应用数学和力学

2006 Vol. 27, No. 11

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Three-Dmensional Interactions of a Circular Crack in a Transversely Isotropic Piezoelectric Space With Resultant Sources

HOU Peng-fei, DING Hao-jiang, LEUNG Andraw-yt

2006, 27(11): 1261-1270.

Abstract(2648) PDF(526)

Abstract:
Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources:force dipoles,electric dipoles,moments,force dilatation and rotation.The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary.Such stress and charge sources may model defects like vacancies,foreign particles,and dislocations.Numerical results are presented at last.

Generalized Vector Variational-Type Inequalities in FC-Spaces

FANG Min, DING Xie-ping

2006, 27(11): 1271-1279.

Abstract(2303) PDF(737)

Abstract:
A class of generalized vector variational-type inequality problems(in short,GVVTIP)are studied in FC-spaces,which include most of vector equilibrium problems,vector variational inequality problems,generalized vector equilibrium problems and generalized vector variational inequality problem as special cases.By using F-KKM theorem,some new existence results for GVVTIP are established in noncompact FC-space.As consequences,some recent known results in literature are obtained under much weaker assumption.

Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method

YUAN Si, HE Xue-feng

2006, 27(11): 1280-1291.

Abstract(2726) PDF(631)

Abstract:
Based on the newly-developed element energy projection(EEP)method for computation of super-convergent results in one-dimensional finite element method(FEM),the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation.As a result, a satisfactory FEM mesh can be obtained,and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance.Even though the error tolerance was not completely satisfied,one or two steps of further local refinements would be sufficient.This strategy has been found to be very simple,rapid,cheap and efficient.Taking the elliptical ordinary differential equation of the second order as the model problem,the fundamental idea, implementation strategy and detailed algorithm were described.Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

A New Method to Estimate Scaling Exponents of Power-Law Degree Distribution and Hierarchical Clustering Function for Complex Networks

YANG Bo, DUAN Wen-qi, CHEN Zhong

2006, 27(11): 1292-1296.

Abstract(3006) PDF(1058)

Abstract:
A new method and corresponding numerical procedure were introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method could overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research.Furthermore,it has been verified to have higher goodness- of-fit than graphical methods by comparing the KS test statistics for 10 CNN networks.

Relaxed Elastic Lines of Second Kind on an Oriented Surface in Minkowski Space

Ayhan Tutar, Ayhan Sarioglugil

2006, 27(11): 1297-1304.

Abstract(2693) PDF(450)

Abstract:
The relaxed elastic line of second kind on an or iented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which was lying on an oriented surface the Euler-Lagr ange equations were derived.Further more,whether these curve lie on a curvature line or not is investigated and some applications are given.

Effect of Empirical Coefficients on Simulation in Two-Scale Second-Order Moment Particle-Phase Turbulence Model

HU Chun-bo, ZENG Zhuo-xiong

2006, 27(11): 1305-1311.

Abstract(2649) PDF(458)

Abstract:
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision was developed,based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision.The proposed model was used to simulate gas-particle downer reactor flows.The simulation results of particle volume fraction and mean velocity are in agreement with the experimental results.The sensitivity of the model prediction to variations in the values for the model constants is investigated,overall,the predictions do not reveal a large sensitivity to the values constants in the downer reactor,but a relatively great change of the constants has important effect on the prediction.

Constant Elasticity of Variance (CEV) Model and Analytical Strategies for Annuity Contracts

XIAO Jian-wu, YIN Shao-hua, QIN Cheng-lin

2006, 27(11): 1312-1318.

Abstract(2640) PDF(1061)

Abstract:
The constant elasticity of variance (CEV) model was constructed to study a defined contribution pension plan where benefits were paid by annuity.It also presents the process that the Legendre transform and dual theory can be applied to find an optimal investment policy during a participant's whole life in the pension plan.Finally,two explicit solutions to exponential utility function in the two different periods (before and after retirement) were revealed.Hence,the optimal investment strategies in the two periods are obtained.

Numerical Method and Application for the Three-Dimensional Nonlinear System of Dynamics of Fluids in Porous Media

YUAN Yi-rang, DU Ning, WANG Wen-qia, HAN Yu-ji, YANG Cheng-shun

2006, 27(11): 1319-1328.

Abstract(2320) PDF(648)

Abstract:
For the system of multilayer dynamics of fluids in porous media,the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward.Some techniques,such as calculus of variations,energy method,multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates were adopted.Optimal order estimates were derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.

Global Exponential Stability of Hopfield Neural Networks With Variable Delays and Impulsive Effects

YANG Zhi-chun, XU Dao-yi

2006, 27(11): 1329-1334.

Abstract(2971) PDF(645)

Abstract:
A class of Hopfield neural network with time-varying delays and impulsive effects is concerned.Some sufficient conditions ensuring the global exponential stability of impulsive delay neural networks by applying the piecewise continuous vector Lyapunov function were obtained.An example and its simulation are given to illustrate the effectiveness of the results.

