THERMODYNAMIC ENTROPY MODELS OF THE FROZEN-WALL SYSTEM(I)

In this paper,the author describes,and comments on the traditional thermal theory onartificial ground freezing,and points out its important significance and shortcomings.Thefrozen-wall is analysed by system analysis methods.According to matter levels,the frozen-wall is divided into three sub-systems:frozen colloid system,frozen soil system and frozen-wall system.They correspond to different characteristics.The frozen-wall system is a largeopen system with multi-levels and multi-aspects.The problems of stability of the system andits control are the key problems in the techniques of artificial ground freezing.Based onnon-equilibrium thermodynamics and dissipative structure theory methods,the authordiscusses and reveals the problems of the formation and stability of the frozen-wall systemand its thermodynamic nature,and proposes the thermodynamic entropy models of thesystem.The result is a great satisfaction.     

THE EQUATIONS OF MOTION OF A SYSTEM UNDER THE ACTION OF THE IMPULSIVE CONSTRAINTS

In order to solve the problem of motion for the system withn degrees offreedom under the action of p impulsive constraints, we must solve the simultaneous equations consisting of n+p equations. In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for the cases of both the generalized coordinates and the quasi-coordinates. Thus there are only n-p equations of impact. Combining these equations with p impulsive constraint equations, we have simultaneous equations consisting of n equations. Therefore, only n equations are necessary to solve the problem of impact for the system subjected to impulsive constraints. The method proposed in this paper is simpler than ordinary methods.     

THE METHOD OF TRANSFORMATION OF THE BOUNDARIES FOR STRUCTURE THE ADMISSIBLE DISPLACEMENTS

In this paper the method of transformation of the boundaries for structure theadmissible displacements with various boundary conditions is presented What is called themethod of transformation of the boundaries is that. first we transform the actual systeminto the basic system and additional boundary forces and displacements on the basis of thesuperposition principle, then apply variational principles to the basic system,finally find thepermissible displacement of the actual system by means of the method of transformation ofthe series.In this paper, we also give mixed energy prinapies under Variation of boundaryconditions. The mixed energy principles as the potential and complementary energyprinciples under variation of boundary conditions are all the chief theoretical fundamentalof the method of transformation of the boundaries.Applying the method of transformation of the boundaries. we form the permissibledisplacements of rectangular plates of plane stress and bending problems with various edgeconditio     

SOME THEOREMS FOR DETERMINING THE DEFINITENESS AND CHANGEABILITY OF SIGN OF FUNCTIONS AND THE APPLICATION TO THE CONDITIONAL STABILITY OF THE MOTION OF THE AXIS OF A SLEEPING TOP

This paper gives some theorems for determiningthe definiteness and changeabilitg of sign of func-tions as well as the application to the axis of asleeping top.The necessarg and sufficient condi-tion of the conditional stabilitg of the rotion isobtained.Which coincides With that.of the stabilitgof nutation angle and also with that of the stabili-ty of total variables in the equations of cotion.     

THE IMPROVEMENT OF THE GENERAL EXPRESSION FOR THE STRESS FUNCTION φ OF THE TWO-DIMENSIONAL PROBLEM

In this paper,it is pointed that the general expression for the stress functionφ_0 of theplane problem in polar coordinates is incomplete.The problems of the curved bar with anarbitrary distributive load at the boundries can’t be solved by this stress function.For thisreason,we suggest two new stress functions and put them into the general expression.Then,the problems of the curved bar applied with an arbitrary distributive load at r=a,bboundaries can be solved.This is a new stress function including geometric boundaryconstants.     

