应用数学和力学

A Time Domain Method for Quasi-Static Analysis of Viscoelastic Thin Plates

ZHANG Neng-hui, CHENG Chang-jun

2001, (10): 1001-1008.

Abstract(2600) PDF(707)

Abstract:
Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Kûrmûn's hypotheses of thin plates with large deflections,a mathematical model for quasi-static problems of viscoelastic thin plates was given.By the Galerkin method in spatial domain,the original integro-partial-differential system could be transformed into an integral system.The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper.Numerical results show that compared with the ordinary finite difference method,the new method in this paper is simpler to operate and has some advantages,such as,no storage and quicker computational speed etc.

The Flow Problem of Fluids Flow in a Fractal Reservoir With Double Porosity

TONG Deng-ke, Zhang Hong-qing

2001, (10): 1009-1016.

Abstract(2202) PDF(655)

Abstract:
The effective radius of oil well is introduced in the inner boundary in the problem of fluids flow through fractal reservoir with double porosity,and thus a new model is established.Taking the wellbore storage and steady-state skin effect into consideration,the exact solutions of the pressure distribution of fluids flow in fractal reservoirs with double porosity are given for the cases of an infinite outer boundary,a finite closed outer boundary and a bounded domain with the constant pressure outer boundary conditions.The pressure behavior of fractal reservoir with double porosity is analyzed by using a numerical inversion of the Laplace transform solution.The pressure responses of changing various parameters are discussed.

B3/4cklund Transformation, Nonlinear Superposition Formulae and Infinite Conserved Laws of Benjamin Equation

ZHANG Hong-qing, ZHANG Yu-feng

2001, (10): 1017-1021.

Abstract(2060) PDF(903)

Abstract:
B3/4cklund transformation,exact solitary wave solutions,nonlinear supperposition formulae and infinite conserved laws are presented by using TU-pattern.The algorithm involves wide applications for nonlinear evolution equations.

Fixed Point Theorem of Composition g-Contraction Mapping and Its Applications

YUN Tian-quan

2001, (10): 1022-1028.

Abstract(2447) PDF(631)

Abstract:
Any composition sequential mapping,periodic composition mapping of a complete nonempty metric space M into M with geometric mean contraction ratio less than 1(simplifying as"g-contraction mapping") has a unique fixed point in M .Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.

Generalized H-KKM Type Theorems in H-Metric Spaces With Applications

DING Xie-ping, XIA Fu-quan

2001, (10): 1029-1036.

Abstract(1903) PDF(735)

Abstract:
The new notions of H-metric spaces and generalized H-KKM mappings were introduced.Some generalized H-KKM type theorems for generalized H-KKM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces.These theorems generalize recent results of Khamsi and Yuan.As applications,some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers,fixed point theorems and minimax inequality are obtained in H-metric spaces.These results generalize a number of known results in recent literature.

Antiplane Problems of Periodical Rigid Line Inclusions Between Dissimilar Anisotropic Materials

LIU You-wen

2001, (10): 1037-1042.

Abstract(2193) PDF(554)

Abstract:
The antiplane shear problems of periodical rigid line inclusions between dissimilar anisotropic materials are dealt with.By using the complex variable method,the closed form solutions are obtained.The stress distribution in the immediate vicinity of the rigid line is examined.The corresponding formulation between dissimilar isotropic materials and in homogeneous anisotropic medium can be derived from the special cases of those in the present paper,and the limit conditions are in agreement with the previously known results.

A New Unsteady Three Dimensional Model for Macromolecular Transport and Water Filtration Across the Arterial Wall

HUANG Hao, WEN Gong-bi

2001, (10): 1043-1057.

Abstract(2633) PDF(604)

Abstract:
A new unsteady three-dimensional convective-diffusive mathematical model for the transportation of macromolecules and water across the arterial wall was proposed .After the formation of leaky junctions due to the mitosis of endothelial cell of the arterial wall,the macromolecular transport happens surrounding the leaky cells.The arterial wall was divided into four layers:the endothelial layer,the subendothelial intima,the internal elastic lamina and the media for the convenience of research.The time-dependent concentration growth,the effect of the shape of endothelial cell and the effect of physiological parameters were analyzed.The analytical solution of velocity field and pressure field of water flow across the arterial wall were obtained;and concentration distribution of three macromolecules;LDL,HRP and Albumin,were calculated with numerical simulation method.The new theory predicts,the maximum and distribution areas of time-dependent concentration with roundshape endothelial cell are both larger than that with ellipse-shape endothelial cell.The model also predicts the concentration growth is much alike that of a two-dimensional model and it shows that the concentration reaches its peak at the leaky junction where atherosclerotic formation frequently occurs and falls down rapidly in a limited area beginning from its earlier-time growth to the state when macromolecular transfer approaches steadily.These predictions of the new model are in agreement with the experimental abservation for the growth and concentration distribution of LDL and Albumin.

