应用数学和力学

1993 Vol. 14, No. 3

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A High Convergent Precision Exact Analytic Method for Differential Equation with Variable Coefficients

Ji Zhen-yi, Ye Kai-yuan

1993, 14(3): 189-194.

Abstract(2086) PDF(483)

Abstract:
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 Fluid through Annular Pipes

Zhu Wen-hui, Liu Ci-qun

1993, 14(3): 195-201.

Abstract(2296) PDF(700)

Abstract:
This paper presents an analytical solution to the unsteady flow of one kind of second-order non-Newtonian fluid by the use of integral transformation,simulates the results,analyses the effect of non-Newtonian coefficient He and other parameters on the flow and shows that when He keeps the same the annular flow has a shorter characteristic time than the general pipe flow and the correspondent velocity and average velocity have a smaller value.When r₁/r₂(η)remains unchanged,the shear stress of inner wall of annular flow changes with the inner radius r₁ compared with the general pipe flow and is always smaller than that of the outer wall.

Nonlinear Bending of Simply Supported Rectangular Sandwich Plates

Liu Ren-huai, Cheng Zhen-qiang

1993, 14(3): 203-218.

Abstract(2108) PDF(467)

Abstract:
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

Li Yi

1993, 14(3): 219-223.

Abstract(2378) PDF(705)

Abstract:
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

Zhou Ding

1993, 14(3): 225-230.

Abstract(1828) PDF(629)

Abstract:
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

Yuan Yi-wu

1993, 14(3): 231-236.

Abstract(1806) PDF(453)

Abstract:
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 Axlsymmetrical Deflection(Ⅰ)——Counting Nonlinear Deformations of Ring Shells and Compressed Angle of Bellows

Hu Liang

1993, 14(3): 237-250.

Abstract(1749) PDF(539)

Abstract:
This paper is a conrinuous study of papers [1,2].There is some progress in dealing with moderately small rotations 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 Visco-Plasticity with an Implicit Time Integration Scheme

Xiong Wen-lin

1993, 14(3): 251-257.

Abstract(2058) PDF(477)

Abstract:
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

Chen Jian-kang, Wang Ru-peng

1993, 14(3): 259-266.

Abstract(1912) PDF(458)

Abstract:
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

Luo Yao-huang, Zhao Yong-da

1993, 14(3): 267-279.

Abstract(2207) PDF(495)

Abstract:
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

Li Guang-yao, Zhou Han-bin

1993, 14(3): 281-286.

Abstract(2109) PDF(551)

Abstract:
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.