应用数学和力学

1988 Vol. 9, No. 7

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A Theory of Classical Spacetime, Part Ⅱ:Eddington’s Identification

Yu Xin

1988, 9(7): 567-570.

Abstract(1655) PDF(450)

Abstract:
Based on the SU(2)-structure, the identification procedures of Eddington and Weyl are followed in order to see what logical conclusions these two schemes lead to.

Weakly Nonlinear Theory versus Theory of Secondary Instability for Plane Poiseuille Flow

Zhao Geng-fu, Zhou Heng

1988, 9(7): 571-576.

Abstract(1798) PDF(482)

Abstract:
In [1] the theory of secondary instability for plane Poiseuille flow was proposed. In this paper the weakly nonlinear theory is used to investigate the same problem. The results are consistent with those of the theorv of secondary instability. It indicates that for plane Poiseuille flow there exists a certain intrinsic relation between the weakly nonlinear theory and the theory of secondary instability.

Numerical Calculation For The Coefficients of Stokes Harmonic Waves of High Order

Song Tao, Li Jia-chun

1988, 9(7): 577-592.

Abstract(1516) PDF(504)

Abstract:
This paper has reformulated the mathematical model and boundary conditions in the semi-physical plan (x,ψ)by using W.H.Hui's method and suggested two new ways of numerical calculation for the coefficients of Stokes harmonic waves of high order. By transforming the perturbation parameter into a new one, we refind Cokelet's results (1977) of phase speed and semi-waveheight expressions.

The Dynamic analysis of the Vasomotion in Microcirculation

Wu Wang-yi, Wu Ning-zhong

1988, 9(7): 593-598.

Abstract(1788) PDF(654)

Abstract:
The vasomolion of the nlicrocireulation which has been observed in experiments is studied with a simple model of the fluid dynamics. The influence of the vasomotion on the blood flow in microvcssels is analysed and the streamlines, velocity and pressure distribution and the variation of the flow rate are presented.

Variational Principle of Hybrid Energy and the Fundamentals of 3-D Laminate Theory——A New Approach for the Analysis of Interlaminar Stresses in Composite Laminates

Huang Qian

1988, 9(7): 599-608.

Abstract(1810) PDF(521)

Abstract:
This paper discusses the discontinuity of stresses and strains atinterlaminar sirfacesof the eomposne laminate and presents a 3-D laminate theory for composite materials.This paper also presents a new type of elastic energy based on the globally continuous variables in laminates, different front the traditional potential energy and complementary energy. Then, a variatinal principle corresponding to the 3-D laminate theory is developed. The theory and the principle could he a basis of verifying the 2-D laminate theory and determining the interlarninar stresses near the free edges.

Shooting Method in Singular Perturbation Problem of Ordinary Differential Eauations with boundary Layers

Ling Fu-hua, Li Ji-yao

1988, 9(7): 609-615.

Abstract(2237) PDF(929)

Abstract:
By using the adaptive steplength integration scheme with a shooting iechnique a rather difficult singualr perturbation problem of ordinctry differential equations with houndary layers can be calculated effectivcly.Computing examples are given in this paper, which show the convergence within one iterdtion of the method in the case of a lintear problem, the efficiency of the method for many boundary lavers and turning points, especially the convenience in calculating muliple solutions. A compartson with traditional difference method is given at the end of this paper.

Investigation of the Stability for Inviscid Compressible Swirling Flow Between Concentric Cylinders

Xia Nan, Yin Xie-yuan

1988, 9(7): 617-628.

Abstract(1882) PDF(458)

Abstract:
The temporal stability on inviscid compressible swirling flow between two concentric cylinders is investigated. First, a linearized differential equation is derived. Two stability criteria are derived for compressible swirling flow by an analytic method analogous to Ludwieg 's method. A finite-difference numerical method is then used to solve the eigenvalue problem of this differential equation, to get temporal growth rate and to check these stabilitv criteria derived. Finally,the effect of compressibility for stability is disscused.

Singular Perturbation Solution of Boundary-Value Problem for a Second-Order Differential-Difference Equation

Xu Jun-tao

1988, 9(7): 629-640.

Abstract(1528) PDF(497)

Abstract:
It this paper, the method of two-variables expansion is used to construct boundary layer terms of asymptotic solution of the boundary-value problem for a second-order DDE. The n-order formal asymptotic solution is obtained and the error is estimated. Thus the existence of uniformly valid asymptotic solution is proved.

The Application of Generalized Variational Principle in Finite Element-Semianalytical Method

Tan Bang-ben

1988, 9(7): 641-649.

Abstract(1611) PDF(397)

Abstract:
The method developed in this paper is inspired by the viewpoint in reference [1] that sufficient attention has not been paid to the value of the generalized varialional principle in dealing with the boundary conditions in the finite element method. This, method applies the generalized varialional principle and chooses the series constituted by spline junction multiplied by sinusoidal junction and added by polynomial as the approximate deflection of plates and shells. By taking the deflection problem of thin plate, it shows that this method can solve the coupling problem in the finite element-semianalytical method. Compared with the finite elementt method and finite stripe method, this method has much fewer unknown variables and higher precision. Hence, it proposes an effective way to solve this kind of engineering problems by minicomputer.

An Analytical Solution of Wave Forces on Large Square Cylinder

Huang He-ning

1988, 9(7): 651-656.

Abstract(1518) PDF(393)

Abstract:
Wave forces on large square cylinder are determined by using the conformal transformation method. It is found that only for square cylinder, the governing equation is still the Helmlwlt equation after the conformal transformation. An analytical solution of wave forces on square cylinder is presented by using the solution of wave forces on a circular cylinder.

On Analytical Solutions of the Equation utt-cu_xx=au=bu³=0

Wang Mao-hua

1988, 9(7): 657-659.

Abstract(1796) PDF(360)

Abstract:
In this paper a set of the analytical solutions of the equation u_tt-cu_xx+au+bu³=0