应用数学和力学

1987 Vol. 8, No. 10

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A New Turbulence Model with the Separate Consideration of Large and Small Vortexes

Tsai Shu-tang, Ma Bai-kun

1987, 8(10): 849-858.

Abstract(1527) PDF(799)

Abstract:
Recently the k-ε model has been widely used, but it is a kind of gradient model. Because the life-time of turbulence vortexes is very long, in common flow problems the influence of up-stream vortexes must be important, and the vortexes are not in quasi-equilibrium. So the usefulness of the k-ε model and other gradient models is limited. In this paper, according to actual cases of the turbulence, the velocity fluctuations are separated into large and small vortexes, and the large vortexes consist of two parts, one comes from up-stream end around, the other is locally generated. Thus we get a turbulence model, which consists of three parts.

Existence Theorems for a Class of Chandrasekhar H-Equation with Perturbation in Transport Theory

Zhang Shi-sheng

1987, 8(10): 859-865.

Abstract(1455) PDF(420)

Abstract:
In this paper, the existence and approximation theorems of positive solutions in space C[0,1] for a class of Chandrasekhar H-equations with perturbation in transport theory ane proved. The results presented in this paper improve and extend some recent results in [1-9].

Dynamic Response of Elastic Layer on Stiff Foundation under Time Harmonic Surface Vertical Concentrated Load

Zheng Jian-long

1987, 8(10): 867-875.

Abstract(1462) PDF(564)

Abstract:
In this paper, the line-load integral equation method proposed in reference [1] is first used for solving the elastodynamic problems. A set of one-dimensional regular integral equation is derived for calculating the dynamic response of elastic layer on stiff foundation under time harmonic surface vertical concentrated load. And the numerical solution of the integral equation is obtained.

A Singular Perturbation Problem for Periodic Boundary Differential Equation

Lin Peng-cheng, Jiang Ben-xian

1987, 8(10): 877-884.

Abstract(1502) PDF(461)

Abstract:
In this paper, we consider a second order ordinary differential equation with a small, positive parameter ε in its highest derivative for periodic boundary values problem and prove that the solution of difference scheme in paper [1] uniformly converges to the solution of its original problem with order one.

Micropolar Continuum Mechanics is More Profound than Classical Continuum Mechanics

Lu Zhang-ji

1987, 8(10): 885-890.

Abstract(1810) PDF(569)

Abstract:
This paper expounds the characteristic features of the micropolar continuum theory by developing micropolar continuum models for the static, dynamic and buckling analysis of beam-like or plate-like lattices with rigid joints, by analysing the Newton-micropolar stratified fluid model for blood and by producing experimental proofs demonstrating the micropolar property for human compact bone. In particular, it explains from the point of view of application that the micropolar continuum mechanics is a theory more profound than classical continuum mechanics. Presented in this paper is also a description of some recent advances in applications.

The Benard Convection in a Layer of Fluid with a Time-Dependent Mean Temperature

Wu Feng

1987, 8(10): 891-900.

Abstract(1361) PDF(432)

Abstract:
The onset of Bénard convection, or the critical Rayleigh number in a layer of fluid with a time-dependent mean temperature has been investigated theoretically. The critical Rayleigh number is regarded as a function of time and is expanded in series of a small parameter. Up to second approximation a simple expression of critical Rayleigh number is obtained for the time region for away from the point of zero.

A Matrix Method of Displacement Analysis of the General Spatial 7R Mechanism

Chen Wei-rong

1987, 8(10): 901-910.

Abstract(1615) PDF(521)

Abstract:
An input-output equation of the general spatial 7R mechanism is derived in this paper by using the method in [1] and applying the rotation matrices. The result is the same as [2], but the process of derivation is simpler. Applying the character of rotation matrices, it is not difficult to obtain the recurrence formulas of direction cosines of Cartesian unit vectors, to calculate the scalar products and triple products of these unit vectors, and to derive the 6th constraint equation. Moreover, an algorithm, which consists of successive applications of row transformation and expansion based on Laplace's Theorem, is given to evaluate the 16×16 determinant according to its characteristic, so that the evaluation is much simplified.

The Steiner Problem on a Surface

Jiang Xin-yao

1987, 8(10): 911-916.

Abstract(1610) PDF(402)

Abstract:
In this paper we generalize the Steiner problem on planes to general regular surfaces. The main result is: Theorem 1. If A,B,C are three points on a regular surface Σ and if another point P on Σ such that the sum of the lengths of the smooth arcs reaches the minimum, then the angles formed by every two arcs at P are all 120°.

A Note about Oden’s Constitutive Variational Principle

Xing Jing-tang

1987, 8(10): 917-924.

Abstract(1463) PDF(427)

Abstract:
A remark about some unreasoning things of Oden's constitutive variationalprinciple described in Ref. [1] is given in this paper. According to Oden's idea, the other two constitutive variational principles, which are complementary to one another, are developed. An example is performed to demonstrate the application of the constitutive variational principles.

Theory of Non-Propagation Solitons Including Surface-Tension Effects

Yan Jia-ren, Huang Guo-xiang

1987, 8(10): 925-929.

Abstract(1580) PDF(468)

Abstract:
In this paper, the surface-tension effects to non-propagating solitons is studied. Thus the Larraza and Putterman's theory has been modified. It is found that the surface-tension makes the frequency range of crosswise Oscillation of solitions larger, the amplitude higher and the width smaller. When the surfacetension coefficient is equal to zero (α=0), the results are consistent with those of Larraza and Putterman.

On the Structure of Continua and the Mathematical Properties of Algebraic Elastodynamic of a Triclinic Structural System

Gu An-hai

1987, 8(10): 931-941.

Abstract(1688) PDF(523)

Abstract:
This paper is neither laudatory nor derogatory but it simply contrasts with what might be called elastosiatic (or static topology), a proposition of the famous six equations. The extension strains and the shearing strains which were derived by A.L. Cauchy, are linearly expressed in terms of nine partial derivatives of the displacement function(u_i, u_j, u_k) =u(xⁱ, x^j, x^k) and it is impossible for the inverse proposition to sep up a system of the above six equations in expressing the nine components of matrix (∂(u_i, u_j, u_k)/∂(xⁱ, x^j, x^k). This is due to the fact that our geometrical representations of deformation at a given point are as yet incomplete^[1]. On the other hand, in more geometrical language this theorem is not true to any triangle, except orthogonal, for "squared length" in space^[2].The purpose of this paper is to describe some mathematic laws of algebraic elastodynamics and the relationships between the above-mentioned important questions.