应用数学和力学

Smale Horseshoes and Chaos in Discretized Perturbed NLS Systems(Ⅰ)——Poincaré Map

GAO Ping, GUO Bo-ling

2005, 26(11): 1261-1270.

Abstract(2157) PDF(766)

Abstract:
The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger (NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions.As a result,the discretized perturbed NLS system is shown to possess an invariant set Lambda on which the dynamics is topologically conjugate to a shift on four symbols.

Smale Horseshoes and Chaos in Discretized Perturbed NLS Systems(Ⅱ)——Smale Horseshoes

GAO Ping, GUO Bo-ling

2005, 26(11): 1271-1277.

Abstract(2275) PDF(557)

Abstract:
The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger (NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions.As a result,the discretized perturbed NLS system is shown to possess an invariant set Lambda on which the dynamics is topologically conjugate to a shift on four symbols.

3-D Dynamic Response of Transversely Isotropic Saturated Soils

WANG Xiao-gang, HUANG Yi

2005, 26(11): 1278-1286.

Abstract(2784) PDF(611)

Abstract:
A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetica harmonic source has been presented by HUANG Yi et al.using the technique of Fourier expansion and Hankel transform.However,the method may not always be valid.The work is extended to the general case being in the rectangular coordinate.The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface.Based on Biot's theory for fluid-saturated porous media,the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions.Then,using the technique of double Fourier transform,the governing differential equations were easily solved.Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained.Furthermore,a systematic study on half-space problem in saturated soils was performed.Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone,considering both case of drained surface and undrained surface,were presented.

Application of Nonlocal Friction in Several Kinds of Plastic Forming Problems

YAN Xiao-qing, LUO Hai-bao, FU Ming-fu, JIANG Wu-gui

2005, 26(11): 1287-1292.

Abstract(2126) PDF(701)

Abstract:
The nonlocal friction law proposed by Oden et al was adopted in order consider the nonlocal friction effect of the asperities on the rough contact surface between the die and the workpiece in several kinds of metal plastic forming problems.The mechanical equilibrium equations with the integral-differential form were obtained by using the engineering method or slab method,and solved approximately by using the perturbation method.The normal stress distributions on the contact surfaces in metal forming problems with nonlocal friction were obtained,and the factors which affect the nonlocal friction effect were analyzed.

Bruck Formula for a Perturbed Lipschitzian Iteration of Lipschitz Pseudocontractive Maps

Krishna Kumar, B. K. Sharma

2005, 26(11): 1293-1300.

Abstract(2137) PDF(698)

Abstract:
The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution(fixed point) of pseudocontractive operators and its variants.The object is to introduce a perturbed iteration method for proving the convergence of sequence of Lipschitzian pseudocontractive mapping using approximate fixed point technique.This iteration can be ued for nonlinear operators which are more general than Lipschitzian pseudocontractive operator and Bruck iteration fails for proving their convergence.Our results generalize the results of Chidume and Zegeye.

Calculating Method of Series for the True Anomaly of a Spacecraft Elliptic Orbit

GU Xiao-qin, TAN Zhao-yang

2005, 26(11): 1301-1306.

Abstract(2805) PDF(1032)

Abstract:
The transcendental equation of a true anomaly was written in a power series instead of a differential form.When the sufficient condition of the iterative convergence is satisfied,the relationship between the true anomaly and the time was gotten by the iterative method.And for the others,the transcendental equation of an eccentric anomaly was solved by the iterative method.After the eccentric anomaly had been calculated,the relationship between the true anomaly and the time was gotten with the numerical integral method.The approximate equation,which included the first five terms in general expansion,was written for the spacecraft quasi-circular orbit.And the true anomaly as the function of the time was also gotten by the iterative method.The numerical simulation results show that these methods are efficient.

Nonlinear Buckling Characteristic of the Graded Multiweb Structure of Heterogeneous Materials

LI Yong, ZHANG Zhi-min

2005, 26(11): 1307-1313.

