应用数学和力学

1983 Vol. 4, No. 6

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Tsai Shu-tang, Liu Yi-xin

1983, 4(6): 737-742.

Abstract(2105) PDF(514)

Abstract:
Many studies on cavitation phenomena were based on the theory of single huhble motion which was first put forward by Rayleigh in his 1917 article and later developed by Plesset et al.^[1]By this theory,only some effects of forces were taken into consideration from hydrodynamics leaving out any thermodynamical effects such as matter inter-change between liquid and gaseous phases. Strictly speaking, the theory map be suitable for discussing expansion or/and contraction motion of a bubble formed in liquid,but this theory does not cope with cavitation behaviors in general. In this paper,the cavitation conditions and similarity problems are discussed with thermodynamic effects taken into consideration in addition to the hvdrodvnamic ones.

The Creeping Motion in the Entry Region of a Semi-Infinite Circular Cylindrical Tube

Wu Wang-yi, Richard Skalak

1983, 4(6): 743-756.

Abstract(2185) PDF(728)

Abstract:
In 1969, Lew and Fung^[1] considered the inlet flow into a semi-infinite circular cyfinder at low Reynolds mumber Dagan, et al.^[2] in 19$Z obtained a series solution for the creeping motion through a pore of finite length directly The numerical results oblained in[1]also describe the entrance flow in tube of a finite length, because the Fourier integrals in the general solutions are replaced by Fourier series.In the present paper, the Fourier integrals are evaluated numerically and the velocity, pressure distribution and the stream function in the entry region of a semi-infinite circular cylindrical tube for a uniform entry velocity are obtained more preciselp.The corresponding inlet length which is equal to (1,2) times the radius of the tube is close to the factor (1.3) suggested hyLew and Fung.^[1] The collucation technique applied in the present paper is shown to converge rapidly and it should be useful in other similar problems.

On the Compatibility Condition of Displacement Field for Finite Deformation of Continuum

Chen Zhi-da

1983, 4(6): 757-761.

Abstract(2528) PDF(712)

Abstract:
The vanishing of Riemann-Christoffel tensor is usually adopted as the compatibility condition of finite deformation, However, we prove in this paper by the method of Cesaro that this condition is necessary but not sufficient for the guarantee of single-valued, continuous displacement field, A new general compatibility condition,based on theorem of strain-rotation decomposition (Chen[4])is derived, The displacement compatible condition reduces to Saint-Venants condition when strain and rotation are infinitesimal.

The Method of Composite Expansions Applied to Boundary Layer Problems in Symmetric Bending of the Spherical Shells

Zhou Huan-wen

1983, 4(6): 763-770.

Abstract(1992) PDF(535)

Abstract:
In this paper,the method of composite expansions, which was proposed by W. Z. Chien (1948,[5]), is extended to investigate two-parameter boundary layer problems.For the problems of symmetric deformations of the spherical shells under the action of uniformly distribution load q, its nonlinear equilibrium equations can be written as follows(2.3a)、(2.3b): where ε and δ are undetermined parameters.If δ=1 and ε is a small parameter, the above-mentioned problem is called first boundary layer problem; if ε is a small parameter, and δ is a small parameter, too, the above-mentioned problem is called second boundary layer problem.For the above problems, however, we assume that the constants ε, δ and p satisfy the following equation: ε³pδ=1-ε In the defining of this condition, using the extended method of composite expansions, we find out the asymptotic solution of the above problems with the clamped boundary condition.

On the Global Stability of Rotational Motion and the Qualitative Analysis of the Behaviour of Disturbed Motion of a Rigid Body Having a Liquid-Filled Cavity

Li Li

1983, 4(6): 771-780.

Abstract(1800) PDF(536)

Abstract:
This paper is a continuation of[1].In this paper we investigate the distribution of steady motions of the liquid-filled-cavity body, decide the stability of each stuady motion and find out the corresponding regions of stability and instability.Besides,the behaviour of disturbed motion is analysed qualitatively.

Vector Analysis of Spatial Mechanisms——(Ⅳ) Dynamics of Spatial Mechanisms

Yu Xin

1983, 4(6): 781-788.

Abstract(1900) PDF(418)

Abstract:
The standard dynamical problems of the previous four spatial mechanisms are here solved by the method of vector equations.The procedure is completely independent of the transfer matrices due to the changes of reference frame from one connecting pair to the next.

Stress Concentration and Stress Intensity Factors for an Infinite Plane with Several Rows of Elliptic Holes and Cracks

Zhou Cheng-fan, Guan Chang-wen

1983, 4(6): 789-800.

