应用数学和力学

1981 Vol. 2, No. 4

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Constitutive Theories for Nonlocal Micropolar Continua with Implicity and with Multiple Interactions

Tai Tien-min

1981, 2(4): 347-352.

Abstract(2095) PDF(456)

Abstract:
In this paper the constitutive theory for nonlocal micropolar continua which was proposed by A. C. Eringen is extended to the cases for nonlocal micropolar continua with implicity and with multiple interactions. Here nonlocal micropolar thermoelastic solids with implicity and with multiple interactions are cited as instances to illustrate the procedure for the establishment of their constitutive theories as well as two relevant theorems concerning the constitutive theories for those solids which are geven in this paper.

Numerical Analysis of the Spallation of Steel Target under the Explosive Loading

Chu Chao-hsiang, Li Yong-chi, Wang Xiao-jun

1981, 2(4): 353-368.

Abstract(2165) PDF(895)

Abstract:
The numerical analysis of the propagation of stress waves and the allied scabbing phenomena in a steel plate under explosive attack is made, by using a model of one-dimensional flow. The results are compared with our experimental results which were carried out several years ago. It is found that, in case the hydrodynamic-elastoplastic model for steel plate and the cumulative damage spall criterion are used, the calculated thickness of the major spall is in reasonable agreement with that obtained in the experiments. An approximate formula for the thickness of the major spall is presented and the "mica-splitting" phenomenon about the minor spalls observed in the experiments is satisfactorily explained.

Bending of Rectangular Cantilever Plate with Discontinuous Loading

Chang Fo-van

1981, 2(4): 369-377.

Abstract(2311) PDF(707)

Abstract:
The cantilever rectangular plates discussed previously ate all loaded continuously. Such as loaded uniformly or by a concentrated load at any point along the free edge.Let us now go a step further to deal with the case of discontinuous loading by taking a concentrated load at the middle of the plate for an illustrative example.For a numencal example, a square plate is taken.As it can expected, the deflected free edge y=a turns out to be almost a horizontal line, and the part of the free edge x=a from y=0.5 to y=a is deflected into an inclined straight line.Moreover, the total bending moment along the clamped edge checks very closely with the statically determined value from equilibrium,All these data conf irm our calculation.

The Differential Equations of Heat Transfer for Some Cases of Variable Thermal Conductivities

Liu Hsien-chih

1981, 2(4): 379-385.

Abstract(1927) PDF(623)

Abstract:
By managing the heat conduction problem in solids the thermal conductivity is usually taken as a constant,but in reality varying thermal conductivity reveals in every heat transfer process, Therefore, in the present paper,we wish to consider it to vary with the space coordinate according to a linear and an ex ponential law; basing on this proposal we have been able to set up six secottd order heat conduction differential equations, By the way,for the case of variable density, specific heat as well as thermal conductivity, we have been successful to deduce other similar six heat transfer differential equations.

Extended Graphical Representation of Rational Fractions with Applications to Cybernetics

Wong Chia-ho

1981, 2(4): 387-396.

Abstract(2262) PDF(523)

Abstract:
In this paper, we discuss the extended graphical frepresentation of the fraction of a complex variable s

Where K is confined to be real. Three figures of the above fraction can be used in feedback systems as well as to study the properties of figures for any one coefficient of a characteristic equation as a real parameter. It is easy to prove the following theorem:
K₁=f⁽ⁿ⁾(s)/(F)^(d)(s),and K₂=F^(d)(s)/f⁽ⁿ⁾(s)
have the same root locus.By this graphical theory, we find out that if the zeros and poles of a fraction are alternatively placed on the axis x, then there is no complex root locus of this fraction, therefore the state of such a system is always non-oscillatory; Using these figures of this fraction, we can discuss its stable interval systematically.

The Solitary Waves in a Gradually Varying Channel of Arbitrary Cross-section

Chou Xian-chu

1981, 2(4): 397-406.

