应用数学和力学

2006 Vol. 27, No. 4

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Study of the Mechanism of Breakdown in Laminar-Turbulent Transition of a Supersonic Boundary Layer on a Flat Plate

CAO Wei, HUANG Zhang-feng, ZHOU Heng

2006, 27(4): 379-386.

Abstract(2759) PDF(865)

Abstract:
Spatial mode direct numerical simulation has been applied to the study of the mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate with Mach number 4.5.Analysis of the result showed that,during the breakdown process in laminar-turbulent transition,the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbance,when they became larger,leads to remarkable change of its stability characteristics.Though the most unstable T-S wave was of second mode for laminar flow,the first mode waves played the key role in the breakdown process in laminarturbulent transition.

Effective Solution Method of Chemical Reaction Kinetics With Diffuse

LÜ He-xiang, QIU Kun-yu, CHEN Jian-feng

2006, 27(4): 387-394.

Abstract(2165) PDF(584)

Abstract:
The time integration method with four-order accuracy,self-starting and implicit for the diffuse chemical reaction kinetics equation or the transient instantaneous temperature filed equation was presented.The examples show that both accuracy and stability are better than Runge-Kutta method with four-order.The coefficients of the equation are stored with sparse matrix pattern,so an algorithm is presented which combines a compact storage scheme with reduced computation cost.The computation of the competitive and consecutitive reaction in the rotating packed bed is taken as examples which shows that the method is effective.

Dynamical Formation of Cavity for Composed Thermal Hyperelastic Spheres in Non-Uniform Temperature Fields

CHENG Chang-jun, MEI Bo

2006, 27(4): 395-403.

Abstract(2311) PDF(593)

Abstract:
Dynamical formation and growth of cavity in a sphere composed of two incompressible thermal-hyperelastic Gent-Thomas materials are discussed under the case of a non-uniform temperature field and surface dead loading.The mathematical model was first presented based on the dynamical theory of finite deformations.An exact differential relation between the void radius and surface load was obtained by using the variable transformation method.By numerical computation,critical loads and cavitation growth curves were obtained for different temperatures.The influence of the temperature and material parameters of the composed sphere on the void formation and growth are considered and compared with that for static analysis.The results show that the cavity occurs suddenly with a finite radius and its evolvement with time displays a non-linear periodic vibration and that the critical load decreases with the increase of temperature and also the dynamical critical load is lower than the static critical load under the same conditions.

Biparametric Perturbation Solutions of the Large Deflection Problem of Cantilever Beams

HE Xiao-ting, CHEN Shan-lin

2006, 27(4): 404-410.

Abstract(2915) PDF(607)

Abstract:
The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.This kind of substitution can transform the basic equation,an integral differential equation into a nonlinear algebraic ones thus simplify computational process.Compared with the present results,it indicates that the large deflection problem solved by using pseudolinear analysis can lead to simple and precise results.

Free Vibration of Anisotropic Rectangular Plates by General Analytical Method

HUANG Yan, LEI Yong-jun, SHEN Hui-jun

2006, 27(4): 411-416.

Abstract(3170) PDF(524)

Abstract:
According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration,a general analytical solution was established.This general solution composed of the composite solutions made by trigonometric function and hyperbolic function,can satisfy the problem of arbitrary boundary conditions along four edges.The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners.Consequently,this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately.The integral constants can be determined by boundary conditions of four edges and four corners.Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero.For example,a composite symmetric angle ply laminated plate with four edges clamped was calculated and discussed.

Finite Element Method on the Numerical Simulation of the Stratum Corneum’s Penetration Property

LIU Yu-hong, QIAO Ai-ke, Dirk Feuchter, Gabriel Wittum, ZENG Yan-jun

2006, 27(4): 417-423.

