应用数学和力学

1994 Vol. 15, No. 4

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The Asymptotic ExPression of the Solutlon of the Cauchy’s Problem for a Higher order Linear ordinary Differential Equation when the Limit Equation Has Singularity

Cai Jian-ping, Lin Zong-chi

1994, 15(4): 283-287.

Abstract(1852) PDF(444)

Abstract:
In this paper we consider the asymptotic expression of the solution of the Cauchy's problem for a higher order equation when the limit equation has singularity.In orderto construct the asymptotic expression of the solution,the region is divided into threesub-areas.In every small region,the solution of the differential equation is different.

Generallzed Strongly Nonlinear Quasi-Complementarlty Problems

Li Hong-mei, Ding Xie-ping

1994, 15(4): 289-296.

Abstract(2044) PDF(455)

Abstract:
Using the algorithm in this paper,we prove the existence of solutions to the generalized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm.Our results improve and extend thecorresponding results of Noor and Chang-Huang.Moreover,a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given.It is shown that the approximate solution obtained by the iterative scheme converges to the exact solution of this quasi-complementarity problem.

The Sliding Surface Algorithms in Three Dimensional Dynamic Finite Element Code

Song Shun-cheng

1994, 15(4): 297-301.

Abstract(1670) PDF(499)

Abstract:
In this paper,the sliding surface algorithms in dynamic finite element analysis ofhigh velocity impact are presented.With these algorithms,the momentum and the angular momentum of the element can be conserved.The calculated examples show that the calculation using these algorithms in dynamic finite element analysis of high velocity is valid and stable.

An lmplicit Algorithm of Thin Layer Equations In Vlscous Transonic,Two-Phase Nozzle Flow

He Hong-qing, Hou Xiao, Cai Ti-min, Wu Xing-ping

1994, 15(4): 303-312.

Abstract(1858) PDF(527)

Abstract:
Omitting viscosity along flow direction,we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations.Using theimplicit approximate-factorization algorithm to solve the gasphase governing equ-ations and the characteristic method to follow the tracks of particles,we then obtainedthe full coupled numerical method of two-phase.transonic,turbulent flow.Here,particle size may be grouped,the subsonic boundary condition at entry of nozzle is ireatedby quasi-characteristic method in reference plane and the algebraic model is used forturbulent flow.These methods are applied in viscous two-phase flow.calculation of rocket nozzle and in the prediciton of thrust and specific impulse for solid propellant rocket motor.The calculation results are in good agreement with the measurerment values.Moreover,the influences of different particle radius,different particle mass fraction and particle size grouped on flow field have been discussed,and the influences of particle two-dimensional radial velosity component and viscosity on specific impulse ofrocket motor have been analysed.The method of this paper possesses the advantage of saving computer time.More important,the effect is more obvious for the calculation of particle size being grouped is more obvious.

Slip-Line Field Theory of Transversely Isotrropic Body

Ruan Huai-ning, Wang Wei-xiang

1994, 15(4): 313-322.

Abstract(2464) PDF(492)

Abstract:
A slip-line field theory of transversely isotropic body is proposed in the presentpaper in order to deal with problems in geology and geotechniques.The Goldenblat-Kopnov failure criterion is employed.The parameters in it are treated as functions of tempperature It is applicable to transverse isotropic media in nonuniform temperature field.The basic equtions of plastic deformation are developed while the associated rules of flow are derived.By means of characteristic line theory,slip-line slope formulas and laws of variation of stress and velocity along slip lines are obtained,The indentation on semi-infinite media is calculated.The theory developed in this paper may be simplified into many classical theories such as Mises,Hill,and Coulomb ones,This complicated theory may be applied to geotechniques,geological structures,petroleum industry,mining engineering,etc.

Effects of AMB Parameters on the Dynamicstability of the Rotor

Wang Hong-li, Wu Zhi-qiang

1994, 15(4): 323-327.

Abstract(1846) PDF(538)

Abstract:
The motion equation of the rotor suspended by active magnetic bearing(AMB) is given in this paper after considering the nonlinear characteristics of the force.Fromthe response equation resulted from this Eq.we gained the functions of the jump ra-nge,and examined the effects of the AMB's parameters.

The General Properties of the SPherical Vortices(SV) of n-th Order and the Chaotic Phenomena and of the Ordered Structures of the SV of 3rd order

Shi Chang-chun, Huang Yong-nian, Ye Yi, Jiang Tao

1994, 15(4): 329-335.

Abstract(2030) PDF(425)

Abstract:
The general properties of the spherical vortices(SV)of n-th order are discussedin this paper Numerical calculations are carried out in the case of n=3.We find outsome interesting phenomena concerning the chaotic regions and ordered islands on the Poincaré sections.Interpretations of these phenomena are also given.

CCD Automated Polariscope System and the Stress Analysis Methods

An Li-qian

1994, 15(4): 337-342.

Abstract(2186) PDF(469)

Abstract:
A Linear CCD(change coupled device) automated measurement system and the stress analysis methods are presented in the present paper.The skeleton and the ordersof photoelastic fringes can be acquired rapidly,precisely and in real time by the system.The automatic stress analysis methods in the paper only uses a small amount ofknown data to analyze the stress precisely.

Exact Solution of the Thick Lamlnated open Cylindrical Shells with Four Clamped Edges

Fan Jia-rang, Ding Ke-wei

1994, 15(4): 343-354.

Abstract(2064) PDF(527)

Abstract:
Giving up any assumptions about displacement models and stress distribution,ba-sed on Refs [1] and [2] and introducing δ-function into the present study,the stateequation for the open cylindrical shells with four clamped edges is established,Anidentical exact solution is obtained for the thin,moderately thick and thick laminated open cylindrical shells.

The Compression LS Estimate of Regression Coefficient in Multivariate Linear Model

Chen Shi-ji, Zeng Zhi-bin

1994, 15(4): 355-363.

Abstract(2116) PDF(506)

Abstract:
In this paper,compression LS estimate of the regression coefficient B is considered when the design matrix present ill-condition in multivariate linear model.The MSE(mean square error)of the estimate =Vec is less than theMSE of LS estimate β^* of the regression coefficient β= Vec(B) by choosing the pa-rameter k.Admissibility,numerical stability and relative efficiency of )are proved.The method of determining k value for practical use is also suggested.

Initlal Boundary Value Problems for a Class of Nonlinear Integro-Partial Differential Equations

Cui Shang-bin, Qu Chang-zheng

1994, 15(4): 365-379.

Abstract(2058) PDF(493)

Abstract:
This paper studies the global existence of the classical solutions to the following problem: This problem describes the nonlinear vibrations of finite rods with nonlinear vis-coelasticity.Under certain conditions on σ and f,we obtained the unique existence of the global classical solution of this problem.