应用数学和力学

2001 Vol. 22, No. 11

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New Principles of Work and Energy as well as Power and Energy Rate for Continuum Field Theories

DAI Tian-min

2001, 22(11): 1111-1118.

Abstract(2038) PDF(748)

Abstract:
New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from the mall corre sponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of gener alized Piola.s the orems were naturally derive dinall and without any additional requirement.Finally,some new balance laws of energy and energy rate for generalized continuum mechanics were established.The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incom-pleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.

Study for the Bifurcation Topological Structure and the Global Complicated Character of a Kind of Non-Linear Finance System(Ⅰ)

MA Jun-hai, CHEN Yu-shu

2001, 22(11): 1119-1128.

Abstract(2591) PDF(715)

Abstract:
Based on the mathematical model of a kind of complicated financial system,all possible things that the model shows in the operation of our country s macro-financial system were analyzed, such as balance,stable periodic,fractal,Hopf-bifurcation,the relationship between parameters and Hopf-bifurcations,and chaotic motion etc.By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system,and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior were analyzed.This study will deepen people s understanding of the lever function of all kinds of financial policies.

Research on the Inelastic Seismic Responses of Shear-Type Multistorey Buildings With Regular Asymmetry

CAI Xian-hui, WU Rui-feng, XU Shi-bin

2001, 22(11): 1129-1134.

Abstract(1973) PDF(489)

Abstract:
The inelastic seismic responses of shear-type multistorey buildings with regular asymmetry were analyzed.The effects of the fundamental lateral period,the fundamental frequency ratio of translational to torsional,the eccentric ratio,earthquake intensity and orthogonal earthquake excitations on inelastic displacement and ductility were studied respectively.Numerical results show that aforementioned factors influence the seismic responses of the buildings.The effect of the orthogonal-input of ground motion is likely to be restricted to the moving status of eccentric elements.

New Bifurcation Patterns in Elementary Bifurcation Problems With Single-Side Constraint

WU Zhi-qiang, CHEN Yu-shu

2001, 22(11): 1135-1141.

Abstract(2381) PDF(675)

Abstract:
Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems,but the present singularity theory doesn't contain any analytical methods and results about it.As the complement to singularity theory and the first step to study on constrained bifurcations,here are given the transition sets and persistent perturbed bifurcation diagrams of 10 elementary bifurcation of codimension no more than three.

Investigation of Random Response of Rotational Shell When Considering Geometric Nonlinear Behaviour

GAO Shi-qiao, JIN Lei, Niemann H J, LIU Hai-peng

2001, 22(11): 1142-1146.

Abstract(2428) PDF(491)

Abstract:
An iteration method of statistic linearization(IMSL)is presented.By this method,an equivalent linear term was formed in geometric relation and then an equivalent stiffness matrix for non-linear term in vibration equation was established.Using the method to solve the statistic linear vibration equations,the effect of geometric nonlinearity on the random response of rotational shell is obtained.

Boundedness and Uniform Boundedness Results for Certain Non-Autonomous Differential Equations of Fourth Order

Cemil Tun

2001, 22(11): 1147-1152.

Abstract(1980) PDF(621)

Abstract:
Sufficient conditions have been obtained so that all solutions of a different fourth order differential equation are bounded and uniformly bounded.

An Edge Crack Problem in a Semi-Infinite Plane Subjected to Concentrated Forces

CHEN Yi-zhou, Norio Hasebe

2001, 22(11): 1153-1162.

Abstract(2523) PDF(442)

Abstract:
An oblique edge crack problem in a semi-infinite plane is discussed.The concentrated forces are applied on the edge crack face,or on the line boundary of the cracked semi-infinite plane. The rational mapping function approach is suggested to solve the boundary value problem and a solution in a closed form is obtained.Finally,several numerical examples with the calculated results are given.

Predicting the Consequences of Seawater Intrusion and Protection Projects

YUAN Yi-rang, LIANG Dong, RUI Hong-xing

2001, 22(11): 1163-1171.

Abstract(2193) PDF(554)

Abstract:
The simulation of this process and the effects of protection projects lays the foundation of its effective control and defence.The mathematical model of the problem and upwind splitting alternating direction method were presented.Using this method,the numerical simulation of seawater intrusion in Laizhou Bay Area of Shandong Provivce was finished.The numerical results turned out to be identical with the real measurements,so the prediction of the consequences of protection projectects is reasonable.

Chaos in Perturbed Planan Non-Hamiltonian Integrable Systems with Slowly-Varying Angle Parameters

CHEN Li-qun

2001, 22(11): 1172-1176.

Abstract(2149) PDF(576)

Abstract:
The Melnikov method was extended to perturbed planan non-Hamiltonian integrable systems with slowly-varying angle parameters.Based on the analysis of the geometric structure of unperturbed systems,the condition of transversely homoclinic intersection was established.The generalized Melnikov function of the perturbed system was presented by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.Chaos may occur in the system if the generalized Melnikov function has simple zeros.

