应用数学和力学

1994 Vol. 15, No. 5

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The General Solution for Dynamic Response of Nonhomogeneous Beam with Variable Cross Section

Ji Zhen-yi, Yeh Kai-yuan

1994, 15(5): 381-388.

Abstract(2397) PDF(730)

Abstract:
In this paper by means of the exact analytic method ^[1],the general solution for dynamic response of nonhomogeneous beam with variable cross section is obtained under arbitrary resonant load and boundary conditions.The problem is reduced to solvea non-positive differential equation.Generally,it is not solved by variational method.By the present method,the general solution for this problem may be written as an ana-lytic form.Hence,it is convenient for structure optimizing problem.In this paper,its convergence is proved.Numerical examples are given at the end of the paper.which in-dicates satisfactory results can be obtained.

Non-Linear Elastic Theory of Rectangular Reticulated Shallow Shell Structures

Nie Guo-huai, Liu Ren-huai

1994, 15(5): 389-397.

Abstract(1915) PDF(724)

Abstract:
Based on fundamental assumptions,an analysis of the constitutive relations be-tween the internal.forces and deformations of discrete rectangular recirculated struturesis given.On the basis of this,an equivalent continuum model is adopted and the ap-plication of the principle of virtual work leads to non-linear governing equations and corresponding boundary conditions.

The Generation of Non-Linear Stiffness Matrix of Triangle Element when Considering Both the Bending and in-Plane Membrane Forces

Zhang Jian-hai, Li Yong-nian, Chen Da-peng

1994, 15(5): 399-408.

Abstract(2309) PDF(540)

Abstract:
Using Stricklin Melhod^[5],we have this paper has derived the formulas for the ge-neration of non-linear element stiffness matrix of a triangle element when considering both the bending and the in-plane membrane forces.A computer programme for the calculation of large deflection and inner forces of shallow shells is designed on theseformulas.The central deflection curve computed by this programme is compared with other pertaining results.

Numerical Simulation for Evolutionary History of Three-Dimensional Basin

Yuan Yi-rang, Wang Wen-qia, Yang Dan-ping, Han Yu-ji, Yang Cheng-shun

1994, 15(5): 409-420.

Abstract(2005) PDF(747)

Abstract:
Numerical simulation for evolutionary history of an oil-and gas-bearing basin is to repeat geological and thermodyanomic history of basin evolution on a computer and then to quantitatc petroleum generation,accumulation and migration.The mathemat-ical model describing geological and thermodynamic history of the basin evolution ischaracterised by an initial-boundary value problem of a system of nonlinear partial dif-ferential equations.In the present paper,a numerical method for three-dimensional problem and the analysis of its stability are established and a numerical result for apractical model is given,which shows that the abnormal pressure and paleo-temperat-ure computed are reasonable and display physical characteristics clearly as well.

Flow of a Viscoplastlc Fluid on a Rotating Disk

Fan Chun

1994, 15(5): 421-427.

Abstract(2179) PDF(514)

Abstract:
The equations describing the flow of a viscoplastic fluid on a rotating disk are de-rived and are solved by perturbation technique and nurmerical computation respectively for 2 cases.This makes it possible to calculate the thickness distribution of film.Twokinds of distribution of thickness have been found.For the viscoplastic fluid for whichboth viscosity and yield stress are independent of radial coordinate r,the thickness h decreases with increasing r.For a Bingham fluid for which both viscosity and yieldstress are function of time and r.the thickness h increases with increasing r.

Determination of Cavitation Noise Limiting Value

Huang Jing-chuan

1994, 15(5): 429-433.

Abstract(2070) PDF(573)

Abstract:
In this paper.the cause of cavitation noise limiting value is analyzed.and the de-termining method of cavitation noise limiting value of body os giving.

Large Amplitude Vibration of Circular Sandwich Plates

Du Guo-jun

1994, 15(5): 435-442.

Abstract(1786) PDF(520)

Abstract:
In this paper,fundamental equations of the axisymmetric large amplitude.free vibration for circular sandwich plates are derived by means of Hamilion principle.Inmosi cases,the sandwich plates are composed of very thin faces,then the preceding fundamental equations are simplified considerably.For an illusirative example,a circu-lar sandwich plate with edge clamped but free to slip is considered,and then we gol a pure analytic solution of the axisvmmetric large amplitude free vibration with the aid of the modified iteration method.and derived an analytic relation for the amplitude-frequency response.

On the(1,3)Distributions of Limit Cycles of Plane Gaudratic Systems

Lin Xiao-lin, Dang Xin-yi

1994, 15(5): 443-455.

Abstract(2558) PDF(487)

Abstract:
In this paper,(a)we rerise Theorem 2 of Ref [1] omit the condition V₇>0₇>0.(b)we discuss the relative positions of six curvesM(s²,r)=0,J(s²,r)=0,L(s²,r)=0,T(s²,r)=0,s²=s> and s²=s Under the condition of the(1.3)distri-butions of limit cycles,we expand the variable regions of parameters(s,r)and clearly.show them in figure,(c)we study the(1,3)distributions of limit cycles of one kind quadratic systems with two singular points at the infinite: and(d)we give a generalmethod to discuss the(1,3)distibutions`of limit cycles of system(1.1)whatever there isone,two or three singular points at the infinite.

A Linearized and Unified Yield Criterion of Metals and Its Application

Xiong Hui-er

1994, 15(5): 457-461.

Abstract(1672) PDF(465)

Abstract:
In this paper a linearized and unified yield crierion of metals is presented,which is in a form of a set of linear functions with two pararneters.The parameters are expressed in terms of tension yield stress and so-called "shear-stretch ratio" and can bereadily determined from experimental data.It is shown that in stress space the set of yield functions is a set of polygons with twelve edges located between the Tresca's hexagon and twin-shear-stress hexagon^[1].In this paper the present yield function isused to analyse the prestressiap loose running fit cylinders.

The Uniqueness and Existence of Solution of the Charac-teristic Problem on the Generalized KdV Equation

Li Wen-shen

1994, 15(5): 463-469.

Abstract(2277) PDF(508)

Abstract:
The generalized KdV equation u_t+αuu_x+μu_x3+εu_x5=0^[1] is a typical integr-able equation.It is derived studying the dissemination of magnet sound wave in coldplasma^[2],Ihe isolated wave in transmission line^[3],and the isolated wave in the bound-ary surface of the divided layer fluid^[4].For the characteristic problem of the gene-ralized KdV equation,this paper,based on the Riemann function,designs a suitable structure,then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding mapping E is a mapping to itself^[5].According to the principle of fixed point,the above integral differential equ-ation has a unique regular solution,so the characteristic problem of the generalized KdV equation has a.unique solution.The iteration solution derived from the integral differential equation sequence is uniformly convegent in Ω
.

The Plane Stress Crack-Tip field for an Incompressible Rubber Material

Shi Zhi-fei, Gao Yu-chen

1994, 15(5): 471-477.

Abstract(2265) PDF(462)

Abstract:
The crack-tip field under plane stress condition for an incompressible rubber material^[1] is investigated by.the use of the fully nonlinear equilibrium theory.It is found thai the crack-tip field is composed of two shrink sectors and one expansion se-ctor.At the crack-tip,stress and strain possess the singularity of R^-1 and R^-1n,respec-tively,(R is the distance to the crack-tip before deformation,n is the material const-ant).When the crack-tip is approached,the thickness of the sheet shrinks to zerowith the order of R^1.4n.The results obtained in this paper are consistent with that ob-tained in [8] when s→χ.