应用数学和力学

2000 Vol. 21, No. 5

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Numerical Schemes With High Order of Accuracy for the Computation of Shock Waves

Yuan Xiangjiang, Zhou Heng

2000, 21(5): 441-450.

Abstract(2610) PDF(1141)

Abstract:
High order accurate scheme is highly desirable for flow computation with shocks. After analysis has been made for the reason of the generation of non-physical oscillations around the shock in numerical computations, a third order, upwind biased, shock capturing scheme was proposed. Also, a new shock fitting method, called pseudo shock fitting method, was suggested, which in principle can be with any order of accuracy. Test cases for one dimensional flows show that the new method is very satisfactory.

Inelastic Coupled Response of Eccentric Buildings With Respect to Different Earthquake Intensity

Cai Xianhui, Wu Ruifeng, Qi Baohui

2000, 21(5): 451-458.

Abstract(2041) PDF(641)

Abstract:
Using five-story shear models, the inelastic torsional coupled response of eccentric buildings to different earthquake intensity was studied. Results show that the torsional couple degree is closely related to the strength distribution of the resisting elements. Generally, the building designed by spectral modal analysis method has a tendency to move translationally as the earthquake intensity increases. The building designed by proportion rigidity method will rotate heavily to moderate earthquake, but when it is intensively excited into the inelastic phase, the coupling would decrease slightly, but could not be neglected.

On Monotone Iterative Method for Initial Value Problems of Nonlinear Second Order Integrodifferential Equations in Banach Spaces

Chen Fangqi, Chen Yushu

2000, 21(5): 459-467.

Abstract(2228) PDF(770)

Abstract:
Using the monot one iterative method and M? nch fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second order integrodifferential equations in Banach spaces were studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.

K-ε-T Model of Dense Liquid-Solid Two-Phase Turbulent Flow and Its Application to the Pipe Flow

Wei Jinjia, Hu Chunbo, Jiang Peizheng

2000, 21(5): 468-476.

Abstract(2140) PDF(723)

Abstract:
To predict the characteristics of dense liquid-solid two-phase flow, K-ε-T model is established, in which the turbulent flow of fluid phase is described with fluid turbulent kinetic energy K_f and its dissipation rate ε_f, and the particles random motion is described with particle turbulent energy K_p and its dissipation rate ε_p and pseudothermal temperature T_p. The governing equations are also derived. With K-ε-T model, numerical study of dense liquid-solid two-phase turbulent up-flow in a pipe is performed. The calculated results are in good agreement with experimental data of Alajbegovic et al. (1994), and some flow features are captured.

On the Refined First-Order Shear Deformation Plate Theory of Kûrmûn Type

Zhang Jianwu, Li Qi, Shu Yongping

2000, 21(5): 477-482.

Abstract(2222) PDF(715)

Abstract:
A new refined first-order shear-deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation are imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be made by the engineering theory to a class of shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear-deformable plates. Reduced forms of the generalized Karman equations are derived consequently, which are found identical to those existing in the literature.

A Discrete Algorithm for Complex Frequency-Domain Convolutions

Cai Kunbao, Yang Ruifang, Yu Jihui

2000, 21(5): 483-487.

Abstract(2349) PDF(628)

Abstract:
A discrete algorithm suitable for the computation of complex frequency-domain convolution on computers was derived. The Durbin's numerical inversion of Laplace transforms can be used to figure out the time-domain digital solution of the result of complex frequency-domain convolutions. Compared with the digital solutions and corresponding analytical solutions, it is shown that the digital solutions have high precision.

Noether’s Theorem for Nonholonomic Systems of Non-Chetaev’s Type With Unilateral Constraints in Event Space

Li Yuancheng, Zhang Yi, Liang Jinghui

2000, 21(5): 488-493.

Abstract(2796) PDF(913)

Abstract:
To study the Noether's theorem of nonholonomic systems of non-Chetaev's type with unilateral constraints in event space, firstly, the principle of D' Alembert-Lagrange for the systems with unilateral constraints in event space is presented, secondly, the Noether's theorem and the Noether's inverse theorem for the nonholonomic systems of non-Chetaev' s type with unilateral constraints in event space are studied and obtained, which is based upon the invariance of the differential variational principle under the infinitesimal transformations of group, finally, an example is given to illustrate the application of the result.

Lie Symmetries and Conserved Quantities of Rotational Relativistic Systems

Fu Jingli, Chen Xiangwei, Luo Shaokai

2000, 21(5): 495-500.

