应用数学和力学

1995 Vol. 16, No. 10

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The Analytical Study on the Laser Induced Reverse-Plugging Effect by Using the Classical Elastic Plate Theory(Ⅰ)——Temperature Fields

Zhou Yichun, Duan Zhuping, Wang Chunqui

1995, 16(10): 851-860.

Abstract(2080) PDF(621)

Abstract:
The temperature distributions in the metallic foils induced by spatially cylindrical long-pulsed laser is examined in order to analyse the newly-discovered reverse-pluggingeffect(RPE).An exact solution for the temperature fields is derived by using the Hankel transform and Laplace transform.Numerical results are obtained for bothspatial distributions with Gaussian and cylindrical types.The results show that thespatially cylindrical distribution of laser offers a formidable potential for the RPE.

A Condensed Method for Linear Complementary Equations of Elasto-Plastic Problems

Yin Fuxin, Sun Huanchun

1995, 16(10): 861-871.

Abstract(1905) PDF(566)

Abstract:
This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promotes the efficiency of the elasto-plastic analvsis for large scale structures.

Two-Phase Flow for a Horizontal Well Penetrating a Naturally Fractured Reservoir with Edge Water Injection

Guo Dali, Liu Ciqun

1995, 16(10): 873-878.

Abstract(1933) PDF(523)

Abstract:
This paper examines the two-phase flow for a horizontal well penetrating anaturally fractured reservoir with edge water injection by means of a.fixed streamlinemodel. The mathematical model of the vertical two-dimensional flow or oil-water for ahorizontal well in a medium with double-porosity is established, and whose accuratesolutions are obtained by using the characteristic method. The saturation distributionsin the fractured system and the matrix system as well as the formula of the time ofwater free production are presented. All these results provide a theoretical basis and acomputing method for oil displacement by edge water from naturally fractured reservoirs.

nvariant Manifolds and Their Stability in a Three-Dimensional Measure-preserving Mapping System

Liu Jie

1995, 16(10): 879-888.

Abstract(2556) PDF(589)

Abstract:
In the paper researches on a three-dimensional measure-preserving mapping system are made,wthich is the three-dimensional extension of the Keplerian mapping.With the formal series method the expressions of the invariant curves and invariant tori are obtained.Finally the stability of these invariant manifolds is also discussed.

Analysis of Stability on Elastic Plates with lnitial lmperfections

Xu Kaiyu

1995, 16(10): 887-894.

Abstract(2257) PDF(591)

Abstract:
On the basis of Marguerre equations,the influence on a bifurcation diagram of am elatic plate affected by initial deflection imperfection and transverse loading is studied with the help of the singularity theory.Thes paper applies universal unfoldingprinciples,it is put forward that the unstable analysis of thes problem can transform into the study of a triple algebraic equation in the neighborhood of a simple eigenvalue.Thus the bifurcated states are decided,and the bifurcation diagrams are drawn up following distinct paramentrs. Then the quantitative series of interfering with eigenvalues are discussed.

Multiplicity Results for a Fourth-Order Boundary Value Problem

Ma Ruyun, Ma Qinsheng

1995, 16(10): 895-902.

Abstract(1932) PDF(452)

Abstract:
This paper deals with multiplicity results for nonlinear elastic equations of the y(1)-α₁y+β₁y"+g(x,y,y")=e,02(0.1),g:[0,1]×R×R→R is a bouuded continuous function. and the pair(α₁,β₁) satisfies α₁+(0+0.5)²π²β₁=(0+0.5)⁴π⁴ and α₁+(k+0.5)²π²β₁≠(k+0.5)⁴π⁴,for all ∀k∈N.

A Model ldentification Method of Vibrating Structures from lncomplete Modal lnformation

Zheng Xiaoping, Yao Zhenhan, Qu Shisheng

1995, 16(10): 903-908.

Abstract(2083) PDF(541)

Abstract:
The accurate mathematical models for complicated structures are very difficult to construct.The work presented here provides an identification method for estimating the mass.damping,and stiffness matrices of linear dynamical systems from incomplete experimental data.The mass,stiffness and damping matrices are assumed to be real,symmetric,and positive definite The partial set of experimental complex eigenvalues and corresponding eigenvectors are given.In the proposed method the least squares algorithm is combined with the iteration technique to determine systems identified matrices and corresponding design parameters.Seeveral illustative examples,are presented to demonstrate the reliability of the proposed method.It is emphasized that the mass,damping and stiffness matrices can be identified simultaneously.

The Exact Solutions of Elastic-Plastic Crack Line Field for Mode Ⅱ Plane Stress Crack

Yi Zhijian, Wang Shijie, Wang Xiangjian

1995, 16(10): 909-916.

Abstract(2598) PDF(652)

Abstract:
The near crack line field analysis method has been used io investigate into theexact elastic-plastic solutions of a mode Ⅱ crack under plane stress condilion in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theory.hare been completely. dbandoned and the correct formulations of matching conditionsat the elaslic-plastic boundary. have been given. By, matching the general solution ofthe plastic slress field(bul not the special solution used to be adopted) with the exactelastic stress field(but not the crack tip K-dominant field) at the elastic-plasticboundary, near the crack line, the plastic stresses, the length of the plastic zone and theunit normal vector of the elastic-plastic boundary.which are sufficiently precise near the crack line region,have been given.

The Calculation of Eigenvalues for the Stationary Perturbation of Couette-Poiseuille Flow

Song Jinbao, Chen Jianning

1995, 16(10): 917-926.

Abstract(1975) PDF(561)

Abstract:
The problem considered is that of two-dimensional viscous flow in a straightchannel.The decay of a stationary perturbation from the Couette=Poiseuille flow in the douwnstream is sought.A differential eigenvalue equation resembling the Orr-Sommerfeld equation is solved by using a spectral method and an initial-value method(the compound matrix method) for values of the Reynolds number R between O and 2000.The eigenvalues are presemed for several of interesting cases with differentmeasures of mass flux These eigenvalues derermine the rate of decay for the purturbation.

Necessary and Sufficient Conditions for the Absolute Stability of Discrete Type Lurie Control System

Zhang Jiye

1995, 16(10): 927-932.

Abstract(2816) PDF(543)

Abstract:
In this paper. it is discussed that the absolute for zero solution of the discrete type Lurie control system in which the nonlinear function f(σ) satisfying conditions follows f(0)=0,σf(σ)>0(σ≠0)(2) or f(0)=0,0≤k₁≤f(σ)/σ≤k₂<+∞(σ≠0)(3) It gives the necessary and sufficient conditions for the absolute stability for system(1) under conditions(2).We also obtain the sufficient for absolute stability of the simplified system of(1) under conditions(3).

Plastic Buckling of Stiffened Torispherical Shell

Hao Gang, Zeng Guangwu, Hao Qiang

1995, 16(10): 933-941.

Abstract(2034) PDF(503)

Abstract:
This paper uses the nonlinear prebuckling consisten theory to analyse the plasticbuckling problem of of stiffned torispherical shell under uniform exlernal pressure. Thebuckling equation and energy expressions of the shell are built. the calculation formulais presented Numerical examples show that method in ths paper has betterprecision and the calculating process is very simple.

The Analysis of Stability of Bingham Fluid Flowing Down and lnclined Plane

Wang Peiguang, Wang Zhendong

1995, 16(10): 943-948.

Abstract(2171) PDF(619)

Abstract:
In this paper, the stability problem of Bingham fluids flowing down an inclinedplane is studied with respect to two dimensional disturbances. The crilical Reynolodsnumber is given in ihe case of long waves, and the effect of yield stress on stability is analysed.