应用数学和力学

1983 Vol. 4, No. 5

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Recent Investigations on Strain and Stress-Rates in Nonlinear Continuum Mechanics

Guo Zhong-heng

1983, 4(5): 587-594.

Abstract(2122) PDF(555)

Abstract:
Presenting some recent considerations and results, the present paper deals with two basic concepts of the continuum mechanics, strain- and stress-rates. Upon a brief systematic survey of concepts of strain and stress, a so far unknown explicit expression for the rate of the right stretch tensor is offered in absolute notation. This paper then suggests to distinguish two ways of defining objective stress-rates, Following the second procedure, after analyzing several particular cases, the author proposes a generalized daumann flux, which contains the majority of the existing definitions for stress-rate and the Hill's result as well.

The Nonlinear Characteristics of U-Shaped Bellows——Calculations by the Method of Perturbation

Chien Wei-zhang, Wu Ming-de

1983, 4(5): 595-608.

Abstract(2274) PDF(574)

Abstract:
In this paper, the linear exact solution and nonlinear solution for U-shaped bellows have been obtained by using the general solution of circular ring shell^[1] and the method of perturbation.

On the Stability of the Rotational Motion of a Rigid Body Having a Liquid Filled Cavity under Finite Initial Disturbance

Li Li

1983, 4(5): 609-620.

Abstract(2073) PDF(608)

Abstract:
In this paper, the problem of the stability of rotational motion of a rigid body which has a liquid filled cavity and a fixed point is investigated. Criteria of stability and instability under finite initial disturbance are obtained, the region of stability is found explicitly and the behaviour of the disturbed motion is discussed.

The Double Velocity Correlation Function of Homogeneous Turbulence with Constant Mean Velocity Gradient

Tsai Shu-tang

1983, 4(5): 621-634.

Abstract(2146) PDF(507)

Abstract:
In this article, as the velocity gradient is taken as a constant value, we obtain the solutions of the equation of fluctuation velocity after Fourier transformation.Under the condition of the the mean velocity gradient being small, they represent the picture of eddies, of whick the homogeneous turbulence(both isotropic and non-isotropic)of the final period is composed. By using the eddies of these types at different times, we may compose the steady turbulent field with the constant velocity gradient and this field may represent the turbulent field in the central part of the channel flow or pipe flow approximately.Then we may obtain the double velocity correlation function of this turbulent field, which involves both longitudinal correlation coeffict f(γ/λ) and the transversal correlation coefficientg(γ/λ).We compare theoretical coefficients with the experimental data of these coefficients at initial period and final period of isotropic homogeneous turbulence. And then we obtain the relation-ship bettyeen the turbulent double velocity correlation coefficient f(γ/λ) and the mean velocity gradient. Finally,we get the expressions of the keynolds stress and the eddy viscosity coefficient.

Vector Analysis of Spatial Mechanisms——(Ⅲ)Kinematics of Spatial Mechanisms

Yu Xin

1983, 4(5): 635-640.

Abstract(2065) PDF(583)

Abstract:
The instantaneous kinematics for the spatial mechanisms considered in parts(Ⅰ)and(Ⅱ) are here established via the mothods of vector decomposition and vector equations.

Photoelectric-Computer Data Processing(PCP) Program in Experimental Photo-Stress Analysis

An Li-chan, Chen Zhi-da

1983, 4(5): 641-647.

Abstract(2361) PDF(481)

Abstract:
In this paper, a photoelectric-computer data processing(PCP) program in experimental photo-stress analysis is presented. Basic equation of photoelastic stress analysis by Chen(1962) is adopted;and a cubic spline function suitable for processing of photoelastic data is derived. This program requires least data input to computer comparing with and other programs It has been proved that the PCP program is more accurate and requires least vomputing time than other methods so lar as we know.

Exact Solution of Unsteady Axisymmetrical Two- Dimensional Flow through Triple Porous Media

Liu Ci-qun

1983, 4(5): 649-655.

Abstract(1910) PDF(425)

Abstract:
This paper seeks for the line source and cylindrical place source solutions of unsteady aaisymmetrical two-dimensional flow through inlinite and finite reservoirs with triple porosity. They not only reveal the essential characters of fractured reservoirs but also generalize and develop the ezistiag primal results of homogeneous and double porous media. Reference[1] obtained the line source solution of unsteady azisymmetrical two-dimensional flow in infinite reservoir with double porosity, in this paper we study the problem of flow through triple porous media.

Singular Perturbation of General Boundary Value Problem for Higher-Order Quasilinear Elliptic Equation Involving Many Small Parameters

Lin Zong-chi, Ni Shou-ping

1983, 4(5): 657-670.