Abstract(2370) PDF(481)

Abstract:
How could the outer substance penetrate through the skin lies in the stratum corneum,because it is the main barrier in the multi-layers of the skin.Supposing the keratin cell with a special geometry as tetrakaidecahedron,the penetration property of stratum corneum was the key proplem which was numerically simulated with finite element method.At first the discretization of the stratum corneum region was given in two steps:first,the discretization of the keratin cell;second,the discretization of fattiness that surrounds the keratin.Then there was the work of numerical simulation.In this procedure,the finite element method and the multi-grid method were used.The former was to obtain the discretization of basic elements,the latter was to decrease the high frequency error.At last the visualization of the numerical simulation was shown.

New Method for Low Order Spectral Model and Its Application

CAO Jie, YOU Ya-lei

2006, 27(4): 424-430.

Abstract(2431) PDF(498)

Abstract:
In order to over come the deficiency existing in classical method of low order spectral model,a new method for low order spectral model was a dvanced.Through calculating the multiple correlation coefficients between combinatio ns of different function and the reco rded data under the least square criterion,the truncated functions which can mostly reflect the studied physical phenomenon was objectively distilled from these data.The new method ov ercame the deficiency of artificially sele cting the truncated functions in the classical low order spectral model.The new method being applied to study the inter-annual variation of summer atmospheric circulation over Northern Hemisphere,the truncated functions were obtained with the atmospheric cir culation data of June 1994 and June 1998.The mechanisms for the two-summer atmospheric circulation variations over Northern Hemisphere were obtained with two-layer quasi-geo strophic baroclinic equation.

Normal Expansion Theory for Penetration of a Projectile Against Concrete Target

GAO Shi-qiao, LIU Hai-peng, LI Ke-jie, HUANG Feng-lei, JIN Lei

2006, 27(4): 431-438.

Abstract(3831) PDF(669)

Abstract:
Based on the equations which describe the dynamic behavior of material under high-velocity and high-pressure shock,corresponding equations at shock front whose surface was general space curve surface were established.For concrete material,a normal expansion theory was proposed by which some deceleration about time history of the projectile can be analytically given.This normal expansion theory is not only suitable for spherical and cylindrical-nose projectile,but alsosuitable for other general nose projectile,for example conical nose or ogive-nose.And it is not only suitable for perpendicular shock but alsosuitable for oblique shock.

Continuous Selection Theorems for Fan-Browder Mappings in Topological Spaces and Their Applications

YANG Ming-ge, DENG Lei

2006, 27(4): 439-446.

Abstract(2417) PDF(625)

Abstract:
The concept of Fan-Browder mappings was first introduced in topological spaces withoutany convex structure.Then a new continuous selection theorem was obtained for the Fan-Browder mapping with range in a topological space without any convex structure and noncompact domain.As applications,some fixed point theorems,coincidence theorems and a nonempty intersection theorem were given.Both the new concept and results unify and extend many known results in recent literature.

Adaptive Regulation of High Order Nonholonomic Systems

MU Xiao-wu, YU Ji-min, CHENG Gui-fang

2006, 27(4): 447-453.

Abstract(2884) PDF(739)

Abstract:
The problem of adaptive regulation for a class of high-order parametric nonholonomic systems chained-form is discussed.Using adding a power integrator technique and state scaling with discontinuous projection technique,a discontinuous adaptive dynamic controller was constructed.The controller guarantees the estimated value of unknown parameter in the prescribed extent.

Crack Propagation in Polycrystalline Elastic-Viscoplastic Materials Using Cohesive Zone Models

WU Yan-qing, ZHANG Ke-shi

2006, 27(4): 454-462.

Abstract(3090) PDF(1367)

Abstract:
Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones.Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals.The grain interior.s material properties (e.g.strain rate sensitivity) characterize the competitions between plastic and cohesive energy dissipation mechanisms.The higher the strain rate sensitivity is,the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy,which delays the cohesive zone rupturing.With the strain rate sensitivity decreased,the material property tends to approach the elastic-plastic responses.In this case,the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding.Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries.Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.

A Domain Decomposition Algorithm With Finite Element-Boundary Element Coupling

YAN Bo, DU Juan, HU Ning, Sekine Hideki

2006, 27(4): 463-469.