Abstract(2172) PDF(655)

Abstract:
This paper deals with the stress concentration in plane with swveral arbitrarily distributed elliptic holes. By using the functions of complex variables, the stress functions in which the interactions of neighbouring holes are taken into consideration can be constructed. By applying the conformed mapping method to satisfy the boundary conditions of each hole, the governing equations can then be transformed into a set of simultaneous equations through boundary integrals. Moreover, the problems with crack can be derived by changing the elliptical rates of the ellipses, thereby an approximate solution of cracking problem may be obtained.Some computing examples are given in the paper.

The Asymptotic Solution of a Kind of Stefan Problem

Liu Zheng-rong

1983, 4(6): 801-808.

Abstract(1987) PDF(577)

Abstract:
In this paper, a kind of Stefan problem subject to general initial condition is studied. The slab considered is divided into three regions. There is a different time scale in each one. By means of PLK method or like multi-scales method, the asymptotic solution of each one is obtained. Finally we discuss the asymptotic solution and draw some conclusions.

The Existence Problem of Optimal Control for Nonlinear Processes

Peng Shi-ge, Chen Zu-hao

1983, 4(6): 809-820.

Abstract(2147) PDF(577)

Abstract:
The existence problem of optimal control systems described by x=f(t,x,u) is discussed in this paper, where f(t.x,u) is a more general function and the class of admissible control functions are general enough to contain those control functions which are frequently used in engineering. The problem for an optimal control approximated by a sequence of control functions being part of certain function classes is considered here, an example in contradiction with the conclusion of ref. [1] about this problem is given, and a correct conclusion is presented.

The Conjugate Gradient Method and Block Iterative Method for Penalty Finite Element of Three-Dimensional Navier-Stokes Equations

Li Kai-tai, Huang Ai-xiang, Li Du, Liu Zhi-xing

1983, 4(6): 821-834.

Abstract(1866) PDF(600)

Abstract:
A conjugate gradient and block iterative algorithm for element solution of penalty variational form of Navier-Stokes equations are presented. Because the algorithm of solving single variable minimizing problem is simplified, the computing time is greatly saved.In this paper numerical examples are also provided.

The Asymptotic Analytical Solution of the Strain-Hardening Elastoplastic Plate Containing a Circular Hole under Simple Tension

Dong Ya-min, Zhu Zu-cheng, Gu Qiu-lin

1983, 4(6): 835-846.

Abstract(1884) PDF(572)

Abstract:
In this paper the general asymptotic analytical solution of plane problem of elasto-plasticity with strain-hardening[2] is used in solving the problem of an infinitely large plate containing a circular hole under simple tension, and the analytical expressions of stress components of the first two approximations are given, These results are compared with the numerical and the experimental results given by other authors[4,5], and a good agreement is obtained. At the end of this paper the authors inspect the correctness of Neuber's formula[9] for this problem.

Earthquake Response of Circular Column Submerged in Water Partially

Chang Hsi-the

1983, 4(6): 847-851.

Abstract(1988) PDF(646)

Abstract:
In this paper, the author studies the earthquake response of circular column partially submerged in water, and obtained the displacement response of column-water couple system and the moment of any section as well as the distribution of earthquake force along the column height.

A Method for Conforma! Mapping of a Two-Connected Region onto an Annuius

Chen Yi-heng

1983, 4(6): 853-860.

Abstract(2163) PDF(505)

Abstract:
This paper presents a method for conformal mapping of a two-connected region onto an annulus. The principle of the method is to find a holomorphic function, the real part of which should be a harmonic function satisfying certain boundary conditions.The key for solving the problem is to determine the inner radius of annulus. According to the theory of complex functions we shall determine it from the condition that the line integral predicted along multiple closed paths should be zero.It is then easy to see that the imaginary part can directly be obtained with the aid of Cauchy-Riemann equations. The unknown integral constants can also be derived by using the one-to-one mapping of previous region onto annulus.Without loss of generality, the method may be used to conformally map other two-connected regions onto an annulus.

An Analytical Solution for Underground Structure-Country Rock Dynamic Interaction

Yang Sheng-tian, Cao Zhi-yuan

1983, 4(6): 861-868.

Abstract(1985) PDF(468)

Abstract:
In this paper according to the results of a great quantity of tests and numerical calculations, it is pointed out that the country rock with thickness of 1/3 span has mechanical characteristics of a thick flexure member in underground rock cave subjected to transverse blast loading, however, it is approaching to stress state of free ffield outside country rock, the equation of thick plate theory under loading of free field pressure may be applicable to solution of this problem.Therefore, the underground structure-cuuntry rock dynamic interaction may be described by dynamic equations of flexure member of thin plate and thick plate, which express liner and country rock respectively.The interaetion force between the liner and country rock is expressed as contacting pressure function q(x,t),Solving the system of simultaneous equations, the analytical solution to riynamic analysis of arch-straight liner including elastic half space interaction effect is given and the analytical expression of function q(x,t) is obtained.This analytic solution will be contributed to the study of some substantive problems of underground structure-medium interaction.