THE NONLINEAR CHARACTERISTICS OF U-SHAPED BELLOWS——CALCULATIONS BY THE METHOD OF PERTURBATION

In this paper,the linear exact solution and nonlinear solutionfor U-shaped bellows have been obtained by using the general so-lution of circular ring shell and the method of perturbation.     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅳ)-CALCULATION FOR U-SHAPED BELLOWS

ＩｎｔｒｏｄｕｃｔｉｏｎＵ＿ｓｈａｐｅｄｂｅｌｌｏｗｓａｒｅｕｓｕａｌｌｙｓｅｅｎｉｎｔｈｅｐｉｐｅｌｉｎｅｓｙｓｔｅｍ (Ｆｉｇ .1) ,ｗｈｉｃｈａｒｅｕｓｅｄｔｏｃｏｍｐｅｎｓａｔｅｆｏｒｔｈｅａｘｉａｌｍｏｖｅｍｅｎｔ,ｔｈｅｒｏｔａｔｉｏｎａｎｄｔｈｅｄｅｆｌｅｃｔｉｏｎｏｆｔｈｅｐｉｐｅｌｉｎｅｓｄｕｅｔｏｔｈｅｔｈｅｒｍａｌａｃｔｉｏｎ ,ｔｈｅｂａｓｅｕｎｅｑｕａｌｓｅｔｔｌｅｍｅｎｔｓａｎｄｔｈｅｉｎｓｔａｌｌａｔｉｏｎｅｒｒｏｒｓ.Ｔｈｅａｘｉｓｙｍｍｅｔｒｉｃａｌｄｅｆｏｒｍａｔｉｏ…     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅲ)-CALCULATION FOR C-SHAPED BELLOWS

ＩｎｔｒｏｄｕｃｔｉｏｎＣ＿ｓｈａｐｅｄｂｅｌｌｏｗｓｏｒｒｅｆｅｒｒｅｄｔｏａｓｓｅｍｉ＿ｃｉｒｃｌｅｂｅｌｌｏｗｓａｒｅｗｉｔｈｃｏｍｐｌｅｘｃｏｎｆｉｇｕｒａｔｉｏｎ(Ｆｉｇ .1) .Ａｔｔｈｅｃｏｎｃａｖｅａｎｄｃｏｎｖｅｘｊｏｉｎｔｓｏｆｔｈｅｓｈｅｌｌ,ｆｏｒｅｘａｍｐｌｅａｔｐｏｉｎｔＣ ,ｔｈｅｌａｔｉｔｕｄｅａｎｇｌｅψｉｎｃｒｅａｓｅｓｂｙ 180°ａｂｒｕｐｔｌｙ .Ｓｏｉｔｉｓｔｈｅｋｅｙｔｏｃａｌｃｕｌａｔｉｏｎｆｏｒｂｅｌｌｏｗｓｔｈａｔｍａｋｉｎｇｕｐｓｏｌｕｔｉｏｎｓｅｘａｃｔ…     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅲ)-CALCULATION FOR C-SHAPED BELLOWS

This is one of the applications of Part (I), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of C-shaped bellows were calculated. The bellows was divided into protruding sections and concave sections for the use of the general solution (I), but the continuity of the stress resultants and the deformations at each joint of the sections were entirely satisfied. The present results were compared with those of the other theories and experiments, and are also tested by the numerically integral method. It is shown that the governing equation and the general solution (I) are very effective. Contributed by HUANG Qian Biography: ZHU Wei-ping (1962-)     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅱ)- CALCULATION FOR OMEGA-SHAPED BELLOWS

ＩｎｔｒｏｄｕｃｔｉｏｎＢｅｌｌｏｗｓ[1,2 ]ｉｓａｓｈｅｌｌｏｆｒｅｖｏｌｕｔｉｏｎｗｉｔｈｗｒｉｎｋｌｅｄｍｅｒｉｄｉａｎ ,ｕｓｕａｌｌｙｎａｍｅｄａｆｔｅｒｉｔｓｍｅｒｉｄｉｏｎａｌｓｈａｐｅｉｎａｐｅｒｉｏｄｏｒｉｔｓｐｒｏｆｉｌｅｏｆａｃｏｎｖｏｌｕｔｉｏｎ ,ｓｕｃｈａｓΩ＿ｓｈａｐｅｄｂｅｌｌｏｗｓ,Ｃ＿ｓｈａｐｅｄｂｅｌｌｏｗｓ,Ｕ＿ｓｈａｐｅｄｂｅｌｌｏｗｓａｎｄｓｏｏｎ .Ｔｈｅｙａｒｅｗｉｄｅｌｙｕｓｅｄｉｎｍａｎｙｆｉｅｌｄｓ,ｆｏｒｅｘａｍｐｌｅ ,ｔｈｅｅｌａｓｔｉｃｓｅｎｓｅ…     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅱ)- CALCULATION FOR OMEGA-SHAPED BELLOWS

is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega-shaped bellows were calculated, and the present results were compared with those of the other theories and experiments. It is shown that the non-homogeneous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself, and be more effective than by the theory of slender ring shells; but if a lateral slide of the bellows support exists the non-homogeneous solution will no longer entirely satisfy the boundary conditions of the problem, in this case the homogeneous solution of (Ⅰ) should be included, that is to say, the full solution of (Ⅰ) can meet all the requirements.     

PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORM TION OF LARGE AXISYMMETRICAL DEFLECTION(Ⅰ)—COUNTING NONLINEAR DEFORMATIONS OF RING SHELLS AND COMPRESSED ANGLE OF BELLOWS

This paper follows the work of[1,2].There are some progress in dealing withmoderately small rotations(the squares of rotation angles are the order of magnitudeof strains)of middle surface normals of inside and outside ring shells and compressedangle of bellows.Calculation results agree with experiments well.To bellow design,the method given in this paper is of practical value and the discussion of the influenceof compressed angle on characteristic relation is helpful.     

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     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega-shaped bellows; (Ⅲ) Calculation for C-shaped bellows; (Ⅳ) Calculation for U-shaped bellows. This paper is the first part.     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｔｈｅｏｒｙｏｆｆｌｅｘｉｂｌｅｓｈｅｌｌｓ,ｅｓｔａｂｌｉｓｈｅｄｂｙＥ .Ｌ .Ａｘｅｌｒａｄ[1,2 ]( 1 976,1 987) ,ｉｓａｓｉｍｐｌｉｆｉｅｄｔｈｅｏｒｙｆｏｒｔｈｉｎｓｈｅｌｌｓ,ｉｎｗｈｉｃｈｓｈｅｌｌｓｏｆｒｅｖｏｌｕｔｉｏｎａｒｅｆｏｒｍｕｌａｔｅｄｉｎｍｅｒｉｄｉｏｎａｌｄｉｒｅｃｔｉｏｎｂｙｂｅｎｄｉｎｇｔｈｅｏｒｙｏｆｔｈｅｓｈｅｌｌｓａｎｄｂｙｔｈｅｍｅｍｂｒａｎｅｔｈｅｏｒｙｉｎｔｈｅｃｉｒｃｕｍｆｅｒｅｎｔｉａｌｄｉｒｅｃｔｉｏｎ .ＴｈｅＡｘｅｌｒ…     

PREDICTION OF THE VISCOELASTIC PROPERTIES OF THE EQUIVALENT PARTICLE FOR THE INTERCALATED MULTI-LAYER STACK OF NANOPLASTICS

The aim of this paper is to apply the asymptotic homogenization method to deter- mining analytically and numerically the transversely isotropic viscoelastic relaxation moduli of the equivalent particle for the intercalated multi-layer stack of intercalated type nanoplastics.A two-phase multilayered material containing n layers is considered.The matrix is assumed to be an isotropic viscoelastic standard linear body and the reinforcement is assumed to be an isotropic elastic body.Final explicit analytical formulae for the effective elastic moduli of the multilay- ered material are derived first;and then the correspondence principle is employed to obtain the homogenized relaxation moduli of the equivalent intercalated particle.A numerical example is given.Final explicit analytical formulae in the time domain derived here make it convenient to estimate the influence of all the particle parameters of micro-structural details on the effective properties of the equivalent intercalated particle.The results of this paper can also be applied to multi-layer composites.     

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 RE－EXAMINATION OF DETERMINING THE COEFFICIENT OF THE AMPLITUDE EVOLUTION EQUATION IN THE NONLINEAR THEORY OF THE HYDRODYNAMIC STABILITY

ＴＨＥＲＥ－ＥＸＡＭＩＮＡＴＩＯＮＯＦＤＥＴＥＲＭＩＮＩＮＧＴＨＥＣＯＥＦＦＩＣＩＥＮＴＯＦＴＨＥＡＭＰＬＩＴＵＤＥＥＶＯＬＵＴＩＯＮＥＱＵＡＴＩＯＮＩＮＴＨＥＮＯＮＬＩＮＥＡＲＴＨＥＯＲＹＯＦＴＨＥＨＹＤＲＯＤＹＮＡＭＩＣＳＴＡＢＩＬＩＴＹＬｕｏＪ...     

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.     

COMPUTER SIMULATION OF THE MOTION OF THE BULLET BELT OF AIRPLANE GUN

ＣＯＭＰＵＴＥＲＳＩＭＵＬＡＴＩＯＮＯＦＴＨＥＭＯＴＩＯＮＯＦＴＨＥＢＵＬＬＥＴＢＥＬＴＯＦＡＩＲＰＬＡＮＥＧＵＮＺｈａｎｇＤｉｎｇｇｕｏ（章定国）（ＲｅｃｅｉｖｅｄＭａｒｃｈ１７，１９９５；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＷｕＲｕｉｆｅｎｇ）Ａｂｓｔｒ...     

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 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.     

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.     

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.