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1981年 第2卷 第3期    刊出日期：1981-05-18

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论文

Variation Transforming Analysis (II)

吴学谋

1981, 2(3):  277-290. 

摘要 ( 460 )   PDF (794KB) ( 777 )  

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This paper introduces some related concepts of pansystems analysis (such as pansystem, pansystem space, pansystem logic space, pometric pansystem, etc), and develops the convex set theory, Banach's theorem of completeness, Lax equivalence theory, theorems of Kuhn-Tucker type and Dubovitsky-Milutin type into the pometric (partial ordered metric) pansystem forms, they are different from traditional results. Furthermore, the general stability of operator equations and MSP transforming principles of approximation are investigated.

The Mechanical Properties of the Slurry and the Resistance Force of a Sphere Moving With Uniform Velocity in the Slurry

蔡树棠

1981, 2(3):  291-296. 

摘要 ( 506 )   PDF (314KB) ( 820 )  

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It is commonly considered that the mechanical properties of the slurry are different from that of ordinary Newtonian fluid, and can be described by that of Bingham fluid. Hence its shearing stress should be described by the formula of the shearing stress of Bingham fluid. But the author holds the contrary opinion and firmly believes that the slurry is a highly viscous fluid with very long relaxation time such as those of asphalt, glass, etc. In this article, we have discussed the mechanical properties of the slurry and the resistance of a sphere moving with uniform velocity in the slurry. In the process of discussion, we use Stokes solution of the viscous fluid passing around a sphere. When the sphere is in equilibrium under the action of gravitational force, the force of buoyancy and the resistance, we get the velocity of sedimentation. When the velocity of sedimentation is equal to zero, we get the relation between the yield stress of Bingham fluid and the diameter of the particles which will not sink. The theoretical results calculated are compared with the experimental data of Northwest Institute of Hydrotechnical Research and Institute of Hydraulic Research, Yellow River Conservancy Commission. They are congruous.

On a Micromechanical Model for Cracked Reinforced Composites

欧阳鬯;陆美子

1981, 2(3):  297-304. 

摘要 ( 418 )   PDF (448KB) ( 412 )  

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In this paper, we consider the fracture process of small scale yielding for reinforced composites. In the outer region of the crack tip, we use the anisotropic continuum description, while for the crack tip region we use the heterogeneous micromechanical model. Three components in heterogeneous region, namely, fibre, interface and matrix, may be considered as nonlinear. The effect of finite deformation is also considered. We construct the solution of the problem by using the combined boundary-layer nonlinear finite element method.

Extended Graphical Representation of Polynomials with Applications to Cybernetics

汪家訸

1981, 2(3):  305-318. 

摘要 ( 422 )   PDF (685KB) ( 1106 )  

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In this paper, the polynomial of a complex variable s(≡x+iy) with real coefficientsis graphically represented by three plane curves which are the projections of a space curve on three coordinate planes of the coordinate system (x, iy. K) in which K is confined to be real. The projection on (x, iy) plane is just the root locus of the polynomial with K as a real parameter. It is remarkable that the equation of the root-locus is m-th degree in y², whether n=2m+1 or n=2m+2. In addition to the real curve K_r = ƒ(x) in the figure (K, x) there exists another curve K_t which is plotted by the real parts of all complex roots against K. The (K, x) curve is particularly important to determine the absolute as well as the relative stable interval of K for linear systems. For cybernetics, the (K,iy) curve can be used to show the relation between the nature frequency and the gain K. Such three figures are useful for studying the theory of equation and cybernetics.

The Eigenvalue Problem and Expansion Theorems Associated with Orr-Sommerfeld Equation

周恒;李骊

1981, 2(3):  319-330. 

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The eigenvalue problem and expansion theorems associated with orr-Sommerfeld equation are fundamental for the investigation of the stability of laminar fluid motion and have been studied by many authors. Nevertheless, the results are still incomplete^[6]. In this paper, this problem is investigated again and some new results have been obtained, namely:(1) The expansion series converges uniformly and absolutely. (2) The co-officients of the expansion series satisfy an inequality of Paley-Wiener type, which is the natural extension of the well-known Bessel equality of a complete orthogonal set.

Pile Analysis by Simple Integral Equation Methods

云天铨

1981, 2(3):  331-348. 

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Two simple integral equation methods are proposed for the analysis of vertical loaded pile. One of them is; let the axisymmetrical loads formed by Mindlin's horizontal point forces be distributed along the axis z in [0, L] of the elastic half-space, and composed with the Boussinesq's point force. The other is: in addition to the above fictitious loads, the. Mindlin's vertical forces are distributed along the axis z in [0, L]. The former reduces the problem of a vertical loaded pile embedded in a half-space with the following boundary conditions.

Superfluous Order and the Proper Solution of the Maxwell Equation

张鸿庆

1981, 2(3):  349-360. 

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In this paper it is proved that Maxwell equation is equivalent to a fourth order equation. Under a certain condition, its general solution is clven by

A Mathematical Interpretation of Dirac δ Function

王进儒

1981, 2(3):  361-364. 

摘要 ( 437 )   PDF (224KB) ( 271 )  

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The two conditions (see[1] p. 58) of the Dirac function are inconsistent in standard analysis.In this paper, the author began by studying the integral of the functions on the nucleon a(o), and then, making use of the point function in infinitesimal analysis to define the Dirac function (x) so that it satisfies the condition (1.2) and δ(X)=o, for X∈R≠0 and X Some various examples of Dirac functions have been presented and some properties of the d function have been derived.

Applying the Generalized Step-function to Solve the Bending Problems of Nonuniform Beams with Variable Cross Section

林新三;许宝元;熊焕国

1981, 2(3):  365-374. 

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The bending problems of nonuniform beams with variable cross-section can be approximated by that of a step beam under sectionally uniform load (including both concentrated forces and couples). In this paper, the concept of Heaviside function {x-a}⁰ will be generalized, and a new function {x-a}⁰, n=0,1,2…,will be defined, which may be named as a generalized step function. The rules of operation will also be given to {x-a}ⁿ{x-b}⁰. The reciprocal of the flexural of rigidity 1/EJ and the bending moment M(x) can all be expressed in terms of {x-a}ⁿ,and substituted into the differential equation of the elastic curve of the beam respectively. Thus we may establish a set of unified method to solve various types of bending problems of straight beams. The general solution of the deflection equation will be given.