应用数学和力学

2001 Vol. 22, No. 6

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Global Solutions of Systems of Nonlinear Impulsive Volterra Integral Equations in Banach Spaces

CHEN Fang-qi, CHEN Yu-shu

2001, 22(6): 551-560.

Abstract(2344) PDF(709)

Abstract:
The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R⁺ with an infinite number of moments of impulse effect in Banach spaces is studied.Some existence theorems of extremal solutions are obtained,which extend the related results for this class of equations on a finite interval with a finite number of moments of impulse effect.The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.

Analyses of the Singularity for the Vertical Contact Problem of Line Crack-Inclusion

SHEN An, TAO Fang-min, TANG Ren-ji

2001, 22(6): 561-566.

Abstract(2115) PDF(669)

Abstract:
Taking the short-fiber composite materials as engineering back-ground,utilizing the existing basic solutions of single inclusion and single crack,the plane problem of vertical contact interactions between line crack and rigid line inclusion in infinite plane(matrix)from the viewpoint of crack fracture mechanics is studied.According to boundary conditions,a set of standard Cauchy-type singular integral equations of the problem is obtainable.Besides,singular indexes,stresses and stress intensity factors around the contact point are expressed.Numerical examples are given to provide references to engineering.

Study of Explicit Analytic Solutions for the Nonlinear Coupled Scalar Field Equations

YAN Zhen-ya, ZHANG Hong-qing

2001, 22(6): 567-571.

Abstract(2325) PDF(775)

Abstract:
By using two different transformations,several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained,which contain soliton solutions,singular solitary wave solutions and triangle function solutions.These results can be applied to other nonlinear equations.In addition,parts of conclusions in some references are corrected.

An Investigation on Random Fatigue Strength of K-Type Tubular Joints and Crack Propagation Behaviors

NIE Guo-hua, ZHANG Ruo-jing, LIU Ren-huai

2001, 22(6): 572-578.

Abstract(2446) PDF(713)

Abstract:
Random fatigue of welded K-type tubular joints subjected to axial or out-of-plane bending load is analyzed.By considering the sizes of initial surface cracks and material constants as random variables with some probabilistic distributions,incorporating the effect of the weld,five hundred random samples are generated.Statistical computational results of life of crack propagation and effect of change of crack shape are finally obtained and compared with experimental data available based on a regression analysis.Meanwhile,crack propagation behaviors are also investigated.

A New Algorithm of Time Stepping in Dynamic Viscoelastic Problems

YANG Hai-tian, GAO Qiang, GUO Xing-lin, WU Rui-feng

2001, 22(6): 579-586.

Abstract(2089) PDF(698)

Abstract:
A new scheme of time stepping for solving the dynamic viscoelastic problems are presented.By expanding variables at a discretised time interval,FEM based recurrent formulae are derived. A self-adaptive algorithm for different sizes of time steps can be carried out to improve computing accuracy.Numerical validation shows satisfactory performance.

The Variational Principle and Application of Numerical Manifold Method

LUO Shao-ming, ZHANG Xiang-wei, CAI Yong-chang

2001, 22(6): 587-592.

Abstract(2926) PDF(832)

Abstract:
The physical-cover-oriented variational principle of numerical manifold method(NMM)for the analysis of linear elastic static problems was put forward according to the displacement model and the characters of numerical manifold method.The thoeretical calculating formulations and the controlling equation of NMM were derived.As an example,the plate with a hole in the center is calculated and the results show that the solution precision and efficiency of NMM are agreeable.

Analytical Treatment of Boundary Integrals in Direct Boundary Element Analysis of Plan Potential and Elasticity Problems

ZHANG Yao-ming, SUN Huan-chun

2001, 22(6): 593-601.

Abstract(2239) PDF(833)

Abstract:
An analytical scheme,which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method(DBEM)of two-dimensional potential and elastic problems,is established.With some numerical results,it is shown that the better precision and high computational efficiency,especially in the band of the domain near boundary,can be derived by the present scheme.

Traveling Wave Speed and Solution in Reaction-Diffusion Equation in One Dimension

ZHOU Tian-shou, ZHANG Suo-chun

2001, 22(6): 602-608.

Abstract(2269) PDF(951)

Abstract:
By Painlev analysis,traveling wave speed and solution of reaction-diffusion equations for the concentration of one species in one spatial dimension are in detail investigated.When the exponent of the creation term is larger than the one of the annihilation term,two typical cases are studied, one with the exact traveling wave solutions,yielding the values of speeds,the other with the series expansion solution,also yielding the value of speed.Conversely,when the exponent of creation term is smaller than the one of the annihilation term,two typical cases are also studied,but only for one of them,there is a series development solution,yielding the value of speed,and for the other,traveling wave solution cannot exist.Besides,the formula of calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.