Abstract(1993) PDF(677)

Abstract:
The graded multiweb structure of heterogeneous anisotropic materials,which makes full use of the continuous,gradual and changing physical mechanical performance of material properties,has a widespread application in aeroplane aerofoil structure and automobile lightweight structure.On the basis of laminate buckling theory,the equivalent rigidity method is adopted to establish the corresponding constitutive relation and the non-linear buckling governing equation for the graded multiweb structure.In finding the solution,the critical load of buckling under different complicated boundary conditions together with combined loads were obtained and testification of the experimental analysis shows that the calculation results can satisfy the requirements of engineering design in a satisfactory way.Results obtained from the research say that:graded materials can reduce the concentrated stress on the interface in an effective way and weaken the effect of initial defect in materials and thereby improve the strength and toughness of materials.

Analysis on Impact Responses of an Unrestrained Planar Frame Structure(Ⅰ)—Formula Derivation

CHEN Rong, ZHENG Hai-tao, XUE Song-tao, TANG He-sheng

2005, 26(11): 1314-1322.

Abstract(2245) PDF(537)

Abstract:
The generalized Fourier-series method was used to derive the impact responses formula of an unrestrained planar frame structure when subjected to an impact of a moving rigid-body.By using these formula,the analytic solutions of dynamic responses of the contact-impact system can be obtained.During the derivation,the momentum sum of elastic responses of the contact-impact system is demonstrated to be zero.From the derivation,it is seen that the modal method can also be used to solve this kind of impact problem.

Analysis on Impact Responses of an Unrestrained Planar Frame Structure(Ⅱ)—Numerical Example Analysis

CHEN Rong, ZHENG Hai-tao, XUE Song-tao, TANG He-sheng

2005, 26(11): 1323-1327.

Abstract(2456) PDF(558)

Abstract:
By using the formula derived in Part(Ⅰ),the instant response of an unrestrained planar frame structure subjected to the impact of a moving rigid-body are evaluated and analysed.The impact force-time history between the structure and the moving rigid-body,shear force and bending moment distribution along the beams,axial force distribution along the bars were calculated.The wave propagation phenomena of the longitudinal wave in the bars,the flexural and shear waves in the beams were also analysed.The numerical results show that the time duration of impact force is controlled by the flexural wave and the longitudinal wave;the shear effect in beams should not be neglected in the impact response analysis of structures.

Useful Relative Motion Description Method for Perturbations Analysis in Satellite Formation Flying

MENG Xin, LI Jun-feng, GAO Yun-feng

2005, 26(11): 1328-1336.

Abstract(2130) PDF(716)

Abstract:
A set of parameters called relative orbital elements were defined to describe the relative motion of the satellites in the formation flying.With the help of these parameters,the effect of the perturbations on the relative orbit trajectory and geometric properties of satellite formation can be easily analyzed.First,the relative orbital elements are derived,and pointed out:if the eccentricity of the leading satellite is a small value,the relative orbit trajectory is determined by the intersection between an elliptic cylinder and a plane in the leading satellite orbit frame reference;and the parameters that describe the elliptic cylinder and the plane can be used to obtain the relative orbit trajectory and the relative orbital elements.Second,by analyzing the effects of gravitational perturbations on the relative orbit using the relative orbital elements,it is found that the propagation of a relative orbit consists of two parts:one is the drift of the elliptic cylinder;and the other is the rotation of the plane resulted from the rotation of the normal of the plane.Meanwhile,the analytic formulae for the drift and rotation rates of a relative trajectory under gravitational perturbations are presented.Finally,the relative orbit trajectory and the corresponding changes were analyzed with respect to the J 2 perturbation.

Onset Condition of Strain Localization in Matrix of Saturated Porous Media

ZHAO Ji-sheng, TAO Xia-xin, SHI Li-jing, OU Jin-ping

2005, 26(11): 1337-1344.

Abstract(2423) PDF(484)

Abstract:
Based on governing equations of saturated porous media and Liapunov's stability here,onset conditions matrix of porous media used by solid stress and Terzaghi's effective stress constitutive description under seepage flow state,are presented,which have different forms with different representation of the solid phase,matrix or skeleton,constitutive model of porous media.The main difference relates with how to describe the interaction between solid phase and liquid phase in constitutive model.The derived onset condition of strain localization under Terzaghi's effective stress description can be used to interpret different failure types,piping effect,landslides and mudflows,by means of the type and the magnitude ratio of relative movement between solid phase and liquid phase.Examples here illuminate the onset condition of how to work.

