应用数学和力学

Analytical Relations Between the Eigenvalues of Circular Plate Based on Various Plate Theories

MA Lian-sheng, WANG Tie-jun

2006, 27(3): 253-259.

Abstract(2800) PDF(548)

Abstract:
Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory(CPT),the first-order shear deformation plate theory(FPT) and the Reddy's third-order shear deformation plate theory(RPT),analytical relations between the eigenvalues of circular plate based on various plate theories are investigated.The eigenvalue problem was transformed to solve an algebra equation.Analytical relationships that were expressed explicitly between various theories were presented.Therefore,from these relationships obtained one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions.The relationships are useful for engineering application,and can be used to check the validity,convergence and accuracy of numerical results for the eigenvalue problem of plates.

Analytical Model of Ceramic/Metal Armor Impacted by Deformable Projectile

ZHANG Xiao-qing, YANG Gui-tong, HUANG Xiao-qing

2006, 27(3): 260-266.

Abstract(2531) PDF(557)

Abstract:
A new analytical model was established to describe the complex behavior of ceramic/metal armor under impact of deformable projectile by assuming some hypotheses.Three aspects were taken into account:the mushrooming deformation of the projectile,the fragment of ceramic tile and the formation and change of ceramic conoid and the deformation of the metal backup plate.Solving the set of equations,all the variables were obtained for the different impact velocities:the extent and particle velocity in rigid zone;the extent,cross-section area and particle velocity in plastic zone;the velocity and depth of penetration of projectile to the target;the reduction in volume and compressive strength of the fractured ceramic conoid;the displacement and movement velocity of the effective zone of backup plate.Agreement observed among analytical result,numerical simulation and experimental result confirms the validity of the model,suggesting the model developed can be a useful tool for ceramic/metal armor design.

Quasi-Static Analysis for Viscoelastic Timoshenko Beams With Damage

CHENG Chang-jun, SHENG Dong-fa, LI Jing-jing

2006, 27(3): 267-274.

Abstract(2475) PDF(552)

Abstract:
Based on convolution-type co nstitutive equations for linear visco elastic materials with damage and the hypotheses of Timoshenko beams,the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived.The quasi-static behavior of the viscoelastic Timo shenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain.The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.

Calculation of Coupled Problem Between Temperature and Phase Transformation During Gas Quenching in High Pressure

CHENG He-ming, WANG Hong-gang, XIE Jian-bin

2006, 27(3): 275-280.

Abstract(2225) PDF(454)

Abstract:
The gas quenching is a modern,effective processing technology.On the basis of nonlinear surface heat-transfer coefficient obtained by Cheng during the gas quenching,the coupled problem between temperature and phase transformation during gas quenching in high pressure was simulated by means of finite element method.In the numerical calculation,the thermal physical properties were treated as the functions of temperature and the volume fraction of phase constituents.In order to avoid effectual "oscillation" of the numerical solutions under smaller time step,the Norsette rational approximate method was used.

Distribution of Random Elements Subjected to a Flexible Boundary Condition

CHEN Han-dong, QIAO Yu

2006, 27(3): 281-284.

Abstract(2819) PDF(612)

Abstract:
The probability distribution function of n random elements subjected to the flexible boundary condition was derived.The probability density is a descending curve and converges to a delta function as n tends to infinity.The distribution of the minimum value was discussed in context of ordered statistics.

Stability of System of Two-Dimensional Non-Hydrostatic Revolving Fluids

SHEN Chun, WANG Yue-peng, SHI Wei

2006, 27(3): 285-292.

Abstract(2578) PDF(711)

Abstract:
Applying the theory of stratification,it was proved that the system of the two-dimensional non-hydrostatic revolving fluids is unstable in the two-order continuous function class.The construction of solution space was given and the solution approach was offered.The sufficient and necessary conditions of the existence of formal solutions were expressed for some typical initial and boundary value problems and the calculating formulae to formal solutions were presented in detail.

Evolutionary Dynamic Model of Population With Niche Construction and Its Application Research

LI Zi-zhen, HAN Xiao-zhuo, LI Wen-long

2006, 27(3): 293-299.

Abstract(2197) PDF(721)

Abstract:
Based on the theories and approaches in biomechanics,the mechanism and pattern of niche construction were discussed systematically.Through establishing the spatial pattern of niche and its measuring-fitness formula,and the dynamic system models of single-and two-population with niche construction,including corresponding theoretical analysis and numerical simulation on their evolutionary dynamics of population and the mechanism of competitive coexistence,the co-evolutionary relationship between organisms and their environments was revealed.The results indicate that population dynamics is governed by positive feedback between primary ecological factors and resource content.Niche construction generates an evolutionary effect in system by influencing the fitness of population.A threshold effect exists in single population dynamic system.In dynamic system of two competitive population,niche construction can lead to alternative competitive consequences,which may be a potential mechanism to explain the competitive coexistence of species.

Space-Time Finite Element Method for the Schrodinger Equation and Its Conservation

TANG Qiong, CHEN Chuan-miao, LIU Luo-hua

2006, 27(3): 300-304.

