应用数学和力学

1994 Vol. 15, No. 7

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Equilibrium in Economics with a Non-Compact lnfinite Dimensional Strategy Space

Ding Xie-ping, Zhuang De-ming

1994, 15(7): 571-575.

Abstract(2105) PDF(441)

Abstract:
We generalize an existence theorem of equilibrium of abstract economics by Tulcea to a non-compact strategy, space. Our theorem also improves a recent result of Tian.

Postbuckling Behavior of Rectangular Moderately Thick Plates and Sandwich Plates

Cheng Zhen-qiang, Wang Xiu-xi, Huang Mao-guang

1994, 15(7): 577-582.

Abstract(2232) PDF(578)

Abstract:
Postbuckling behavior is investigated for Reciangular Reissner's moderately thickplates and sandwich plates. The fundamental equations and boundary conditions areevpressed in unified dimensionless form for reciangular moderaiely thick plaies and sanduich plaies. Exact solutions of series form with a number of different boundary conditions, especially with unsmmetrical boundary conditions, are oblained bydeveloping a new technique of mixed Fourier series in nonlinear analisis. The nonlinear parlial differenlial equalions are reduced to an infinite set of simultaneous nonlinear algebraic equations, which are truncated by iteration in numerical compulations.

An Exsistence Theorem of Generalized Sawyer-Eliassen Equation

Yu Qing-yu, Xu Qin

1994, 15(7): 583-586.

Abstract(1840) PDF(471)

Abstract:
In this paper, we obtain an existence theorem for generalized Sawyer-Eliassen equation which has played an important role in the study of frontal circulation of atmosphere.

A General Solution And the Applicatlon of Space Axisymmetric Problem in Piezoelectric Material

Wang Zi-kung, Chen Geng-chao

1994, 15(7): 587-598.

Abstract(2439) PDF(627)

Abstract:
According to the structure feature of the governing equations of space axisymmetric problem in transversely, isotropic piezoelectric material. using the method of introducing potential function one by one, in this paper we obtain the so-called general solution of displacement and eleclric potential function denoied by unique poiential function which satisfies specific partiality equations. As an applying example of the general solution, we solve problem of semi-infinile body made of piezoelectric material, on the surface of the semi-infinite body a concentrative force is applied, andget the analytic formulations of stress and electric displacement comiponenis. The general solution provided by this paper can be used as a tool to analyse the mechanical-electrical coupling behavior of piezoelecrtic material which conlains defects such ascavity, inclusion, penny-shape crack, and so on. The result of the solved problem canbe used directly to analyse contact problems which take place between two piezoelectric bodies or piezoelectric body and elastic body.

1994, 15(7): 599-613.

Abstract(1782) PDF(590)

Abstract:

The Curvillinear Integral Problems to Velocity Field for Drawing Through Parabolic Dies

Zhao De-wen, Liu Xiang-hua, Wang Guo-dong, Li Gui-fan

1994, 15(7): 619-625.

Abstract(2082) PDF(587)

Abstract:
In this paper with Von Karmani's basic assumptions a kinematically admissible continuous velocity field has been established to drawing through parabolic dies (or called trumpet dies). Then by using the curvilinear and the integral as a function of the upper limit an upper bound analytical solution of the drawing stress is obtained.

Analytical Solutions of the Helical Flow of Non-Newtonian Fluid in Eccentric Annular Space

Zhang Hai-qiao, Wu Ji-zhou

1994, 15(7): 627-638.

Abstract(3013) PDF(613)

Abstract:
Many problems in petroleum and chemical industry can be reduced to the solutions of the helical flow of Non-newtonian fluid in eccentric annular space This paper studies the flow law of the laminar helical flow of the power law fluid and Bingham fluid in eccentric annular space and the determination of the flow state Intheory, by the priciple of the fluid mechanics with methematical methods based on our theory of the helical flow in concentric annular space and through the infinite subdivision method for the flow field of eccentric annular space helical flow, the apparent viscosity distribution the velocity distribution the flow rqte and the pressure drop equation of this field cat be given, and then the stability parameter,characterizing the transition from laminar to turbulent flow,is established,

Whittaker’s Reduction Method for Poincare’s Dynamical Equations

Q. K. Ghori

1994, 15(7): 639-645.

Abstract(2216) PDF(420)

Abstract:
Whitlaker's reduction method invokes the energy integral to reduce the order of Lagrange's equations of motion of aholonomic dynamical system This paper treats the coresponding result for a nonholonomic conservative system deseribed by poincar's equations which are constructed form the standpoint of the theory of Lie groups.

On the Completeness for a 3-D Linear Theory of Composite Laminate

Jiang You-liang

1994, 15(7): 647-655.

Abstract(2372) PDF(533)

Abstract:
In ref [1], a model of 3-D composite laminate theory was described. In the present paper,based on the basic equations about 3-D linear elasticity and classical rariational principles,by the block matrix operation and the Lagrange's method of multipliers, a series of basic equations and variational principles are obtained which are more complere and more systematic than that in ref [1].

The Calculation of the MultipIy-Connected Elastic Plane Problems by Means of Stress Functions of Multiple Complex Variables

Wang Lin-jiang, Lin Jia-keng

1994, 15(7): 657-664.

Abstract(2346) PDF(719)

Abstract:
On the basis of mathematical elastic theory, the stress functions of multiple complex variables are derived in an infinite multiply-connecied plate by using,nultiple conformal represeniations. The funciions are developed in Fou ries series on unit circles,the unknown coefficients of the functions are deiermined by cornparing coefficient method, then the stresses in the plaie can be calculaied. A plate conlaining multiple elliptical hofes is discussed, the corresponding FORTRAN77 program is finished. Two examples are given, they show that this method is very effective and convenient.