应用数学和力学

1992 Vol. 13, No. 5

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On the Application of ADI Method to Numerical Simulation of the Marangoni Convection Controlling in Liquid Bridge Model

Huang Wei-zhang, Zhang Suo-chun, Xie Zuo-heng, Li Jia-chun

1992, 13(5): 373-381.

Abstract(1616) PDF(568)

Abstract:
An ADI scheme is suggested to simulate the Marangoni convection controlling with emphasis on investigating application of the technique numerically.Numerical experiments conducted in the present paper turn out both successful andefficient.Hence, ADI scheme is expected to be extended to the study of other convection processes related to material manufacturing.

The Random Variational Principle and Finite Element Method

Zhang Ru-qing, Gao Hang-shan

1992, 13(5): 383-388.

Abstract(2227) PDF(739)

Abstract:
In this paper, we introduced the random materials, geometrical shapes, force and displacement boundary condition directly into the functional variational formulations and developed a unified random variational principle and finite element method with the small parameter perturbation method.Numerical examples showed that the methods have the advantages of the simple and convenient program implementation, and are effective for the random mechanics problems.

Head-on Collision between Two mKdV Solitary Waves in a Two-Layer Fluid System

Zhu Yong

1992, 13(5): 389-399.

Abstract(3416) PDF(562)

Abstract:
In this paper, based on the equations presented in [2], the head-on collision between two solitary waves described by the modified KdV equation (the mKdVequation, for short) is investigated by using the reductive perturbation method combined with the PLK method.These waves propagate at the interface of a two-fluid system, in which the density ratio of the two fluids equals the square of the depth ratio of the fluids.The second order perturbation solution is obtained.It is found that in the case of disregarding the nonuniform phase shift, the solitary waves preserve their original profiles after collision, which agrees with Fornberg and Whitham's numerical result of overtaking collision[6] whereas after considering the nonuniform phase shift, the wave profiles may deform after collision.

The Buckled States of Rectangular Plates

He Lu-wu, Cheng Chang-jun

1992, 13(5): 401-406.

Abstract(2314) PDF(546)

Abstract:
In this paper, based on the generalized variational principle of plates, the buckled states of rectangular plates under uniaxial compression are studied by use of the finite element method and the numerical analysis results under various boundary conditions are obtained by using the continuation calculation method.

Investigation on an Internal Thermal Flow of Non-Newtonian Fluid

Han Shi-fang, Xiao Fan

1992, 13(5): 407-419.

Abstract(2988) PDF(617)

Abstract:
In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the flow into axisymmetric mould cavity.In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied.For the flow into mould cavity the constitutive equation of power-law fluid is used as a Theological model of polymer fluid.The apparent viscosity is considered as a function of shear rate and temperature.A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity.As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field.However, the temperature field of the fluid flow is considered as an unsteady one.The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form.The present system of equations has been solved numerically by the splitting difference method.The numerical results show that the splitting difference method is suitable for the 2D problem of non-Newtonian fluid.The present application of the splitting diffference method is at first developed by us for non-Newtonian case.For the unsteady flow in the tube the finite difference scheme is given which leads to a tridiagonal system of equations.

Accurate Computation and Interpolation Technique of Finite Analytic Coefficients

Zhang Shi-xiong

1992, 13(5): 421-428.

Abstract(1704) PDF(547)

Abstract:
The finite analytic method (FA) developed in the last decade is an effective numerical method for solving fluid flow problems.However, because of the limitation in the present computer, large round-off errors are found in calculating FA coefficients when Reynolds number is large.This paper investigates the cause of this difficulty and presents a special programming technique in making an accurate computation of FA coefficients.Then a fundamental function known as "P_e" is tabulated by the accurate computation.In practical application the interpolation technique is employed so that the FA coefficients can be obtained reliably and quickly.

Structure of Rod Shell Theories in Hilbert Space

Zheng Quan-shui, Yang De-pin, Song Gu-quan

1992, 13(5): 429-442.

Abstract(2271) PDF(581)

Abstract:
This paper builds symmetrically general theories of rods and shells under mathematical frame of "Hilbert Space", and successfully obtains the error estimate to the system of theory.

Natural Convection in an Infinite Square under Low-Gravity Conditions

Ma Yun-li

1992, 13(5): 443-448.

Abstract(1987) PDF(413)

Abstract:
In order to study natural convection effects on fluid flows under low-gravity in space, we have expanded variables into a power series of Grashof number by using perturbation theory to reduce the Navier-Stokes equations to the Poisson equation for temperature T and biharmonic equation for stream function Φ.Suppose that a square infinite closed cylinder horizontally imposes a specified temperature of linear distribution on the boundaries, we investigate the two dimensional steady flows in detail.The results for stream function Φ, velocity u and temperature T are gained.The analysis of the influences of some parameters such as Grashof number G_r and Prandtl number P_r on the fluid motion lead to several interesting conclusions.At last, we make a comparison between two results, one from approximate equations, the other from the original version.It shows that the approximate theory correctly simplifies the physical problem, so that we can expect the theory will be applied to unsteady or three-dimensional cases in the future.

An Approximate Method on the Conformal Mapping from a Unit Circle to an Arbitrary Curve

Zheng Zhi-qiang

1992, 13(5): 449-457.

Abstract(1894) PDF(894)

Abstract:
In this paper, the conformal mapping problem on the transformation from the interior of a unit circle to the interior of the simply connected region or exterior with an arbitrary curvilinear boundary (including an arbitrary curvilinear cut crack) is discussed.The boundary of the simply connected region is approximated by a polygon.The mapping function from a unit circle to a polygon is founded by using the Schwartz-Christoffel integral.A numerical calculation method to determine the unknown parameters in the Schwartz-Christoffel integral is given.

An Equation of Motion for a Thick Viscoelastic Plate

Yang Zheng-wen, Yang Ting-qing

1992, 13(5): 459-467.

Abstract(1781) PDF(509)

Abstract:
In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia.This equation is the generalization of equations of motion for the corresponding thick elastic plate, and it can be degenerated into several types of equations for various special cases.

Study of the Stress Intensity Factor of Preformed V Shape Fracture Tip

Wang Cheng-duan

1992, 13(5): 469-477.

Abstract(2266) PDF(671)

Abstract:
This paper gives the complex stress function of preformed V shape fracture under the blasting joad.With Westergaard's method,the stress field and displacement field of preformed V shape fracture tip are derived,and hence its stress intensity factor is obtained.The blasting test result shows that tho formulas derived are correct and effective.