应用数学和力学

Wu Xue-mou

1981, 2(3): 255-265.

Abstract(2105) PDF(573)

Abstract:
This papdr introduces some related concepts of panspstems analysis(such as pansystem,pansystem space,panspstem logic space,pometric panspstem,etc),and develops the convex set theory,Banach's theorem of completeness,Lax equivaleace theory,theorems of Kuhn-Tucker type and Dubovitskp-Milutin type into the pometric paaspstem forms,which are different from traditional results,Furthermore,general stability of operator equations and MSP transforming principles of approximation are investigated,and in the final section we present a sort of extension and unified functional frame work concerning traditional extremal theqrem,variation calculus,reciprocity principle,variation theorem of quadratic functional and unilateral variation principles.

The Mechanical Property of the Slurry and the Resistance Force of a Sphere Moving with Uniform Velocity in the Slurry

Tsai Shu-tang

1981, 2(3): 267-272.

Abstract(2357) PDF(629)

Abstract:
The shear stress of the slurry flowing in the tube or two-dimensional channel is epressed by the shear stress of Bingham fluid,usually.ie Where τ_B is the yield stress of Bingham fluid and η is the coefficient of rigidity.The author disapproves this point of view The author thinks that the mechanical property of the slurry may be more like that of highly viscous fluid than that of Bingham fluid.Basing on this idea,we adopt another method to treat the mechanical problem.We assume that,for the case of small Reynolds number,the velocity distribution of the slurry is very close to that of Stokes solution,Thus,we map apply the method.of effective viscosity to calculate the resistance force of a sphere moving in the slurry with uniform velocity.

On a Micromechanical Model for Cracked Reinforced Composites

Ouyang Chang, Lu Mei-zi

1981, 2(3): 273-280.

Abstract(1933) PDF(491)

Abstract:
In this paper,We consider the fracture process of small scale yieldiag 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 solutioa of the problem by using the combined boundary layer-nonlinear finite ele went method.

Extended Graphical Representation of Polynomials with Applications to Cybernetics

Wong Chia-ho

1981, 2(3): 281-293.

Abstract(1944) PDF(550)

Abstract:
In this paper,the polynomial of a complex variable s(≡x+iy) with real coefficients K=f(s)≡a₀sⁿ+a₁s^n-1+……+a_n-1s+a_n is 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 polynomial with K as a real parameter,It is remarkable that the equation of the root locus is mth degree of y²,whether。n=2m+1 or n=2m+2.In addition to the real curve K_r=f(x) in the figure(K,x),there exists another curve K_c which is plotted by the real parts of all complex roots against those of K.The(K,iy)curve is particularly important to determine the absolute as well as the relative stability interval of K for linear systems,For cybernetics,the(K,iy)curve can be used to show the relation between the natural frequency ω 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

Zhou Heng, Li Li

1981, 2(3): 295-305.

Abstract(2339) PDF(590)

Abstract:
The eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation,which is fundamental for the investigation of the problem of stability of laminar fluid motion,have been investigated by several authors,but the results are still imcomplete[6].In this paper,this problem is reinvestigated,and some new results are obtained,which are;(1)The expassion series converges not only uniformly but also absolutely;(2)The coefficients 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

Yun Tian-quan

1981, 2(3): 307-320.

Abstract(2357) PDF(528)

Abstract:
Two simple integral equation methods are proposed for the aaalysis of vertical loaded pile.One of them is; let the aaisymmetrical loads formed by Mindlin's horizontal point forces be distributed along the azis 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 azis 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 Maxwell’s Equation

Zhang Hong-qing

1981, 2(3): 321-331.

Abstract(2303) PDF(689)

Abstract:
Let pu=f in Ω has solution for every f,in which p-as arbitarp linear partial differential operator with constant coefficients.In this paper we prove Maxwell's equation is a four order,equation and the general solution for homogeneous Mas well's equation is given by where ф_i satisfies □ф_i i=1.2.

A Mathematical Representation of Dirac δ Function

Wang Jin-ru

1981, 2(3): 333-338.

Abstract(2498) PDF(565)

Abstract:
Dirac's definition of a δ function δ(x)in the real number system R is the idealization of a function satisfying the following conditions These conditions in standard analysis are inconsistent since the integral of any function which has a value of zero with the exception of that which at one point.

Apply Generalized Step Function to Solve the Bending Problem of Statically Indeterminate Beams with Variable Flexural Rigidity

Lin Xin-san, Xu Bao-yuan, Xiong Huan-guo

1981, 2(3): 339-346.

Abstract(2024) PDF(617)

Abstract:
The present paper defines a generalized step function {x-a}ⁿ and the reciprocal of bending rigidity of beams 1/EJ as well as the bending moment are expressed in such a form {x-a}ⁿ,Thus a general procedure for calculating the deformation of all types of straight beams is given and the general form of equation of elastic curve of beams is obtained.

1981 Vol. 2, No. 3