应用数学和力学

1996 Vol. 17, No. 1

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The Dynamic Buckling Problem Caused by Propagation of Stress Wave in Elastic Cylindrical Shells under impact Torque

Han Qiang, Ma Hongwei, Zhang Shanyuan, Yang Guitong, Wu Jike

1996, 17(1): 1-7.

Abstract(2312) PDF(672)

Abstract:
The buckling problem of cylindrical shells has been studied by many mechanic researchers from different points of view. In this paper,an elastic cylindrical shell with semi-infinite length is studied Let its dynamic buckling under impact torque be reduced to a bifurcation problem caused by propagation of foe torsional stress wave. The bifurcation problem is converted to a solution of nonlinear equations,the lateral inertia effect on the dynamic buckling is also discussed.Finally, numerical computation is carried out,from this,some beneficial conclusions are obtained.

A Comparative Study on the h-Convergence of 4-Node and 8-Node Quadrilateral Elements

Duan Mei, Miyamoto Yutaka, Zhou Benkuan, Chen Dapeng

1996, 17(1): 9-14.

Abstract(1954) PDF(579)

Abstract:
The present paper is mainly,concerned theoretically with the compartive stuudy on n-convergence of 4-node versus 8-node quadrilateral elements.It is found by the present authors that 8-node quadrilateral elements provided favourably enhances convergence rate over the 4-node ones.The fact is further justified via numerical examinations.

Study on Steady Surge Pressure for Yield-Pseudoplastic Fluid in a Concentric Annulus

Wang Haige, Liu Xisheng

1996, 17(1): 15-22.

Abstract(2210) PDF(661)

Abstract:
Surge pressure caused by pipe moving through the wellbore full of drilling fluid is the main factor affecting wellbore stability, on which the additional mud density isdesigned. Thus if is desired to predict the surge pressure with high accuracy. While this is closely, related with the selection of mud rheological models. Yield-Pseudoplastic model which has three parameters and is famous for its higher accuracy has been used to describe the mud rheological properties in recent years. Based on this model the paper presents a new theoretical model for calculating surge pressure caused by mud viscosity during tripping or casing in a concentric annulus of directional wells under steady laminar situation. For convenience, the paper plots the distribution of the coefficients of surge pressure for different conditions. An example is given. These results provide the basis for controlling pressure surges and tripping velocity.

Shearing Flow near a Bypass with a Ball in it

Chen Yaosong, Ma Xinmin, Liang Guoping, Dai Min

1996, 17(1): 23-27.

Abstract(1967) PDF(477)

Abstract:
This article contributes to the variation of a shearing flow near the entrance of a bypass with a ball in it.In order to fit more complicated geometry,the finite element method is used. Especially,the automatic FEM Code Composition System is used.It reduces the computing work tremendously.

Discussion on the Periodic Solutions for Linear Equation of Neutral Type with Constant Coefficients

Si Jianguo

1996, 17(1): 29-37.

Abstract(2014) PDF(527)

Abstract:
In this paper we apply the theory of Fourier Series to give some necessary and sufficient conditions of the existence of periodic solutions for linear equations of neutral type with constant coefficients[1].

Coupled Variational Principles and Generalized Coupled Variational Principles in Photoelasticity

Fu Baolian

1996, 17(1): 39-44.

Abstract(1995) PDF(689)

Abstract:
In this paper, by applying Lagrange, multiplier method and high order Lagrange multiplier method^[1], we systematically derive coupled potential energy principle coupled complementary energy principle,and generalized coupled potential energy principles and generalized coupled complementary energy principles with two and three kinds of variables in photo elasticity.

Approximate Formulas of Impact Force for Normal Impact of a Finite Elastic Beam on Elastic Foundation by a Finite Rod

Ren Wenmin, Huang Jianmin, Chen Wen

1996, 17(1): 45-51.

Abstract(2050) PDF(580)

Abstract:
The normal impact of an elastic initially static beam of finite length on an elastic foundation by a finite elastic rod with initial velocity is investigated in this paper. The approximate formulas for the impact force are obtained by the Galerkin principle.Some discussions are made and conclusions are drawn.

The Equations of Complete Depth-Averaged Turbulence Model in General Orthogonal Coordinates

Ding Yan, Zhou Xueyi, Yu Changzhao, Liang Dong

1996, 17(1): 53-61.

Abstract(1669) PDF(588)

Abstract:
For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account.The depth-averaged equations of k-turbulence model are also obtained. Because it Accounts for the three-dimensional effect, this model is named as the complete Depth-averaged model.The boundaries of natural water bodies are usually curved.In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems.

Codimension Two Bifurcations and Hopf Bifurcations of an Impacting Vibrating System

Xie Jianhua

1996, 17(1): 63-73.

Abstract(1885) PDF(886)

Abstract:
In this paper,a spring-mass system impacting against an infinite large plane is analyzed. We have proved that phenomena of codimension two bifurcations exist when coefficient of restitution is near one and ratios of frequency near the same special values.By method of normal forms, we reduced Poincaré maps into normal forms containing two parameters, After studying these normal forms, we obtained period doubling bifurcations and Hopf bifurcations of period-one and period-two.The results have been verified by numerical works.

Application of Spinor Method to the Dynamic Analysis of Robot

Lin Ruilin, Jiang Shaoyin, Lin Bi

1996, 17(1): 75-80.

Abstract(1979) PDF(518)

Abstract:
A method known as spinor method is applied to the study of dynamic model of robot.It merges velocity and angular velocity.Force and moments into an organic whole by their internal relation, and mates Newton-Euler method more concise and efficient.A reference system is formed with respect to the mass center of the arms of robot, which simplifies the calculation of inertial lensor and mass center acceleration.And further reduces work load in calculation, and thus ensures a fast real-time calculation.

The BEM for Solving the Nonhomogeneous Helmholtz Equation with Variable Coefficients

Wang Shouxin, Liu Xiping, Peng Tianguo, Zhao Zhongsheng, Zhao Suhua

1996, 17(1): 81-85.

Abstract(1782) PDF(582)

Abstract:
Considering the fundamental solution of the Laplace equation as the weight function,we give the iterative format for solving the nonhomogeneous Helmholtz equation with variable coefficients. Furthermore, the iteration method of BEM for solving the equation mentioned above is obtained. The numerical example is given in this paper. Finally, the iteration method of BUM mentioned above is compared with the coupled method of BEM that was presented before then by authors.

Interpolation Perturbation Method for Solving the Boundary Layer Type Problems

Yuan Yiwu

1996, 17(1): 87-93.

Abstract(2111) PDF(643)

Abstract:
In this paper,on the basis of Ref.[1],the author studies the boundary-value problems of the second-order differential eqs.,the highest order derivation of which contaisn the small parameters.Numerical examples show that the calculating process of this paper is quite simple and its accuracy is even higher than that of the multiple scales method(first order approximation).