Applied Mathematics and Mechanics (English Edition)

A HIGH CONVERGENT PRECISION EXACT ANALYTIC METHOD FOR DIFFERENTIAL EQUATION WITH VARIABLE COEFFICIENTS

纪振义;叶开沅

1993, 14(3): 201-207.

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The exact analytic method was given by [1].It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision.In this paper, a new high precision algorithm is given based on [1], through a bending problem of variable cross-section beams.It can have the fourth convergent precision without increasing computation work.The present computation method is not only simple but also fast.The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements.The correctness of the theory in this paper is confirmed.

ANALYTICAL SOLUTION OF FLOW OF SECOND-ORDER NON-NEWTONIAN FLUIDS THROUGH ANNULAR PIPES

朱文辉;刘慈群

1993, 14(3): 209-215.

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This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method.Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed.It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a_c nailer value for a given H_c.Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.

NONLINEAR BENDING OF SIMPLY SUPPORTED RECTANGULAR SANDWICH PLATES

刘人怀;成振强

1993, 14(3): 217-234.

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In this paper, fundamental equations and boundary conditions of the nonlinear bending theory for a rectangular sandwicl slate with a soft core are derived by means of the method of calculus of variations.Then the nonlinear bending for a simply supported rectangular sandwich plate under the uniform lateral load is investigated by use of the perturbation method and a quite accurate analytic solution is obtained.

FOUR-POINT EXPLICIT DIFFERENCE SCHEMES FOR THE DISPERSIVE EQUATION

黎益

1993, 14(3): 235-239.

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A class of three-level explicit difference schemes for the dispersive equation ut=auxxx tare established.These schemes have higher stability and involve four mesh points at the middle level.Their local truncation errors are O(t+h)and stability conditions are from |R|≤0.25 to |R|≤10,where |R|=|a|ι/h³, which is much better than |R|≤0.25^[1]

AN APPROXIMATE SOLUTION WITH HIGH ACCURACY OF TRANSVERSE BENDING OF THIN RECTANGULAR PLATES UNDER ARBITRARILY DISTRIBUTED LOADS

周叮

1993, 14(3): 241-246.

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Ritz method is an effective way widely used to analyze the transverse bending of thin rectangular plates.Its accuracy depends completely on the basis functions selected.This paper selects the superposition of sine series with polynomials as the basis functions of thin rectangular plates.The calculating formulae are not only simple and easily programmed, but also have high accuracy.Finally, two numerical results are given and compared with those obtained by the classical method.

THE MORE GENERAL DISPLACEMENT SOLUTIONS FOR THE PLANE ELASTICITY PROBLEMS

袁镒吾

1993, 14(3): 247-252.

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In this paper, the author obtains the more general displacement solutions for the isotropic plane elasticity problems.The general solution obtained in ref.[1] is merely the particular case of this paper, In comparison with ref.[1], the general solutions of this paper contain more arbitrary constants.Thus they may satisfy more boundary conditions.

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

胡俍

1993, 14(3): 253-267.

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This paper follows the work of [1,2].There are some progress in dealing with moderately small rotations (the squares of rotation angles are the order of magnitude of strains) of middle surface normals of inside and outside ring shells and compressed angle 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 influence of compressed angle on characteristic relation is helpful.

SYMMETRIC FORMULATION OF TANGENTIAL STIFFNESSES FOR NON-ASSOCIATED VISCOPLASTICITY WITH AN IMPLICIT TIME INTEGRATION SCHEME

熊文林

1993, 14(3): 269-276.

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A numerical scheme is presented which enables the use of symmetric equation solvers in tangential stiffness programs for non-associated viscoplastic materials.

PERTURBATION SOLUTION FOR THERMAL EXPANSION BUCKLING OF NO EXPANSION JOINT SLOPE PAVEMENT PLATE

陈建康;王汝鹏

1993, 14(3): 277-284.

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In this paper, the mechanical mechanism of thermal expansion buckling of no expansion joint slope pavement undergoing the action of a temperature field is analysed.By using regular perturbation method, the formula of perturbation solution for this problem is derived, the relationship between critical laying temperature difference of slope pavement and of level straight pavement is studied, and the unified solution and its.numerical results are also obtained.In terms of this research, rational laying temperature of no expansion joint slope pavement is given.

ROUTH'S EQUATIONS FOR GENERAL NONHOLONOMIC MECHANICAL SYSTEMS OF VARIABLE MASS

罗耀煌;赵永达

1993, 14(3): 285-298.

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In this paper, Routh's equations for the mechanical systems of the variable mass with nonlinear nonholonomic constraints of arbitrary orders in a noninertial reference system have been deduced not from any variational principles, but from the dynamical equations of Newtonian mechanics.And then again the other forms of equations for nonholonomic systems of variable mass are obtained from Routh’s equations.

A FINITE DIFFERENCE METHOD AT ARBITRARY MESHES FOR THE BENDING OF PLATES WITH VARIABLE THICKNESS

李光耀;周汉斌

1993, 14(3): 299-304.

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A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper.The method is completely general with respect to various boundary conditions, load cases and shapes of plates.This difference scheme is simple and the numerical results agree well with those obtained by other methods.

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