应用数学和力学

1994 Vol. 15, No. 3

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Rudimental Equations for Thermo-Elasto-Plastic Stress Analysis during Continuous Casting with Phase Change

Zhao Xing-hua, Cheng Xiao-di

1994, 15(3): 189-197.

Abstract(1825) PDF(511)

Abstract:
Coupled relations among temperature, phase transformation and stress have beendiscussed here in the present paper. Thermo-elasto-plastic constitutive equationsincluding creep and iterative finite element formulation during continuous casting withphase change have also been presented.

The Expression of Stress and Strain at the Tip of Three Dimensional Notch

Qian Jun, Long Yu-qiu

1994, 15(3): 199-208.

Abstract(1931) PDF(589)

Abstract:
The singularity of stress and strain at the tip of three-dimensional notch isanalysed by the power expansion method.the eigenquation of the notch is gainedthrough the boundary conditions of the notch, the eigenvalues under different innerangles of the notch are obtained, the expression of stress and strain at the tip of thenotch is finally derived.

The Conservation Law and the Radiation of General Relativity

Lam ru-yao

1994, 15(3): 209-214.

Abstract(1886) PDF(609)

Abstract:
This paper presents the conservation law of Einstein's General Relativity, in whichthe continuity equation of matter and gravitational field is implicitly derived from theequation of motion of matter. Although the obtained energy-momentum tensor is thesame as the Landau-Lifshitz pseudotensor. the physical and conceptual foundation aredifferent. Two alternative methods to obtain the gravitational radiation are proposed inthis paper as well The radiation will be derived from the equation of motion of matterand geodesic equation separately.

Solution to the Form of Poission Equation by the Boundary Element Methods

Liu Xi-yun

1994, 15(3): 215-220.

Abstract(2042) PDF(631)

Abstract:
In this paper, the domain integral of the form of Poisson equation is translatedinto complete boundary integral by the fundamental solution of higher-order Laplaceoperator, the dimensions of the problem can be contracted into one. The numericalexamples for Stokes equations show that this method is efficient.

Solutions of the General n-th Order Variable Coefficients Linear Difference Equation

Zhou Zhi-hu

1994, 15(3): 221-231.

Abstract(2156) PDF(647)

Abstract:
In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski's sequence convergence.After turning ageneral variable coefficient linear difference equation of the n-th order wichi is turned into a set of operatorequations.we can obtain the solutions of the general n-theth order variable coefficientlinear difference equation.

Effect of Magnetic Fields on Viscous Liquid Column with Finite Length in a Vertical Stralght Tube

Wen Gong-bi, Sun Ke-li

1994, 15(3): 233-243.

Abstract(1665) PDF(616)

Abstract:
The formation of thrombus is closely related to the hydrodynamical conditions.Chandler's experiment and further research shows that the cause thrombus formed inthe lower meniscus may be that the fluid particles at relatively high speed strike on thelower meniscus leading to the gathering of platelet and red blood cells(RBC).Thispaper deals with the motion of viscous liquid column with finite length and two freesurfaces in a vertical straight tube under the action of magnetic fields,numericalsolution is obtained by the time-dependent method in a finite difference technipues.The results show that under the action of a proper magnetic field. the axial velocity atthe lower meniscus near the axis will decrease. strike on the lower meniscus will bereduced and then thrombus formation at the lower meniscus can be avoided.Thisresult provides a guide to further experimental research on the mechanism of thrombusformation and medical treatment to thrombus.

Necessary and Sufficient Criteria for Absolute Stability of the Direct Control System

Zhang Ji-ye, Shu Zhong-zhou

1994, 15(3): 245-251.

Abstract(2102) PDF(456)

Abstract:
In this paper,some necessary and sufficient conditions for absolute stability ofseveral classes of direct control system are given,and the two simplified forms of thecontrol systems obtained twice^[2,4] are discussed.The corresponding results in [7-12]are improved.

Singular Perturbation of lnitial-boundary Value Problems of Reaction Diffusion Equation with Delay

Zhang Xiang

1994, 15(3): 253-258.

Abstract(2123) PDF(486)

Abstract:
In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.

Three-Dimensional Nonlinear Analysis of drill String Structure in Annulus

Liu Yan-qiang, Lü Ying-min

1994, 15(3): 259-272.

Abstract(1904) PDF(529)

Abstract:
Three-dimensional nonlinear analysis of drill string structure in annulus of curvedwellbore is done by using the theory of finite element and Newton-Raphson method.According to the characteristics of its deformation,a method of the description andcomputation of taking different forms of elements for different parameters is advanced.The penalty function method is applied for finding the unknown boundary.the nonlinear effects of curvature of wellbore on the side forces on bit ae shown by the computation.

The Existnece of Periodic Solution of the Fourth Ordinary Non-Linear Differential Equation Caused by Flow-induced Vibration

Gu Qing-fang, Tang Da-qing

1994, 15(3): 273-282.

Abstract(1565) PDF(550)

Abstract:
The vortex-induced vibration is a well-known problem in mechanics,In this paper,with the help fixed point principle, we study. this problem and find the existencecondition of the periodic solution as well as the region of parameters.