Abstract(3062) PDF(496)

Abstract:
A domain decomposition algorithm coupling the finite element and the boundary element is presented.It essentially involves subdivision of the analyzed domain into sub-regions being indepen dently modeled by the two methods,i.e.,the finite element method (FEM) and the boundary element method(BEM).The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm.To speed up the conver gence rate of the iterative algorithm,a dynamically changing relaxation parameter during iteration was introduced.An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent.The validity of the algorithm is demonstrated by the con sistence of the results of a numerical example obtained by the proposed method and those by the FEM,the BEM and a present finite element-boundary element (FE-BE) coupling method.

Viscoplastic Solution to the Field at Steadily Propagating Crack Tip in Linear-Hardening Materials

JIA Bin, WANG Zhen-qing, LI Yong-dong, LIANG Wen-yan

2006, 27(4): 470-476.

Abstract(2653) PDF(627)

Abstract:
An elastic-viscoplastic constitutive model was adopted to analyze asymptotically the tipfield of moving crack in linear-hardening materials under plane strain condition.Under the assumption that the artificial viscosity coefficient was in inverse proportion to power law of the rate of effective plastic strain,it is obtained that stress and strain both possess power law singularity and the singularity exponent is uniquely determined by the power lawexponent of the rate of effective plastic strain.Variations of zoning structure according to each material parameter were discussed by means of numerical computation for the tip-field of modeòdynamic propagating crack,which show that the structure of crack tip field is dominated by hardening coefficient rather than viscosity coefficient.The secondary plastic zone can be ignored for weak hardening materials while the secondary plastic zone and the secondary elastic zone both have important influence on crack tip field for strong hardening materials.The dynamic solution approaches to the corresponding quasi-static solution when the crack moving speed goes to zero,and further approaches to the HR (Hui-Riedel) solution when the hardening coefficient is equal to zero.

Numerical Study of Particle Distribution in the Wake of Liquid-Particle Flows Past a Circular Cylinder Using Discrete Vortex Method

HUANG Yuan-dong, WU Wen-quan

2006, 27(4): 477-483.

Abstract(3021) PDF(714)

Abstract:
Particle-laden water flows past a circular cylinder are numerically investigated.The Dis crete vortex method was employed to evaluate the unsteady water flow fields and a Lagrangian ap proach was applied for tracking individual solid particles.A dispersion function was defined to repre sent the dispersion scale of the particle.The wake vortex patterns,the distributions and the time se ries of dispersion functions of particles with different Stokes numbers were obtained.Numerical re sults show that the particle distribution in the wake of the circular cylinder is closely related to the particles Stokes number and the structure of wake vortices:1) the intermediate sized particles with Stokes numbers,St,of 0.25,1.0 and 4.0 can not enter the vortex cores and concentrate near the pe ripheries of the vortex structures;2) in the circular cylinder wake,the dispersion intensity of particles decreases as St is increased from 0.25 to 4.0.

Recurrent Neural Network Model Based on Projective Operator and Its Application to Optimization Problems

MA Ru-ning, CHEN Tian-ping

2006, 27(4): 484-494.

Abstract(2603) PDF(537)

Abstract:
The recurrent neural network (RNN) model based on projective operator is studied.Different from the former study,the value region of projective operator in the neural network which they study was a general closed convex subset of n demensional Euclidean space and it wasn't a compact convex set in general,that is,the value region of projective operator was probably unbounded.They prove that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions.After that,the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems.In addition,simulation experiments confirm the efficiency of the RNN.

Dynamic Behavior of a Thin Rectangular Plate Attached to a Moving Rigid

XIAO Shi-fu, CHEN Bin

2006, 27(4): 495-504.

Abstract(3165) PDF(628)

Abstract:
A nonlinear dynamic model of a thin rectangular plate attached to a moving rigid is established by employing the general Hamilton.s variational principle.Based on the new model,both phenomena of dynamic stiffening and dynamic softening can occur in the plate was proved theoretically when the rigid undergoes different large overall motions including overall translational and rotary motions.It was also proved that dynamic softening effect even can make the trivial equilibrium of the plate lose its stability through bifurcation.Assumed modes method was employed to validate the theoretical result and analyze the approximately critical bifurcation value and the post-buckling equilibria.