THE OPTIMAL POINT OF THE GRADIENT OF FINITE ELEMENT SOLUTION

We consider the first boundary value problem of the second order elliptic equation andserendipity rectangular elements.Papers[2,3,9]proved that the gradients of finite elementsolution possess superconvergence at Gaussianpoint.In this paper,we extend the results inpapers[2,3,9]in the sense that the coefficients of the elliptic equations are discontinuous ona curve S which lies in the bounded domain Ω.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper,three dimensional analyses of some general constraintparameters and fracture parameters near the crack tip of Mode I CT specimens in twodifferent thicknesses are carried out by employing ADINA program.The results revealthat the constraints along the thickness direction are obviously separated into twoparts:the keeping similar high constraint field(Z_1)and rapid reducing constraintsone(Z_2).The two fields are experimentally confiremed to correspond to the smoothregion and the shear lip on the fracture face respectively.So the three dimensionalstress structure of Mode I specimens can be derived through discussing the two fieldsrespectively.The distribution of the Crack Tip Opening Displacement(CTOD)alongthe thickness direction and the three dimensional distribution of the void growth ratio(V_9 )near the crack tip are also obtained.The two fracture parameters are in similartrends along the thickness direction,and both of them can reflect the effect ofthickness and that of the loading l     

GENERAL SITUATION OF THE PARTICIPATION OF EDITORIAL BOARD MEMBERS OF APPLIED MATHEMATICS AND MECHANICS IN THE 16th.INTERNATIONAL CONGRESS OF THEORETICAL AND APPLIED MECHANICS

The 16th.International Congress of Theoretical and Applied Mechanics(ICTAM),which isheld every four years under the auspices of International Union of Theoretical and AppliedMechanics(IUTAM),was held on Aug.19,1984 Aug.25,1984 in Lyngby Industrial University.Copenhagen.Denmark.35 representatives of the People’s Republic of China participated in this     

THE METHOD OF CONTINUOUS DISTRIBUTION OF SINGULARITIES TO TREAT THE STOKES FLOW OF THE ARBITRARY OBLATE AXISYMMETRICAL BODY

This paper deals with the Stokes flow of the arbitrary oblate axisymmetrical body bymeans of constant density and quadratic distribution function approximation for themethod of continuous distribution of singularities.The Sampson spherical infinite series arechosen as fundamental singularities.The convergence.accuracy and range of application ofboth two approximations are examined by the unbounded Stokes flow past the oblatespheroid.It is demonstrated that the drag factor and pressure distribution both conformwith the exact solution very well.Besides.the properties,accuracy and the range ofapplication are getting better with the improving of the approximation of the distributionfunction.As an example of the arbitrary oblate axisymmetrical bodies,the Stokes flow ofthe oblate Cassini oval are calculated by these two methods and the results are convergentand consistent.Finally,with the quadratic distribution approximation the red blood cell.which has physiologic meaning.is considered and for the first time     

THE THEORY OF SIMILARITY AND THE PROFILE OF VERTICAL DISTRIBUTION OF CONCENTRATION OF SAND PARTICLES

In this article,we treat the problem of two-dimensionaluniform steady channel flow of turbid water with theory ofsimilarity.Under the condition of similarity of turbulentfluctuation velocity and fluctuation of concentration ofsand particles,we obtain the profile of the vertical dis-tribution of concentration of sand particles.This profileof vertical distribution of concentration of sand particlesis slightly different from that obtained by diffusion theory,and departs from that obtained by gravitational theory.     

THE EFFECTS OF ROUGHNESS CHANGE ON THE SURFACE LAYER OF THE ATMOSPHERE (I)——THE VARIATIONS OF WIND SPEED AND SHEAR STRESS

A general four-layer structure linear theory for predicting the effects of arbitrarily distributed roughness change on the variations of wind speed and shear stress in the surface layer of 3D and 2D atmospheres was presented. The results derived by the theory were agreeable to the previous ones.     

ON THE GLOEAL STABILITY OF THE ROTATIONAL MOTION AND THE QUALITATIVE ANALYSIS OF THE BEHAVIOUR OF DISTURBED MOTION OF A RIGID BODY HAVING A LIQUID-FILLED-CAVITY

This paper is a continuation of[1].In this paper we inves-tigate the distribution of steady motions of the liquid-filled-cavity body,decide the stability of each steady motion and findout the corresponding regions of stability and instability.Be-sides.the behaviour of disturbed motion is analysed qualitatively.     