Symplectic Structure of Poisson System

SUN Jian-qiang, MA Zhong-qi, TIAN Yi-min, QIN Meng-zhao

2005, 26(11): 1345-1350.

Abstract(2888) PDF(502)

Abstract:
When the Poisson matrix of Poisson system is non-constant,classical symplectic methods,such as symplectic Runge-Kutta method,generating function method,cannot preserve the Poisson structure.The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform.Arbitrary order symplectic method was applied to the transformed Poisson system.The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme.Numerical results show the effectiveness of the nonlinear transform.

Newton Method for Solving a Class of Smooth Convex Programming

YAO Yi-rong, ZHANG Lian-sheng, HAN Bo-shun

2005, 26(11): 1351-1358.

Abstract(2021) PDF(568)

Abstract:
An algorithm for solving a class of smooth convex programming is given.Using smooth exact multiplier penalty function,a smooth convex programming is minimized to a minimizing strongly convex function on the compact set was reduced.Then the strongly convex function with a Newtonon method on the given compact set was minimized.

Electromechanical Coupling Model and Analysis of Transient Behavior for Inertial Reciprocating Machines

HU Ji-yun, YIN Xue-gang, YU Cui-ping

2005, 26(11): 1359-1364.

Abstract(2047) PDF(556)

Abstract:
The dynamical equations for a inertial reciprocating machine excited by two rotating eccentric weights were built by the matrix methodology for establishing dynamical equations of discrete systems.A mathematical model of electromechanical coupling system for the machine was formed by combining the dynamical equations with the state equations of the two motors.The computer simulation to the model was performed for several values of the damping coefficient or the motor power,respectively.The substance of transient behavior of the machine is unveiled by analyzing the results of the computer simulation,and new methods are presented for diminishing the transient amplitude of the vibrating machine and improving the transient behavior.The reliable mathematical model is provided for intelligent control of the transient behavior and engineering design of the equipment.

Two-Grid Method for Characteristics Finite-Element Solution of 2D Nonlinear Convection-Dominated Diffusion Problem

QIN Xin-qiang, MA Yi-chen, ZHANG Yin

2005, 26(11): 1365-1372.

Abstract(2335) PDF(516)

Abstract:
For two dimension nonlinear convection diffusion equation,a two-grid method of characteristics finite-element solution was constructed.In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step.For the nonlinear convection-dominated diffusion equation,this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency.The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship the two-grid solution and the characteristics finite-element solution have the same order of accuracy.The numerical example confirms that the two-grid method is more efficient than that of characteristics finite-element method.

Numerical Simulation of 2D Fiber-Reinforced Composites Using Boundary Element Method

KONG Fan-zhong, ZHENG Xiao-ping, YAO Zhen-han

2005, 26(11): 1373-1379.

Abstract(3970) PDF(665)

Abstract:
The boundary element method was improved for the 2D elastic composites with randomly distributed inclusions.This problem can be reduced to a boundary integral equation for a multi-connected domain.Further,considering the matrices of the tractions and displacements for each group of the identical inclusion were the same,an effective computational scheme was designed,since the orders of the resulting matrix equations can be greatly reduced.Numerical examples indicate that this boundary element method scheme is more effective than the conventional multi-domain boundary element method for such a problem.The present scheme can be used to investigate the effective mechanical properties of the fiber-reinforced composites.

New Algorithm of Identifying the Shape of Flaws or Cracks in Eddy Current Testing

ZHUANG Hong-wei, MA Yi-chen, ZHANG Zhi-bin, WANG Ying-xi, CAO Jian-feng

2005, 26(11): 1380-1386.

Abstract(2398) PDF(503)

Abstract:
Eddy-current inverse technique is a very important method to reconstruct the shape of flaws or cracks.Using the domain derivative of the far-field pattern for eddy-current inverse problem with Dirichlet boundary condition,a new algorithm to recover the shape of cracks was constructed and some numerical examples were given.The algorithm demonstrates that the algorithm is feasible and correct for obtaining a reasonable reconstruction of a shape of flaws or cracks from the far-field measurements even though using less data of directions of incidence and observations for fewer wave numbers are gived.

2005 Vol. 26, No. 11