应用数学和力学

2005 Vol. 26, No. 6

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New Approach to Minimize Dispersion Induced by Turn in the Capillary Electrophoresis Channel Flows

LI Zhi-hua, LIN Jian-zhong, NIE De-ming

2005, 26(6): 631-636.

Abstract(2416) PDF(540)

Abstract:
The mechanism of dispersion induced by turn in the capillary electrophoresis channel flows was analyzed firstly.Then the mathematical model of electroosmotic flow is built,and the dispersion of the flow,with different distribution of charge at inner and outer wall in the turns,was simulated numerically using the finite differential method.A new approach of altering the distribution of charge at inner and outer wall in the turns was presented,based on the computational results,to minimize the dispersion induced by turn.Meanwhile,an optimization algorithm to analyze the numerical results and determine the optimal distribution of charge in the turns was also developed.It is found that the dispersion induced by turn in the capillary electrophoresis channel flows could be significantly suppressed by this approach.

Description and WENO Numerical Approximation to Nonlinear Waves of a Multi-Class Traffic Flow LWR Model

ZHANG Peng, DAI Shi-qiang, LIU Ru-xun

2005, 26(6): 637-644.

Abstract(2534) PDF(634)

Abstract:
A strict proof of the hyperbolicity of the multi-class LWR(Lighthill-Whitham-Richards) traffic flow model,as well as the descriptions on those nonlinear waves characterized in the traffic flow problems were given.They were mainly about the monotonicity of densities across shocks and in rarefactions.As the system had no characteristic decomposition explicitly,a high resolution and higher order accuracy WENO (weighted essentially non-oscillatory) scheme was introduced to the numerical simulation,which coincides with the analytical description.

Nonlinear Dynamical Characteristics of Piles Under Horizontal Vibration

HU Yu-jia, CHENG Chang-jun, YANG Xiao

2005, 26(6): 645-652.

Abstract(2041) PDF(611)

Abstract:
The pile-soil system is regarded as a visco-elastic half-space embedded pile.Based on the method of continuum mechanics,a nonlinear mathematical model of pile-soil interaction was established-a coupling nonlinear boundary value problem.Under the case of horizontal vibration,the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain.The effects of parameters,especially the axis force on the stiffness were studied in detail.The numerical results suggest that it is possible that the pile applying an axis force will lose its stability.So,the effect of the axis force on the pile is considered.

Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅸ)-Thermomechanics

DAI Tian-min

2005, 26(6): 653-658.

Abstract(2429) PDF(649)

Abstract:
The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out.New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated.From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced.The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time.It should be emphasized to note that,the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua,is believed to be clarified.

Long Time Behavior for the Solution of the Initial-Boundary Value Problem of One Class of Systems With Multidimensional Inhomogeneous GBBM Equations

FANG Shao-mei, GUO Bo-ling

2005, 26(6): 659-664.

Abstract(2814) PDF(619)

Abstract:
The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony (GBBM) equations is reviewed.The existence of global attractors of this problem was proved by means of a uniform a priori estimate for time.

Modified H-R Mixed Variational Principle for Magnetoelectroelastic Bodies and State-Vector Equation

QING Guang-hui, QIU Jia-jun, LIU Yan-hong

2005, 26(6): 665-670.

Abstract(3146) PDF(610)

Abstract:
Based upon the Hellinger-Reissner(H-R) mixed variational principle for three-dimensional elastic bodies,the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established.The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations.To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates,the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle.Finally,it is pointed out that the modified H-R mixed variational principle for pure elastic,single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.

Stability and Bifurcation Behaviors Analysis in a Nonlinear Harmful Algal Dynamical Model

WANG Hong-li, FENG Jian-feng, SHEN Fei, SUN Jing

2005, 26(6): 671-676.

Abstract(2409) PDF(519)

Abstract:
A food chain made up of two typical algae and a zooplankton was considered.Based on ecological eutrophication,interaction of the algal and the prey of the zooplankton,a nutrient nonlinear dynamic system was constructed.Using the methods of the modern nonlinear dynamics,the bifurcation behaviors and stability of the model equations by changing the control parameter r were discussed.The value of r for bifurcation point was calculated,and the stability of the limit cycle was also discussed.The result shows that through quasi-periodicity bifurcation the system is lost in chaos.

Calculation Analysis of Shearing Slip for Steel-Concrete Composite Beam Under Concentrated Load

LIU Han-bing, LIU Wen-hui, ZHANG Yun-long

2005, 26(6): 677-682.

Abstract(2556) PDF(609)

Abstract:
The strain's difference of steel and concrete under vertical concentrated load was analyzed on the basis of elastic theory,and was compared with ideal solution of steel and concrete under vertical uniform load.The results indicate that the computing formula concluded from the paper is believable.The practical structure usually bears concentrated load,so it can be used in the practical engineering.

Careful Numerical Simulation and Analysis of Migration-Accumulation of Tanhai Region

YUAN Yi-rang, DU Ning, HAN Yu-ji

2005, 26(6): 683-693.

Abstract(2140) PDF(537)

Abstract:
Numerical simulation of careful parallel arithmetic of oil resources migration-accumulation of Tanhai Region(three-layer) was done.Careful parallel operator splitting-up implicit iterative scheme,parallelar ithmetic program,parallel arithmetic infor mation and alternating-direction mesh subdivision were put forward.Parallel arithmetic and analysis of different CPU combinations were done.This numerical simulation test and the actual conditions are basically coincident.The conver-gence estimation of the model problem has successfully solved the difficult problem in the fields of permeation fluid mechanics,computational mathematics and petroleum geology.

Numerical Investigation of Effect of Rolling Manipulation of Traditional Chinese Medical Massage on Blood Flow

XU Shi-xiong, JI Lin, WANG Qing-wei

2005, 26(6): 694-700.