General Form of Matching Equation of Elastic-Plastic Field Near Crack Line for Mode Ⅰ Crack Under Plane Stress Condition

YI Zhi-jian, YAN Bo

2001, (10): 1058-1066.

Abstract(2257) PDF(542)

Abstract:
Crack line field analysis method has become an independent method for crack elastic-plastic analysis,which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty.With this method,the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained.But up to now all solutions obtained by this method were for different concrete problems,no general steps and no general form of matching equations near crack line are given out.With crack line analysis method,this paper proposes the general steps of elastic-plastic analysis near crack line for mode crack in elastic-perfectly plastic solids under plane stress condition,and in turn given out the solving process and result for a specific problem.

Nonlinear Dynamics Modeling of Mechanical Periodicity of End Diastolic Volume of Left Ventricle

XU Shi-xiong, MAO Xiao-chun

2001, (10): 1067-1074.

Abstract(2199) PDF(743)

Abstract:
The cardiovascular system with a lumped parameter model is treated,in which the Starling model is used to simulate left ventricle and the four-element Burattini & Gnudi model is used in the description of arterial system.Moreover,the feedback action of arterial pressure on cardiac cycle is taken into account.The phenomenon of mechanical periodicity (MP) of end diastolic volume (EDV) of left ventricle is successfully simulated by solving a series of one-dimensional discrete nonlinear dynamical equations.The effects of cardiovascular parameters on MP is also discussed.

The Asymptotic Behavior of Solution for the Singularly Perturbed Initial Boundary Value Problems of the Reaction Diffusion Equations in a Part of Domain

LIU Qi-lin, MO Jia-qi

2001, (10): 1075-1080.

Abstract(2275) PDF(621)

Abstract:
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered.Using the operator theory the asymptotic behavior of solution for the problems is studied.

The Method of Multiple Scales Applied to the Nonlinear Stability Problem of a Truncated Shallow Spherical Shell of Variable Thickness With the Large Geometrical Parameter

KANG Sheng-liang

2001, (10): 1081-1091.

Abstract(2234) PDF(658)

Abstract:
Using the mo difie d method of multiple scales,the no nlinear stability of a truncated shallow spherical shell of variable thicknes swith a nondefor ma ble rigid body at the center under co mpound loads is investigated.When the geometrical parameter kislarger,the uniformly valid as ymptotic solutions of this problem are obtained and the remainder terms are estimated.

A Conservative Difference Scheme for Conservative Differential Equation With Periodic Boundary

CAI Xin

2001, (10): 1092-1096.

Abstract(2262) PDF(727)

Abstract:
The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied,and a conservative difference scheme was constructed.Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation,it is proved that the scheme converges uniformly to the solution of differential equation with order one.

Conservation Law and Application of J-Integral in Multi-Materials

WANG Li-min, CHEN Hao-ran, XU Shi-lang

2001, (10): 1097-1104.

Abstract(2413) PDF(734)

Abstract:
The conservation law of J integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method.Then a schedule model was established that an interface crack is inserted in four media.According to the J-integral conservation law on multi-media,the energy release ratio of-type crack was considered to be conservation when the middle medium layers are very thin.And the conservation law was also convinced by numerical method.By means of the dimension analysis on the model,the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.

Maximal Elements and Equilibrium of Abstract Economy

LIU Xin-ge, CAI Hai-tao

2001, (10): 1105-1109.

Abstract(2007) PDF(996)

Abstract:
An existence theorem of maximal elements for a new type of preference correspondences which are Q_θ-majorized is given.Then some existence theorems of equilibrium for abstract economy and qualitative game in which the constraint or preference correspondences are Q_θ-majorized are obtained in locally convex topological vector spaces.

2001 Vol. 22, No. 10