Abstract(1975) PDF(488)

Abstract:
In this paper, the solitary waves in an arbitrary cross-section channel which gradually changes in the streamwise have been studied. The KdV equation with slowly varying coefficients is derived. Thus, we produced the first term of its asymptotic solution, travel speed of solitary waves and the relation between the amplitude of wave and the geometric size of channel. The results have been applied to the cases of triangular and rectangular channels. For the channel with varying depths and breadths they are fairly consistent with those of Johnson, Shuto and Mile.

The Motion of Viscous Liquid Cylinder with Finite Length in a Vertical Capillary Tube

Wu Wang-yi, Qian Min-quan, Wen Gong-bi

1981, 2(4): 407-418.

Abstract(1944) PDF(711)

Abstract:
This paper deals with the motion of viscous liquid column with finite length and two free surfaces in a vertical straight capillary tube. It is assumed that fluid is Newtonian. Linearizing the boundary conditions, analytic expressions in the form of infinite series have been obtained for velocity, piessure and free surface at low Reynolds number. The numerical calculation is carried out for a set of cylinder's length of water and blood. It has been revealed that there are considerable circulating currents at the upper and lower meniscuses. Its maximum velocity is about 57% of the average velocity of the mainstream. Inertial effect is also studied in this paper. Using the time-dependent method in finite difference techniques, numerical solution of the corresponding nonlinear equation at R_e<24.5 is computed. Comparing it with analytic exact solution at low Reynolds number shows that inertial effect is negligible provided R_e<24.5.

Exact Solution for the Compressible Flow Equations Through a Medium with Triple-Porosity

Liu Ci-qun

1981, 2(4): 419-424.

Abstract(2081) PDF(660)

Abstract:
This paper obtains the exact solution for the unsteady radial flow equations of the slightly compressible liquid through a medium with triple-porosity by using, the method of decomposition. This solution not only reveals the essential characters of the unsteady flow of liquid through a medium with multiple-porosity, but also comprises the existing primal results.

On Laminar Boundary Layers with Suction

Huang Ze-yan

1981, 2(4): 425-438.

Abstract(1927) PDF(499)

Abstract:
In this paper, we obtain the asymptotic solution of the general equation for laminar boundary-layer flows with suction. Formulae for calculating the displacement thickness, momentum thickness, and skin friction are then derived. And further, the problem of determining the separation point is dealt with. Finally, as a numerical example, we compute certain characteristic boundary-layer parameters for the case of uniform flow over flat plate with constant suction. Our numerical results obtained are in good agreement with those of Iglisch's.

Some Discussions on Finite Deformation of Continuous Media

Cheng Yuan-sheng

1981, 2(4): 439-444.

Abstract(1958) PDF(507)

Abstract:
Three problems are discussed in this paper: 1. The physical significance of the characteristic tensor of finite deformation is discussed as a complement to the literature^[2]. 2. The four characteristic tensors of finite deformation, introduced in the litera ture^[4], ard analyzed and discussed more thoroughly.3. The representation of the general finite deformation through simple loading process is not always possible, the condition for its realization being that the given finite deformation satisfies the equations of compatibility. It is pointed out in this paper that for the finite deformation set forth by L.I. Sedov in an illustrative example in [9], the equations of compatibility cannot be satisfied even for k=1, henceforth for whatever value of k, the finite deformation set forth by Sedov can not be represented through simple loading process.

On the Solution of Elliptic Equation Σa_kΔ^kφ=0 and Its Application in Mechanics

Gai Bing-zheng

1981, 2(4): 445-454.

Abstract(2278) PDF(565)

Abstract:
In this paper, the solution of elliptic equation is discussedin detail by the method of separation of variables in complex field. The general solution which can be used in the approximation to the boundary conditions of the practical problems is presented. Two practical examples in mechanics are given.

Discussion on “Rectangular Plates with Free Edges on Elastic Foundations”

Fan Ja-shen, Li Ja-you

1981, 2(4): 455-460.

Abstract(1769) PDF(542)

Abstract:
This paper points out the subject mentioned in this work has the demerit that the boundary condition defining no concentrated force which exists at the four corner points was not fulfilled, We put forward the improved method.