Abstract(1978) PDF(546)

Abstract:
In this paper applyiag M. I. Visik and L. A. Lpusternik's^[1] asymptotic method and principle of fixed point of functional analysis, we study the singular perturbation of general boundary value problem for higher order quasilinear elliptic equation in the case of boundary perturbation combined with equation perturbation. We prove the existence and uniqueness of solution for perturbed problem. We give its asymptotic approximation and estimation of related remainder term.

General Solution of Multi-Valued Displacement Problem of an Eccentric Circular Ring

Tang Ren-Ji, Zhen Ji-qing

1983, 4(5): 671-677.

Abstract(2004) PDF(432)

Abstract:
In this paper,by using Мусхелишвили's method, a multi-valued displacement problem is considered for an encentric circular ring.The general expression of stress function is derived in the bi-polar co-ordinate system, Here its application is explained.

Circular Welding Problems with a Crack

Lu Jian-ke

1983, 4(5): 679-690.

Abstract(2063) PDF(464)

Abstract:
In this paper,the problem of an infinite plane with a circular hole welded by a nearly circular plate with a crack of different material is considered. The problem is transformed to solve certain boundary value problem of analytic functions and then reduced to solve a singular integral equation along the crack. The formulas and some numerical results of the factors of stress intensity for the cases Mode Ⅰ and Mode Ⅱ are obtained at the end of the paper.

Asymptotic Solution to a Nonlinear Diffusion Process by Chien-Latta’s Method

Liang Jian-hua

1983, 4(5): 691-702.

Abstract(1947) PDF(477)

Abstract:
In this paper, by using Chien Wei-zang-Latta's composite expansion Method^[5], we have obtained the first-order asymptotic solution to a system of equations for a nonlinear diffusion process, therefore, simplifying and improving the previous work^[4] considerably. Moreover, a kind of complete analytical solution has been given for a special case, and the periodic solution at the bifurcation point has been discussed, the related result being in agreement with the experiments.

A Hydrodynamic Design of the Flooding Port of Cell Separator Blood Processor and the Physical Parameters Affecting the Blood Separation

Zhu Yue-rui, Zhang Xiao-ci

1983, 4(5): 703-709.

Abstract(2207) PDF(441)

Abstract:
On the basis of "A Boundary Perturbation Solution for the Hydrodynamic Stability of Blood Flow in a Cone-Type Blood Processor"^[1], this paper analyses the phenomenon of that the stratified blood composition Lecomes a mixture again, which occurs in the process of trial-producing with the blood processor, presents a reasonable shape of the flooding port and analyses each physical parameter affecting the blood separation.These theoretical analyses are in agreement with the experimental observations, which have heen made by Shanghai Medical Instruments Institute.

Large Deflection of Circular Plate under Compound Load

Hwang Qian

1983, 4(5): 711-720.

Abstract(2139) PDF(675)

Abstract:
By means of the perturbation method, this paper presents an approximate solution for large deflection of clamped circular plate under uniform pressure together with a concentrated load at the center. The special case of vanishing central deflection is also discussed. In this paper, a load distribution function is introduced so as to make the compound loads depend on a single load parameter, and average angular deflection is being used as the single displacement perturbation parameter.

Finite Element Analysis of Seepage in Viscoelastic Media

Jin Wen-lu, Wu Gan-qing

1983, 4(5): 721-730.

Abstract(2337) PDF(529)

Abstract:
R. S. Sattdhu and E, L, Wilson presented "Finite Element Analysis of Seepage in Elastic Media"^[1], by which complex problems in engineering can be solved, In this paper, it is extended to the case of viscoelastic media, If the soil skeleton is regarded as the viscoelastic media, the stress-strain relation will be changed with time, which increases the complexity of the problems. By making use of finite-element method to solve such problems, the linear stress-strain increment relation is considered in every preselective interval of time.The linear proportional constants here is called "equivalent elastic tensor". On the basis of the equivalent elastic tensor, this paper deduces the formulation to solve problems in visco-elastic media.

On the Strong Singular Method for the Problems of Subsonic Flow Past Obstacles

Ye Jing-tang

1983, 4(5): 731-736.

Abstract(2163) PDF(384)

Abstract:
The purpose of this paper is to give a new research for the doublet elementary solution method to solve the problem of subsonic flow. A strong singular integral equation is produced. The definition and the calculating formula of the effective principle value of strong singular integral are given. From this integral equation, some numerical methods corresponding to whole continuous distribution of elementary solution can be deduced. This tpethod is applicable to calculate subsonic aerodynamic force.