Ishikawa Iterative Process in Uniformly Smooth Banach Spaces

HUANG Zhen-yu

2001, 22(11): 1177-1180.

Abstract(2206) PDF(811)

Abstract:
Let E be a uniformly smooth Banach space,K be a nonempty closed convex subset of E, and suppose:T:K→K is a continuous 5-strongly pseudocontractive operator with a bounded range. Using a new analytical method,under general cases,the Ishikawa iterative process {x_n} converges strongly to the unique fixed point x^* of the operator T were proved.The paper generalizes and extends a lot of recent corresponding results.

A Mode-Ⅱ Griffith Crack in Decagonal Quasicrystals

GUO Yu-cui, FAN Tian-you

2001, 22(11): 1181-1186.

Abstract(2447) PDF(598)

Abstract:
By using the method of stress functions,the problem of mode-Ⅱ Griffith crack in decagonal quasicrystals was solved.First,the crack problem of two-dimensional quasicrystals was decomposed into a plane strain state problem superposed on anti-plane state problem and secondly,by introducing stress functions,the 18 basic elasticity equations on coupling phonon-phason field of decagonal quasicrystals were reduced to a single higher-order partial differential equations.The solution of this equation under mixed boundary conditions of mode-Ⅱ Griffith crack was obtained in terms of Fourier transform and dual integral equations methods.All components of stresses and displacements can be expressed by elemental functions and the stress intensity factor and the strain energy release rate were determined.

The Bounds of the General M and J Sets and the Estimations for the Hausdorff’s Dimension of the General J Set

LIU Xiang-dong, YAN De-jun, ZHU Wei-yong

2001, 22(11): 1187-1192.

Abstract(1979) PDF(661)

Abstract:
The bounds of the general M and J sets were analytically offered.Some of the bounds were optimal in certain meaning.It not only solved the primary problem of the construction of fractal sets by escape time algorithm,and followed from the conclusion,but also offered two estimations of some special Julia set's Hausdorff’s dimension by approximate linearization method.

Analytic Sensitivity Analysis for Shape Optimization

ZHANG De-xin, JIANG Yun-zheng, CAI Jian

2001, 22(11): 1193-1200.

Abstract(2140) PDF(689)

Abstract:
Analytic sensitivity analysis technology for the boundary element method(BEM)is presented,combined with a shape optimization system for structural analysis.A shape optimization was done for an elastomer under planar stress,based on this new algorithm.A multi-object problem was studied as an illustrative example for the programmer,using weighted summing method.The result is feasible.

The Smooth and Nonsmooth Travelling Wave Solutions in a Nonlinear Wave Equation

LI Shu-min

2001, 22(11): 1201-1210.

Abstract(2172) PDF(609)

Abstract:
The travelling wave solutions(TWS)in a class of P.D.E.is studied.The travelling wave equation of this P.D.E.is a planar cubic polynomial system in three-parameter space.The study for TWS becomes the topological classifications of bifurcations of phase portraits defined by the planar system.By using the theory of planar dynamical systems to do qualitative analysis,all topological classifications of the cubic polynomial system can be obtained.Returning the results of the phase plane analysis to TWS,u(N),and considering discontinuity of the right side of the equation of TWS when ξ=x-ct is varied along a phase orbit and passing through a singular curve,all conditions of existence of smooth and nonsmooth travelling waves are given.

The Analysis of Dynamic Stress Intensity Factor for Semi-Circular Surface Crack Using Time-Domain BEM Formulation

ZHONG Ming, ZHANG Yong-yuan

2001, 22(11): 1211-1216.

Abstract(2235) PDF(591)

Abstract:
The time-domain BEM was developed to analyze the dynamic stress intensity factor(DSIF) of 3-D elastodynamic crack problems.To simulate the stress singularity along the front of a crack, eight-node isoparametric singular elements were used,and the DSIF for a semi-circular surface crack was firstly calculated based on displacement equation using the time-domain BEM formulation.The new scheme to determine the time step was brought forward.By the dynamic analysis program of time-domain BEM compiled by us,several numerical examples are presented,which demonstrate the unconditional stability and high accuracy of time-domain BEM applied to 3-D elastodynamic crack problems.

The Extinction Behavior of the Solutions for a Class of Reaction-Diffusion Equations

CHEN Song-lin

2001, 22(11): 1217-1220.

Abstract(2576) PDF(732)

Abstract:
The methods of L^p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boudnary values A sufficient and a necessary condition about the extinction of the solutions is given.Here λ>0,γ>0,β>0 are constants,Ω⊂R^N is bounded with smooth boundary Ω.At last,it is simulated with a higher order equation by using the present methods.