Fredholm and Compact Mappings Sharing a Value

J. M. Soriano

2001, 22(6): 609-612.

Abstract(2120) PDF(778)

Abstract:
Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values.The proof is essentially based upon continuation methods.

The Space-Time Finite Element Method for Parabolic Problems

LI Hong, LIU Ru-xun

2001, 22(6): 613-624.

Abstract(2446) PDF(898)

Abstract:
Adaptive space-time finite element method,continuous in space but discontinuous in time for semi-linear parabolic problems is discussed.The approach is based on a combination of finite element and finite difference techniques.The existence and uniqueness of the weak solution are proved without any assumptions on choice of the space-time meshes.Basic error estimates in L^∞(L²)norm,that is maximum-norm in time,L²-norm in space are obtained.The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.

Statistical Property of Threshold-Crossing for Zero-Mean-Valued, Narrow-Banded Gaussian Processes

HE Wu-zhou, YUAN Ming-shun

2001, 22(6): 625-632.

Abstract(2003) PDF(691)

Abstract:
Based on a comprehensive discussion of the calculation method for the threshold crossing statistics of zero mean valued,narrow banded Gaussian processes of various practical engineering problems,including the threshold-crossing probability,average number of crossing events per unit time,mean threshold-crossing duration and amplitude,a new simple numerical procedure is proposed for the efficient evaluation of mean threshold-crossing duration.A new dimensionaless parameter, called the threshold-crossing intensity,is defined as a measure of the threshold-crossing severity, which is equal to the ratio of the product of average number of crossing events per unit time and mean threshold-crossing duration and amplitude over the threshold.It is found,by the calculation results for various combinations of stochastic processes and different thresholds,that the threshold-crossing intensity,irrelevant of the threshold and spectral density of the process,is dependent only on the threshold-crossing probability.

Global Attractivity and Global Exponential Stability for Delayed Hopfield Neural Network Models

PU Zhi-lin, XU Dao-yi

2001, 22(6): 633-638.

Abstract(2521) PDF(949)

Abstract:
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model,under the weaker assumptions on nonlinear activation functions,are concerned.By constructing suitable Liapunov function,some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural networks with time delays are presented.

The Mean Value Theorem and Converse Theorem of One Class the Fourth Order Partial Differential Equations

TONG Xiao-jun, TONG Deng-ke, CHEN Mian-yun

2001, 22(6): 639-644.

Abstract(2205) PDF(701)

Abstract:
For the formal presentation about the definite problems of ultra-hyperbolic equations,the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed for ultra-hyperbolic partial differential equations of the second order.So it is important to develop Asgeirsson mean value theorem.The mean value of solution for the higher order equation has been discussed primarily and has no exact result at present.The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value Theorem and the properties of derivation and integration.Moreover,the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials.Its converse theorem is also proved.The obtained results make it possible to discuss on continuation of the solutions and well posed problem.

Extended Mild-Slope Equation

HUANG Hu, DING Ping-xing, LÜ Xiu-hong

2001, 22(6): 645-650.

Abstract(2459) PDF(808)

Abstract:
The Hamiltonian formalism for surface waves and the mild-slope approximation were empolyed in handling the case of slowly varying three-dimensional currents and an uneven bottom,thus leading to an extended mild-slope equation.The bottom topography consists of two components:the slowly varying component whose horizontal length scale is longer than the surface wave length,and the fast varying component with the amplitude being smaller than that of the surface wave.The frequency of the fast varying depth component is,however,comparable to that of the surface waves. The extended mild-slope equation is more widely applicable and contains as special cases famous mild-slope equations below:the classical mild-slope equation of Berkhoff,Kirby.s mild-slope equation with current,and Dingemans.s mild-slope equation for rippled bed.The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.

On the Resonant Generation of Weakly Nonlinear Stokes Waves in Regions With Fast Varying Topography and Free Surface Current

HUANG Hu, ZHOU Xi-reng

2001, 22(6): 651-660.

Abstract(2357) PDF(549)

Abstract:
The effect of nonlinearity on the free surface wave resonated by an incident flow over rippled beds,which consist of fast varying topography superimposed on an otherwise slowly varying mean depth,is studied using a WKBJ-type perturbation approach.Synchronous,superharmonic and in particular subharmonic resonance were selectively excited over the fast varying topography with corresponding wavelengths.For a steady current the dynamical system is autonomous and the possible nonlinear steady states and their stability were investigated.When the current has a small oscillatory component the dynamical system becomes non-autonomous,chaos is now possible.