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1995年 第16卷 第3期    刊出日期：1995-03-18

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论文

APPROXIMATION THEORY OF THREE DIMENSIONAL ELASTIC PLATESAND ITS BOUNDARY CONDITIONS WITHOUT USINGKIRCHHOFF-LOVE ASSUMPTIONS

钱伟长

1995, 16(3):  203-224. 

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The classical small deflection theory of elastic plates id based on the Kirchhoff-Lore assumptions[1,2].Ther are used on the basis of the thinness of plate and the smallness of deflection.In terms of Cartesian tensor coordinates x_i(i=0, 12)these basic assumptions are:(1)the transversal normal strain may be neglected i.e.₀₀=0;(2)the transversal shear strain may be neglected i.e.e_0α=0(α= 1, 2)(3)the transversal normal stress may be neglected i.e.. σ₀₀=0.In classical theory of elastic plates,the strain-displacement relations and the corresponding stress-displacement relations are established on the basis of these assumptions. And the equations of the classical theory for a set of undetermined quantities defined on the middle surface are established through integrating the three dimensional equations of equilibrium of stress over the thickness.In the previous papers[3,4,5],an approximation theory is given on the basis of Ihree dimensional theory of elastic plates without using Kirchhoff-Love assumptions.However,no uniqueness study is given,and also the boundary conditions have never been studied. In this paper.the same problems are studied on the basis of generalizedvariational principle of the three dimensional theory of elastic bodies￣[6].The stationary conditions of variation give an unique and complete set of field equations and the related boundary conditions for the approximation theory.In this paper,the first order approximation theory is studied in detail.

ON THE CLOSURE PROBLEM OF TURBULENCE MODEL THEORY

蔡树棠;刘宇陆

1995, 16(3):  225-227. 

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It is a wrong viewpoint that the turbulence closure problem is due to thenon-linearity, of N-S equation, because if we omit the non-linear terms in N-Sequation,many, physical quantities can not be obtained other than the mean-values. Inthis paper, we proof that the closure problem of turbulence be induced by lack ofstatistical disiribution in present turbulence theory. And the restriction of turbulencemodel theory and shortcoming of direct numerical simulation of N-S to solve theturbulence have been pointed out.

CHAOTIC BEHAVIOUR OF FORCED OSCILLATOR CONTAINING A SQUARENONLINEAR TERM ON PRINCIPAL RESONANCE CURVES

裴钦元;李骊

1995, 16(3):  229-236. 

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In this paper based on [1]we go further into the study of chaotic behaviour of theforced oscillator containing a square nonlinear term by the methods of multiple scalesand numerical simulation. Relation between the chaotic domain and principal resonance curve is discussed. By analyzing the stability of principal resonance curve weinfer that chaotic motion would occur near the frequency at which the principalresonance curve has vertical tangent.Results of numerical simulation confirm thisinference.Thus we offer an effective way to seek the chaotic motion of the systems which are hard to he investigated by Melnikoy method.

ON THE STABILITY OF NONHOLONOMIC MECHANICAL SYSTEMS WITHRESPECT TO PARTIAL VARIABLES

朱海平;梅凤翔

1995, 16(3):  237-245. 

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In this paper. a method to study the stability of nonholonomic systems withrespect to partial variables is given and several stability theorems of nonholonomicsystems with respect to partial variables are obtained. Moreover, a relationshipbetween the stability of a nonholonomic system with respect to all variables and thatto partial variables is obtained.

SAMPLING FORMULAE OF HIGHER ORDER

陈达段;刘晓明

1995, 16(3):  247-255. 

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Shannon sampling theorem is the basic theorem in signal reconstruction based ondiscrete sampling values in communication theory. The convergence rate of thisformula, however, is very slow. Professor Pen Rui-reng. after some slight compromiseon sampling rate, has come to the 3rd order, the 4th order and the 5th order samplingformulae. The calculation of the third order formula on the computer proves that itconverges much faster than the Shannon formula. This paper gives a general methodto comstruct a higher order sampling formula.

THERMOELASTICITY ANALYSIS OF FINITE COMPOSITE LAMINATESWEAKENED BY MULTIPLE ELLIPTICAL HOLES

许希武;孙良新;范绪箕

1995, 16(3):  257-267. 

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A finite composite laminate weakened by multiple elliptical holes of arbitrarydistribution, arbitrary orientation and arbitrary dimension, is treated as an anisotropic,finite multiple connected thin plate. Using the complex potential method in planetheory of heat conduction and elastictiy of an anisotropic body, the analytical solutionof a finite composite laminated plate subjected io arbitrary mechanical and thermalloads with multiple elliptical holes is. obtained by means of the Faber series expansion,mapping and the least square boundary collocation technique. The effects of someparameters on the thermostress distribution are studied in detail. Some conclusions aredrawn.

THE PANSYSTEMS VIEW OF PREDICTION AND BLOW-UP OF FLUID

欧阳首承

1995, 16(3):  269-277. 

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From the pansystems view of prediction, the paper investigates the blow-up andpost blow-up of fluid in rotation and convergence.The results show that the motion includes certain characteristics of reverse transformation the counter clockwiserotation can be developed into clockwise,and vice versa;the convergence can be changed into divergence through blow-up, and the divergence will die out continuously.The real forecasting must look this mechanism in the face. Generally speakinq, theforecasting of evolution for fluid can’t be considered only as traditional Cauchy pro-blem. The traditional forecast models should be rediscussed questioningly.

INITIAL VALUE PROBLEM FOR HIGH DIMENSIONAL DYNAMIC SYSTEMS

朱长江

1995, 16(3):  279-282. 

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In this paper. we prove the existence of the global classical solutions and the uniform stability of the zero solution to the initial value problem for a class of high dimensional dynamic systems which contain the degenerate case.

VARIABLE STRUCTURE CONTROL OF INDEFINITE-DIMENSIONAL SYSTEMS

李文林;边文明

1995, 16(3):  283-291. 

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In lhis paper, we study the variable structure control of indefinite-dimensionalcontrol systems with the functional analysis method. The reaching conditions, stabilityconditions and the approximating conditions of sliding mode, as well as the generalform of the variable structure control law are given. and the elementary frame of thevariable structure control of indefinite-dimensional systems is built.

AN ANALYTICAL SOLUTION TO LARGE DEFLECTION EQUATIONS OFSIMPLY-SUPPORTED RECTANGULAR HYPERBOLOIDAL SHALLOWSHELLS OF ORTHOTROPIC COMPOSITES

董文堂

1995, 16(3):  293-299. 

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Based on the product rule of the Fourier series and some relevant results inreferences[1,2]. a method on solving the large deflection equations of plates and shells by means of the Fourier series is proposed in the present paper,Applying this method.we derive a type solution to the Navier’s solution of the nonlinear differential equations of the rectangular hyperboloidal shallow shells of the orthotropic compositessimply supported.This solution is suitable for plates and shells with large deflection orsmall deflection whether it is isotropic or orthotropic.Their data processing results are correlative with those found in the classical examples and from the experiments.