应用数学和力学

1993 Vol. 14, No. 7

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Theory of Gravitational Radiation of the(Ω,A_μv)-Field

Alfred Yu(Yu Xin)

1993, 14(7): 567-574.

Abstract(1650) PDF(880)

Abstract:
Further exploration of the Ω-field theory as first proposed by Yu(1989) is here presented to cover the equation of motion of a test particle which induces gravitational radiation.The same theory is shown to contain an exact gravitational radiation equation derived as a logical consequence of field equations without extra postulates.In this general dynamic context the theory is renamed "The(Ω,A_μv) field Theory".

Ekeland’s Variational Principle and Caristi’s Coincidence Theorem for Set-Valued Mappings in Probabilistic Metric Spaces

Chang Shih-sen

1993, 14(7): 575-582.

Abstract(2028) PDF(470)

Abstract:
By using the partial ordering method,a more general type,of Ekeland's variational principle and a set-valued Caristi's coincidence theorem in probabilistic metric spaces are obtained.In addition,we give a simple direct proof of the equivalence between these two theorems in probabilistic metric spaces.

The Exact Analytical Solutions to the New Model of Reservoir Filtration Problem

Li Xiao-ping, Zhao Zi-gang

1993, 14(7): 583-592.

Abstract(1614) PDF(667)

Abstract:
In this paper,under considering wellbore storage and skin,the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtration,and through various forms of limits.we have obtained the exact analytical solutions of pressure distribution on two kinds of general reservoirs the three common reservoirs(fissure reservoir,homogeneous reservoir) and under three conditions,i.e.,infinite boundary,finite sealed boundary and the finite boundary at constant pressures.

Studies on the Law of Laminar Helical Flow of Power-Law Fluid in Eccentric Annuli

Li Bang-da, Liu Yong-jian, Zhang Jing-fu

1993, 14(7): 593-600.

Abstract(2418) PDF(613)

Abstract:
According to the principle of fluid mechanics,the law of laminar,helical flow of power-law fluid in eccentric annuli is studied extensively in this paper.The apparent viscosity,velocities distribution of laminar helical flow of power-law fluid are discussed and calculating methods of flow rate and pressure loss are presented.The factors influencing flow are also analysed.On the basis of theoretical studies some new results of the present paper are compared with the theories of the helical flow of the power-law fluid in concentric annuli.The test verified that theoretical formulas in this article are proper and general.They can be used for calculating hydraulic parameters in drilling engineering.

A Finite Element——Mathematical Programming Method for Elastoplastic Problems Based on the Principle of Virtual Work

Zhu Chang-ming, Jin Yong-jie

1993, 14(7): 601-608.

Abstract(2297) PDF(614)

Abstract:
By expanding the yielding function according to Taylor series and neglecting the high order terms,the elastoplastic constitutive equation is written in a linear complementary form.Based on this linear complementary form and the principle of virtual work,a finite element-complementary method is derived for elastoplastic problem.This method is available for materials which satisfy either associated or nonassociated flow rule.In addition,the existence and uniqueness of solution for the method are also discussed and some useful conclusions have been reached.

Anisotropic Plastic Stress Field at a Mixed-Mode Crack Tip under Plane and Anti-Plane Strain

Lin Bai-song

1993, 14(7): 609-614.

Abstract(2195) PDF(601)

Abstract:
On condition that any perfectly plastic stress component at a crack tip is nothing but the function of by making use of equilibrium equations,unisotropii plastic stress-strain-rale relations,compatibility equations and Hill anisotropic plastic vivid condition,in the present paper,we derive the generally analytical expressions of the anisotropic plastic stress field at a mixed-mode crack tip under plane and anti-plane strain.Applying these generally analytical expressions to the mixed-mode cracks,we can obtain the analytical expressions of anisotropic plastic stress fields at the tips of mixed-mode Ⅰ-Ⅲ,Ⅱ-Ⅲ and Ⅰ-Ⅱ-Ⅲ cracks.

Huai Wen-xin, Li Wei

1993, 14(7): 615-623.

Abstract(1930) PDF(608)

Abstract:
The κ-ε turbulence model,considering the effect of buoyancy on turbulent kinetic energy and its dissipation rate,is adopted to present a mathematical model for round plumes and jets.There are similarity solutions in the uniform environment.Taking into account the conservation of momentum and heat flux.Finite Analytic Method is applied to obtain the similarity functions of velocity,temperature and turbulent kinetic energy.The agreement between the calculated and experimental data is good.

The Analysis of the Three-Dimensional Stress Structure Near the Crack Tip of Mode Ⅰ CT Specimens in Elastic-Plastic State(Ⅰ)——The Analysis of Constraint Parameters and Fracture Parameters

Yue Zhu-feng, Zheng Chang-qing

1993, 14(7): 625-633.

Abstract(1929) PDF(565)

Abstract:
In the present paper,three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program.The results reveal that the constraints along the thickness direction are obviously separated into two parts:the keeping similar high constraint field(Z₂) and rapid reducing constraints one(Z₂).The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively.So the three dimensional stress structure of Mode Ⅰ specimens can be derived through discussing the two fields respectively.The distribution of the Crack Tip Opening Displacement(CTOD) along the thickness direction and the three dimensional distribution of the void growth ratio(V_g) near the crack tip are also obtained.The two fracture parameters are in similar trends along the thickness direction,and both of them can reflect the effect of thickness and that of the loading level to a certain degree.

Noether’s Theory of Vacco Dynamics

Zhang Jie-fang

1993, 14(7): 635-641.

Abstract(2128) PDF(514)

Abstract:
In this paper,we first study the latent relation between the conservative quantity and the symmetry of nonholonomic dynamical systems without any additional restrictive conditions to its virtual displacement,and then establish Noether's theorem and Noether's inverse theorem of Vacco dynamics.Lastly,we give two examples to illustrate the application of result of this paper.

Excitation of Spherical Symmetric Exploding Wave With Moving Boundary

Lü Guo-hao, Dong Lian-ke, Guan Zhong-xin

1993, 14(7): 643-649.

Abstract(1863) PDF(484)

Abstract:
In this paper we have given an analytic excitation solution of exploding wave in infinite elastic body with growing spherical inner boundary,and the convergence region of series in this solution determined.Some characters of the displacement wave have also been discussed.

Common Fixed Point Theorems for(sub) Compatible and Set-Valued Generalized Nonexpansive Mappings in Complete Convex Metric Spaces

Liu Li-shan

1993, 14(7): 651-658.

Abstract(2223) PDF(599)

Abstract:
In this paper,using some conditions of(sub) compatibility between a set-valued mapping and a Single-valued mapping,we establish a necessary and sufficient condition and a sufficient condition for set-valued generalized nonexpansive mappings to have a unique common fixed point in complete convex metric spaces.The results improve,extend and develop the main results in [2-7].