Abstract(2884) PDF(719)

Abstract:
The Lie symmetries and conserved quantities of the rotational relativistic holonomic and nonholonomic systems were studied. By defining the infinitesimal transformations' generators and by using the invariance of the differential equations under the infinitesimal transformations, the determining equations of Lie symmetries for the rotational ralativistic mechanical systems are established. The structure equations and the forms of conserved quantities are obtained. An example to illustrate the application of the results is given.

Least-Squares Mixed Finite Element Method for a Class of Stokes Equation

Gu Haiming, Yang Danping, Sui Shulin, Liu Xinmin

2000, 21(5): 501-510.

Abstract(2163) PDF(732)

Abstract:
A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal L² and H¹ -error estimates are derived under the standard regularity assumption on the finite element partition(the LBB-condition is not required). For the evolutionary equation, optimal L² estimates are derived under the conventional Raviart-Thomas spaces.

Study of the Nonlinear Three-Dimensional Debye Screening in Plasmas

Lin Chang, Zhang Xiulian

2000, 21(5): 511-515.

Abstract(1827) PDF(687)

Abstract:
The nonlinear three-dimensional Debye screening in plasmas is investigated. A new kind of analytical equation, which is in agreement with the three-dimensional Poisson equation for the nonlinear Debye potential, is obtained. It is shown that the symmetry distribution of the Debye screening in plasmas can be described by the equation.

Some Bounded Results of θ(t)-Type Singular Integral Operators

Zhao Kai

2000, 21(5): 516-522.

Abstract(2433) PDF(613)

Abstract:
Let B be a Banach space in UMD with an unconditional basis. The boundedness of the θ(t) -type singular integral operators in L_B^p(Rⁿ), (1≤p<+∞) and H_B¹(Rⁿ) spaces are discussed.

Comprehensive Mathematical Model of Microcirculatory Dynamics(Ⅱ)——Calculation and the Results

Guo Zhongsan, Xiao Fan, Guo Siwen, Wu Yueqing, Gu Leye

2000, 21(5): 523-528.

Abstract(2347) PDF(688)

Abstract:
The mathematical model described in Part I was solved using "influence line method" combining analytical method and finite element method. Many important aspects of microcirculatory dynamics were analyzed and discussed. It show that interstitial fluid pressure changes its sign twice within one arteriolar vasomotion period and it is therefor not important that interstitial fluid pressure is a little higher or lower than atmospheric pressure; arteriolar vasomotion can periodically result in lymph formation and interstitial total pressure plays an important role in this procedure; local regulation of microcirculation can meet metabolic need to some extent in the form of dynamic equilibrium. The property of arteriole as a "resistant vessel" and the efficiency of microvascular network as heat exchanger are also shown. These results show that the comprehensive mathematical model developed in Part I is physiologically reasonable.

Oscillation of Solutions for a Class of Nonlinear Neutral Parabolic Differential Equations Boundary Value Problem

Wang Peiguang

2000, 21(5): 529-534.

Abstract(2192) PDF(738)

Abstract:
A class of nonlinear neutral partial differ ential equations was considered, and some oscillation criteria for such equations subject to two different boundary value conditions are established.

Bending of Rectangular Plate With Each Edges Arbitrary a Point Supported Under a Concentrated Load

Bian Yuhong

2000, 21(5): 535-540.

Abstract(2454) PDF(519)

Abstract:
The reciprocal theorem was applied to solve the bending of the rectangular plates with each edges arbitrary a point supported under a concentrated load, the exact solutions and computation example are given.

An Analogue Rotated Vector Field of Polynomial System

Shen Boqian

2000, 21(5): 541-546.

Abstract(2270) PDF(625)

Abstract:
A class of polynomial system was structured, which depends on a parameter δ. When D monotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand (or reduce) together with the δ. But the expansion (or reduction) of these limit cycles is not surely monotonous. This vector field is like the rotated vector field. So these limit cycles of the polynomial system are called to constitute an "analogue rotated vector field" with δ. They may become an effective tool to study the bifurcation of multiple limit cycle or fine separatrix cycle.

The Comprehension, Some Problems and Suggestions to Symbolic Vector Method and Some Defenses for Gibbs’ Symbol

Sheng Kemin, Xue Zhenting, Tang Jinsheng, Huang Xuemei

2000, 21(5): 547-550.

Abstract(2291) PDF(1020)

Abstract:
The comprehension of Prof. Tai's symbolic vector method in vector analysis is presented, some problems are found and some suggestions are provided to solve them. Some defenses for Gibbs' symbol have been made as well.