Applied Mathematics and Mechanics (English Edition)

THERMODYNAMICS ON CAVITATION

蔡树棠;刘一心

1983, 4(6): 825-831.

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Many studies on cavitation phenomena were based on the theory of single bubble 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 interchange between liquid and gaseous phases. Strictly speaking, the theory may be suitable for discussing ex-pansior. 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 hydrodynamic ones.

THE CREEPING MOTION IN THE ENTRY REGION OF A SEMI-INFINITE CIRCULAR CYLINDRICAL TUBE

吴望一;Richard Skalak

1983, 4(6): 833-848.

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In 1969, Leu and Fung considered the inlet flow into a semi-infinite circular cylinder at low Reynolds number. Dagan et al[2] in 1982 obtained a series Solution for the creeping motion through a pore of finite length directly. The numerical results obtained in [1] also describe the entrance flow in a tube of a finite, length as the Fourier integrals in the general solutions are replaced by Fourier series. In the present paper, the Fourier integralss are evaluated numerically and the velocity, pressure distribution and the stream function in the entry region of a somi infinite circular cylindrical tube is close to the factor 1.3 suggested by Lew and Fung[1].The collocation 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

陈至达

1983, 4(6): 849-854.

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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 guarantee of a single-valued, continuous displacement field. A new general compatibility condition, based on the theorem of strain-rotation decomposition(Chen[4]) is derived. The displacement compatible condition reduces to Saint-Venant's condition when strain and rotation are infinitesimal.

THE METHOD OF COMPOSITE EXPANSIONS APPLIED TO EOUNDARY LAYER PROBLEMS IN SYMMETRIC BENDING OF THE SPHERICAL SHELIS

周焕文

1983, 4(6): 855-863.

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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:

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-mentioned problems, however, we assume that the constants ε, δ and p satisfy the following equation: εp=1-ε In defining this condition by using the extended method of composite expansions, we find the asymptotic solution of the above-mentioned problems with the clamped boundary conditions.

ON THE GLOEAL STABILITY OF THE ROTATIONAL MOTION AND THE QUALITATIVE ANALYSIS OF THE BEHAVIOUR OF DISTURBED MOTION OF A RIGID BODY HAVING A LIQUID-FILLED-CAVITY

李骊

1983, 4(6): 865-874.

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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 MECHANISM——(IV)Dynamics of Spatial Mechanisms

余燊

1983, 4(6): 876-884.

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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, as used by Yang and Bagci[1][2].

STRESS CONCENTRATION AND STRESS INTENSITY FACTORS FOP AN INFINITE PLANE WITH SEVERAL ROWS OF ELLIPTIC HOLES AND CRACKS

周承芳;关长文

1983, 4(6): 885-897.

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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

刘曾荣

1983, 4(6): 899-907.

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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

彭实戈;陈祖浩

1983, 4(6): 909-925.

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The existence problem of optimal control systems described by x=ƒ(t,x,u)is discussed in this paper, where ƒ(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 EQUATION

李开泰;黄艾香;李笃;刘之行

1983, 4(6): 927-941.

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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 ANALYEICAL SOLUTION OF THE STRAIN-HARDENING ELASTO-PLASTIC PLATE CONTAINING A CIRCULAR HOLE UNDER SIMPLE TENSION THE ASYMPTOTIC ANALYEICAL SOLUTION OF THE STRAIN-HARDENING ELASTO-PLASTIC PLATE CONTAINING A CIRCULAR HOLE UNDER SIMPLE TENSION

董亚民;朱祖成;顾求林

1983, 4(6): 943-954.

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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 PARTTIALLY

张悉德

1983, 4(6): 955-959.

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In this paper, the author studies the earthquake response of circular column partially submerged in water. He has 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 CONFORMAL MAPPING OF A TWO-CONNECTED REGION ONTO AN ANNULUS

陈宜亨

1983, 4(6): 961-968.

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This paper presents a method for conformal of a two-connected region □ onto an annulus. The philosophy of the method is to convert the problem into a Dirichlet problem and to prove the real part of the analytic function transformation should be a harmonic function satisfying certain boundary conditions. According to the theory of harmonic function ws can determine tl,e inner radius of the annulus from the condition that the harmonic function defined in two-connected region should be single-valued. It is then easy to see that the imaginary part can directly be obtained with the aid of Cauchy-Riemann conditions. The unknown constants of integration only influence the argument of image points and can easily be derived by using the one-to-one mapping of □ region onto an annulus. Without loss of generality, the method can be used to conformally map other two-connected regions onto an annulus if they can be subdivided into several rectang-ulars. The method has been programmed for a digital computer. It is demonstrated that the method is efficient and economical. The corresponding numerical results are shown in the Table.

AN ANALYTICAL SOLUTION FOR UNDERGROUND STRUCTURE-COUNTRY ROCK DYNAMIC INTERACTION

杨昇田;曹志远

1983, 4(6): 969-976.

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In this paper according to the results of a great quantity of tests and numerical calculations, it is pointed out that the surrounding rock with thickness of 1/3 span has mechanical characteristics of a thick flexural member in underground rock cave subjected to transverse blast loading. However, it approaches the stress state of free field outside country rock and the equation of thick plate theory under the loading of free field pressure may be applied to the solution of this problem. Therefore, the underground structure-country rock dynamic interaction may be described by dynamic equations of flexural members of thin plate and thick plate, which express linear and country rock respectively. The interaction force between the linerand country rock is expressed as contacting pressure function g(x,t). By solving system of simultaneous equations, the analytical solution for the dynamic analysis of arch-straight liner including elastic half space interaction effect is given and the analytical expression of function g(x,t) is obtained.This analytic solution will contribute to the study of some substantive problems of underground structure-medium dynamic interaction theoretically.

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