and LU-SGS method is developed in order to calculate the Navier-Stokes equations at all speeds. The equations were discretized using AUSMPW scheme in conjunction with the third-order MUSCL scheme with Van Leer limiter. The present method was applied to solve the multidimensional compressible Navier-Stokes equations in curvilinear coordinates. Characteristic boundary conditions based on the eigensystem of the preconditioned equations were employed. In order to examine the performance of present method, driven-cavity flow at various Reynolds numbers and viscous flow through a convergent-divergent nozzle at supersonic were selected to test this method. The computed results were compared with the experimental data or the other numerical results available in literature and good agreements between them are obtained. The results show that the present method is accurate, self-adaptive and stable for a wide range of flow conditions from low speed to supersonic flows.

Role of Underground Structure Deformation Velocity in the Analysis of Blast-Resistant Structures

ZHAO Xiao-bing, FANG Qin

2002, 23(4): 436-440.

Abstract(2367) PDF(419)

Abstract:
The strucural deformation velocity plays a significant role in the dynamic calculation of underground blastresistant stuctures. The motion differentiating equation of a structure system taking into account the role of deformation velocity of the structure will truthfully describe the actual situation of structural vibration. With the one-dimensional plane wave theory, the expression of load on the structural periphery is developed, and the generalized variation principle for the dynamic analysis of underground arched-bar structures is given. At the same time, the results of the numerical calculation are comparted.