Applied Mathematics and Mechanics (English Edition)

RECENT INVESTIGATIONS ON STRAIN AND STRESS RATES IN NONLINEAR CONTINUUM MECHANICS

郭仲衡

1983, 4(5): 639-648.

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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 Jaumann 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

钱伟长;吴明德

1983, 4(5): 649-665.

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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

李骊

1983, 4(5): 667-680.

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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 without any approximation. Criteria of stability and instability under finite disturbance are obtained. The region of stability is found out explicitly.

THE DOUBLE VELOCITY CORRELATION FUNCTION OF HOMOGENEOUS TURBULENCE WITH CONSTANT MEAN VELOCITY GRADIENT

蔡树棠

1983, 4(5): 681-697.

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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 transform. When the mean velocity gradient is small, they represent the picture of eddies, of which 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 longitudinalcorrelation coefficient fγ/λ and the transversal correlation coefficient gγ/λ Me compare these theoretical coefficientswith the experimental data of these coefficients at initial period and final period of isotropic homogeneous turbulence. And then we obtain the relationship between the turbulentdouble velocity correlation coefficient fγ/λ and the meanvelocity gradient. Finally, we get the expressions of the Reynolds stress and the eddy viscosity coefficient.

VECTOR ANALYSIS OF SPATIAL MECHANISMS——(Ⅲ) Kinematics of Spatial Mechanisms

余燊

1983, 4(5): 699-706.

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The instantaneous kinematics for the spatial mechanisms considered in Parts 1 and 2 are established via straightforward vector algebra.

PHOTOELECTRIC-COMPUTER DATA PROCESSING (PCP) PROGRAM IN EXPERIMENTAL PHOTO-STRESS ANALYSIS

安里千;陈至达

1983, 4(5): 707-715.

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A photoelectric-computer data processing (PCP) program in experimental photo-stress analysis is presented in this paper. The basic equation of photoelastic stress analysis by Chen (1962)^[1] is adopted, and a cubic spline function suitable for processing photoelastic data is derived. This program requires minimum data input to the computer. It has been proved that the program is more accurate and more time-saving than any other methods so far as we know.

EXACT SOLUTION OF UNSTEADY AXISYMMETRICAL TWO-DIMENSIONAL FLOW THROUGH TRIPLE ROROUS MEDIA

刘慈群

1983, 4(5): 717-724.

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This paper seeks for the line source and cylindrical plane source solutions of unsteady axisynmetrical two-dimensional flow through infinite and finite reservoirs with triple porosity. They not only reveal the essential characteristics of fractured reservoirs but also generalize and develop che existing primal results of homogeneous and porous media.Ref. [1] gives the line source solution of unsteady axi-symmetrical 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 ELLIPTCI EQUATION INVOLVING MANY SMALL PARAMETERS

林宗池;倪守平

1983, 4(5): 725-741.

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In this paper applying M. I. Visik’s and L. R. Lyuster-nik’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

汤任基;甄继庆

1983, 4(5): 743-750.

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In this paper, by using N.I, Muskhelishvili’s method a multi-valued displacement problem is considered for an eccentric circular ring. The general expression of stress function is derived in the bipolar coordinate system and its application is explained.

CIRCULAR WELDING PROBLEMS WITH A CRACK

路见可

1983, 4(5): 751-763.

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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 into solving a certain boundary value problem of analytic functions and then reduced to solving 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 this paper.

ASYMPTOTIC SOLUTION TO A NONLINEAR DIFFUSION PROCESS BY CHIEN-LATTA'S METHOD

梁建华

1983, 4(5): 765-777.

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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, thus 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 results 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

朱月锐;张效慈

1983, 4(5): 779-789.

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On the basis of "A Boundary Perturbation Solution for the Hydrodynamic Stability of Blood Flow-in a Cone-Type Blood Processor", this paper analyses the phenomenon of the stratified blood compositions being mixed again. This phenomenon occurs in the process of trial-producing with the blood processor. This paper puts forward a reasonable shape of the flooding port and analyses the various physical parameters affecting the blood separation.These theoretical analyses are verified by the results of the laboratory experiments which were made by Shanghai Medical Instruments Institute.

LARGE DEFLECTION OF CIRCULAR PLATE UNDER COMPOUND LOAD

黄黔

1983, 4(5): 791-804.

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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 tne center. Tne 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 used as the single displacement perturbation parameter.

FINITE ELEMENT ANALYSIS OF SEEPAGE IN IVSCOELASTIC MEDIA

金问鲁;吴淦卿

1983, 4(5): 805-814.

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R. S. Sandhu 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 viscoe-lastic media. If the soil skeleton is regarded as viscoelastic media, the stress-strain relation will be changed with time, which increases the complexity of problems. By making use of the finite-element method to solve such problems, the linear stress-strain increment relation is considered in every preselective interval of time. The linear proportional constant here is called "equivalent elastic tensor". On the basis of the equivalent elastic tensor, this paper deduces the formulation for solving problems in viscoelastic media.

ON THE STRONG SINGULAR METHOD FOR THE PROBLEMS OF SUBSONIC FLOW PAST OBSTACLES

叶敬棠

1983, 4(5): 815-823.

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The purpose of this paper is to give a new investigation on the doublet elementary solution method of solving 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 the whole continuous distribution of elementary solution can be deduced. This method is applicable to calculating subsonic aerodynamic force.

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