Abstract(2624) PDF(824)

Abstract:
The hemodynamic mechanism of rolling manipulation(RM) of TCMM (traditional Chinese medical massage) is investigated.An axisymmetrical non-liner model and an arbitrary Lagrangian Eulerian finite element method(ALE-FEM) with rezoning algorithm were introduced to study the viscous flow through an axisymmetrical rigid tube with axially moving stenosis to simulate the rolling manipulation.Flow rate and wall shear stress were obtained by solving complete Navier-Stokes equations numerically.The numerical results show that the stenosis moving frequency,namely the frequency of rolling manipulation,has great effect on the disturbance of flow and the wall shear stress.The stenosis coefficient,which characterizes the severity of the stenosis,another adjustable parameter in rolling manipulation,also shows the significant effect on flow rate and wall shear stress.These numerical results may provide some data that can be taken into consideration when massage is used in clinic.

New Method for Measuring the Random Thresholds of Long Fatigue Crack Propagation

ZHAO Yong-xiang, YANG Bing, LIANG Hong-qin, WU Ping-bo, ZENG Jing

2005, 26(6): 701-706.

Abstract(2713) PDF(583)

Abstract:
A so-called "local probabilistic Paris relation method" was presented for measuring the random thresholds of long fatigue crack propagation.A check was made to the conventional method,in which the thresholds were measured statistically and directly by the test data.It was revealed that this method was not reasonable because the test data have seldom a unified level of crack growth rates.Differently,in the presented method the Paris-Erdogan equation was applied to model the local test data around the thresholds.Local probabilistic relations with both the survival probability and the confidence were established on a lognormal distribution of the stress density factors.And then,the probabilistic thresholds were derived from the probabilistic factors with a given critical level of growth rate.An analysis on the test data of LZ50 axle steel for the Chinese railway vehicles verifies that the present method is feasible and available.

Liquid-Gas Coexistence Equilibrium in a Relaxation Model

WANG Ping, TANG Shao-qiang

2005, 26(6): 707-713.

Abstract(2701) PDF(557)

Abstract:
Stability of liquid-gas coexistence equilibrium in a relaxation model for isothermal phase transition in a sealed one-dimensional tube was discussed.With matched asymptotic expansion,a linear system for first order perturbations was derived formally.By solving this system analytically,it is shown that small initial perturbations are damped out in general;yet they may maintain at certain level for special cases.Numerical evidence is presented.This manifests the regularization effects of relaxation.

Higher Order Boussinesq-Type Equations for Water Waves on Uneven Bottom

WANG Ben-long, LIU Hua

2005, 26(6): 714-722.

Abstract(2895) PDF(752)

Abstract:
Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived.The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain.The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation.Taking the velocities on half relative water depth as the fundamental unknowns,terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution,with which the problem was closed.With enhancements of the finite order Taylor expansion for the velocity field,the application range of the present model was extended to the not so mild slope bottom.For linear properties,some validation computations of linear shoaling and Booij's tests were carried out.The problems of wave-current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents.All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.

Stationary Random Waves Propagation in 3D Viscoelastic Stratified Solid

GAO Qiang, LIN Jia-hao

2005, 26(6): 723-733.

Abstract(2814) PDF(485)

Abstract:
Propagation of stationary random waves in viscoelastic stratified transverse isotropic materials is investigated.The solid was considered multi-layered and located above the bedrock,which was assumed to be much stiffer than the soil,and the power spectrum density of the stationary random excitation was given at the bedrock.The governing differential equations are derived in frequency and wave-number domains and only a set of ordinary differential equations (ODEs) must be solved.The precise integration algorithm of two-point boundary value problem was applied to solve the ODEs.Thereafter,the recently developed pseudo-excitation method for structural random vibration is extended to the solution of the stratified solid responses.

Computation of Field Structure and Aerodynamic Characteristics of Delta Wings at High Angles of Attack

YANG Li-zhi, GAO Zheng-hong

2005, 26(6): 734-742.

Abstract(2542) PDF(826)

Abstract:
A numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented.Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics that are dominated by the effect of the breakdown of the leading-edge vortices.The methods that analyze the flowfield structure quantitatively were given by using flowfield data from the computational results.In the region before the vortex breakdown,the vortex axes are approximated as being straight line.As the angle of attack increases,the vortex axes are closer to the root chord,and farther away from the wing surface.Along the vortex axes,as the adverse pressure gradients occur,the axial velocity decreases,that is lambda is negative,so the vortex is unstable,and it is possible to breakdown.The occurrence of the breakdown results in the instability of lateral motion for a delta wing,and the lateral moment diverges after a small perturbation occurs at high angles of attack.However,after a critical angle of attack is reached,the vortices breakdown completely at the wing apex,and the instability resulting from the vortex breakdown disappears.

Stability Analysis of Viscoelastic Curved Pipes Conveying Fluid

WANG Zhong-min, ZHANG Zhan-wu, ZHAO Feng-qun

2005, 26(6): 743-748.

Abstract(2386) PDF(477)

Abstract:
Based on the Hamilton's principle for elastic systems of changing mass,a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method,and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method.The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed.For greater dimensionless delay time,the behavior of the viscoelastic pipe is that the first,second and third mode does not couple,while the pipe behaves divergent instability in the first and second order mode,then single-mode flutter takes place in the first order mode.

An Effective Boundary Element Method for Analysis of Crack Problems in a Plane Elastic Plate

YAN Xiang-qiao

2005, 26(6): 749-756.

Abstract(2671) PDF(564)

Abstract:
A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented.The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiao-qiao.In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries.Test examples (i.e.,a center crack in an infinite plate under tension,a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems.In addition,specifically,the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed.These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body,and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.