THE THEOREM OF THE STABILITY OF LINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION

In the paper a theorem on the stability of linear nonautonomous system under thefrequently-acting perturbation has been given and proved on the basis of Malkin＇sTheorem.     

APPLICATION OF THE FINITE PART OF A DIVERGENT INTEGRAL IN THE THEORY OF ELASTICITY

Using the finite part of a divergent integral,we transform Kelyin’s solutions,Boussinesq’s solutions and Mindlin’s solutions in the three-dimensional theory of elasticityinto corresponding solutions in the two-dimensional theory.Besides,its application in planeproblems is also given.     

THE SINGULARITY ANALYSIS OF THE STRESS AND STRAIN FIELDS FOR MODE I FRACTURE IN ELASTIC-PLASTIC STATE

The stress and strain singularities of power hardening material for Mode I fracrure areanalysed according to the fundamental equations of elastic-plastic mechanics. It is foundthat the singularities of all stress and strain components do not change in the thick direction,and neither the six stress components nor the six strain components have the samesingularity.     

ON THE MECHANISM OF TURBULENT COHERENT STRUCTURE (I)──THE PYSICAL MODEL OF THE COHERENT STRUCTUREFOR THE SMOOTH BOUNDARY LAYER

In this paper, based on the discussion of properties of the turbulent coherent structure for smooth boundary layer, a physical model has been established. The width of slowly-moving streak line and bursting time of coherent structure expressed by momentum thickness Reynolds number of boundary layer have been obtained, which are in agreement with the experimental data^[3,4,5,7] Project supported by the National Natural Science Foundation of China     

APPLICATION OF THE METHOD OF THE RECIPROCAL THEOREM TO FINDING DISPLACEMENT SOLUTIONS OF CUBES

In this paper the method of reciprocal theorem is extended to find solutions of three-Dproblems of elasticity.First we give the basic solution of the cube with six surfaces fixed as the basic systemand then using the reciprocal theorem between the basic system acted on by unitconcentrated loads and the actnal system with Precribed surface displacements,we finddisplacement solution of the actual system.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(II)—THE ANALYSES OF THE STRESS STRUCTURE

Based on [1], the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper. The characteristics of the stress structure in the smooth region have been found that the variable z can separated out; the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality. The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction. The obtained expressions of the stresses are very simple and visualized. The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree. A new degree parameter of the plane strain state has been put forward and studied. The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level. The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.     

THE PERTURBATION-ITERATIVE METHOD APPLIED TO THE PROBLEMS OF THE LARGE DEFLECTION OF THE ELASTIC CIRCULAR THIN PLATES

In this paper, we present a perturbation-iterative method for solving certain boundary value problems encountered in the nonlinear theory of elastic circular thin plates. At the same time, with this method, we strictly prove the convergence of the solutions for the large deflection equations of circular plates subjected to certain distributed loads.     

THE SEPARATION OF LARGE VORTEXES AND THE CLOSED EQUATIONS OF TURBULENCE MODEL

This paper presents a new kind of average for the locally-generated large vortexes sothat the physical quantities of the locally-generated large vortexes and the external largevoriexes can be rigorously separated from the equations for the large vortexes proposed in aprevlous paper.To the equations the two kinds of large vertexes.some auxiliaryrelations are introduced,and the value of the length-scale l_N of energy dissipation of theexternal large vortexes may be determined according to the actual circumstances of thedisturbance of external sources.Thus,the resulting equations of second moments ofturbulent velocity fluctuations for the two kinds of large vortexes can be made closed.Meanwhile,the corresponding coefficients of diffusion in the previous paper areimproved.Finally,a closed set of numerically-solvable equations of turbulence model areobtained.