Analysis Model on Gradual Change Principle of Effect Zones of Layer Face for RCCD

GU Chong-shi, SONG Jing-xiang, FANG Hai-ting

2006, 27(11): 1335-1340.

Abstract(2289) PDF(676)

Abstract:
The effect zones of layer face for roller compacred concrete dan(RCCD)have gradual changing characteristics.Based on the analysis thought of complex material,a model was built to an alyze above principle of RCCD by use of series-wound and shunt-wound connection.Some methods were proposed to determine the instantaneous elastic modulus,delayed elastic modulus and viscosity coefficient of effect zones of layer face.Above models and methods were used to mine the principle of gradual change of key calculation parameters which can respond the characteristics of effect zones. The principle of gradual change was described.A model was established to analyze the three-dimen sional viscoelastic problem of RCCD.Above programs were developed.The examples show that the proposed models and methods determining the key calculation parameters of effect zones can reflect the status of RCCD accurately.

Thermal Consolidation of Layered Porous Half-Space to Variable Thermal Loading

BAI Bing

2006, 27(11): 1341-1348.

Abstract(2905) PDF(728)

Abstract:
An analytical method was derived for the thermal consolidation of layered,saturated porous half-space to variable thermal loading with time.In the coupled governing equations of linear thermoelastic media,the influences of thermo-osmosis effect and thermal filtration effect were introduced.Solutions in Laplace transform space were first obtained and then numerically inverted.The responses of a double-layered porous space subjected to exponential decaying thermal loading were studied.The influences of the differences between the properties of the two layers(e.g.the coefficient of thermal consolidation,elastic modulus)on thermal consolidation were discussed.The studies show that the coupling effects of displacement and stress fields on temperature field can be completely neglected,however,the thermo-osmosis effect has an obvious influence on thermal responses.

Torsional Vibrations of a Rigid Circular Plate on Transversely Isotropic Saturated Soil

WU Da-zhi, CAI Yuan-qiang, XU Chang-jie, ZHAN Hong

2006, 27(11): 1349-1356.

Abstract(2791) PDF(792)

Abstract:
An analytical method is presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil.By employing the technique of Hankel transform,the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions,the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established.By appropriate transform,the dual integral equations were converted into a Fredholm integral equation of the second kind.Subsequently,the dynamic compliance coefficient,the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly.Selected examples are presented to analyse the influence of saturated soil.s anisotropy on the foundation.s vibrations.

Bifurcations of Travelling Wave Solutions for the Generalized Drinfeld-Sokolov Equations

LONG Yao, RUI Wei-guo, HE Bin, CHEN Can

2006, 27(11): 1357-1362.

Abstract(2712) PDF(704)

Abstract:
Ansatz method and the theory of dynamical systems are used to the study of the traveling wave solutions for the generalized Drinfeld-Sokolov equations.Under two groups of the parametric-conditions,more solitary wave solutions,kink and anti-kink wave solutions and periodic wave solutions were obtained.Exact explicit parametric representations of these travelling wave solutions are given.

Asymptotic Behaviour and Exponential Stability for a Thermoelastic Problem With Localized Damping

GAO Hong-jun, ZHAO Yu-juan

2006, 27(11): 1363-1372.

Abstract(2444) PDF(576)

Abstract:
A semi-linear thermoelastic problem with localized damping is considered,which is one of the most important mathematical models in material science.The existence and decays exponentially to zero of solution of this problem were obtained.Moreover,the existence of absorbing sets was achieved in the non-homogeneous case.The result indicates that the system which we studied here is asymptotic stability.

On Double Peak Probability Density Functions of a Duffing Oscillator to Combined Deterministic and Random Excitations

RONG Hai-wu, WANG Xiang-dong, MENG Guang, XU Wei, FANG Tong

2006, 27(11): 1373-1379.

Abstract(2761) PDF(833)

Abstract:
The principal resonance of Duffing oscillator to combined deterministic and random external excitation is investigated.The random excitation was taken to be white noise or harmonic with separable random amplitude and phase.The method of multiple scales was used to determine the equations of modulation of amplitude and phase.The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method.These two one-peak- density functions were combined using the probability of realization of the two stable stationary solutions to obtained the double peak probability density function.The theoretical analyses are verified by numerical results.

Asymptotic Stabilities of Stochastic Functional Differential Equations

SHEN Yi, JIANG Ming-hui, LIAO Xiao-xin

2006, 27(11): 1380-1386.

Abstract(2832) PDF(745)

Abstract:
Asymptotic characteristic of the solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Liapunov functions for locating the limit set of the solution.Moreover,from them many effective criteria on stochastic asymptotic stability,which enable us to construct the Liapunov functions much more easily in application were obtained.The results show that the well-known classical theorem on stochastic asymptotic stability is a special case of our more general results.In the end,application in stochastic Hopfield neural networks is given to verify the results.