Abstract(2697) PDF(739)

Abstract:
Energy conservation of non-linear Schrêdinger ordinary differential equation was proved through using ordinary differential equation's continuous finite element methods;Energy integration conservation was proved through using space-time all continuous fully discrete finite element methods and electron nearly conservation with higher order error through using time discontinuous only space continuos finite element methods of non-linear Schrêdinger partial equation.The numerical results are in accordance with the theory.

Numerical Method Based on Hamilton System and Symplectic Algorithm to Differential Games

XU Zi-xiang, ZHOU De-yun, DENG Zi-chen

2006, 27(3): 305-310.

Abstract(2745) PDF(836)

Abstract:
The resolution of differential games often concerns the difficult problem of Two Point Border Value(TPBV),then ascribe linear quadratic differential game to Hamilton system.To Hamilton system,the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and to keep the measure of phase plane.From the point of view of Hamilton system,the symplectic characters of linear quadratic differential game were probed;And as a try,Symplectic-Runge-Kutta algorithm was inducted to the resolution of infinite horizon linear quadratic differential game.An example of numerical calculation was presented,and the result can illuminate the feasiblity of this method.At the same time,it embodies the fine conservation characteristics of symplectic algorithm to system energy.

Pressure and Pressure Gradient in an Axisymmetric Rigid Vessel With Stenosis

YAO Li, LI Da-zhi

2006, 27(3): 311-315.

Abstract(2634) PDF(743)

Abstract:
Based on an improvement of the Karman-Pohlhausen's method,using nonlinear polynomial fitting and numerical integral,the axial distributions of pressure and its gradient in an axisymmetric rigid vessel with stenosis were obtained,and the distributions related to Reynolds number and the geometry of stenotic vessel were discussed.It shows that with the increasing of stenotic degree or Reynolds number,the fluctuation of pressure and its gradient in stenotic area is intense rapidly,and negative pressure occurs subsequently in the diverging part of stenotic area,especially the axial range of stenosis extended,the flow of blood in the diverging part be more obviously changed.In higher Reynolds number or heavy stenosis,theoretical calculation is mainly in accordance with past experiments.

Hamiltonian Mechanics on K3/4hler Manifolds

ZHANG Rong-ye

2006, 27(3): 316-324.

Abstract(2700) PDF(795)

Abstract:
The mechanical principle,the theory of Modem geometry and advanced calculus,Hamiltonian mechanic was generalized to K3/4hler manifolds,and the Hamiltonian Mechanic on K3/4hler Manifolds was established.Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations etc was obtained.

Large-Scale Vortical Structures Produced by an Impinging Density Jet in Shallow Crossflow

FAN Jing-yu, WANG Dao-zeng, ZHANG Yan

2006, 27(3): 325-330.

Abstract(2552) PDF(510)

Abstract:
The large-scale vortical structures produced by an impinging density jet in shallow crossflow were numerically investigated in detail using RNG turbulence model.The scales,formation mechanism and evolution feature of the upstream wall vortex in relation to stagnation point and the Scarf vortex in near field were analyzed.The computed characteristic scales of the upstream vortex show distinguished three-dimensionality and vary with the velocity ratio and the water depth.The Scarf vortex in the near field plays an important role in the lateral concentration distributions of the impinging jet in crossflow.When the velocity ratio is relatively small,there exists a distinct lateral high concentration aggregation zone at the lateral edge between the bottom layer wall jet and the ambient crossflow,which is dominated by the Scarf vortex in the near field.

Thermal Stress Filed When Crack Arrest in an Axial Symmetry Metal Die Using Electromagnetic Heating

FU Yu-ming, TIAN Zhen-guo, ZHENG Li-juan

2006, 27(3): 331-336.

Abstract(2985) PDF(578)

Abstract:
In order to solve the thermal stress field around crack tip in metal die when crack prevention using electromagnetic heating,a metal die with a half-embedded round crack was selected as the study object.The complex function method was used as a basis for the theoretical model of the space crack prevention in metal dies using electromagnetic heating.The crack arrest was accomplished by a pulse current discharge through the inner and outer.The theoretical analysis results show that the temperature around the crack tip rises instantly above the melting point of the metal.Small welded joints are formed at a small sphere near the crack tip inside the metal die by metal melting as a result of the heat concentration effect when the current pulse discharged.The thermal compressive stress field appears around the crack tip at the moment.The research results show that the crack prevention using electromagnetic heating can decrease the stress concentration and forms a compressive stress area around the crack tip,and also prevents the main crack from propagating further,and the goal of crack preventing can be reached.

Dynamic Buckling of Elastic-Plastic Column Impacted by a Rigid Body

HAN Zhi-jun, CHENG Guo-qiang, MA Hong-wei, ZHANG Shan-yuan

2006, 27(3): 337-341.

Abstract(2664) PDF(710)

Abstract:
The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body is discussed by using the energy law.The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method.The equation of lateral disturbance used to analyize the problem is developed by taking into account the effect of elastic-plastic stress wave.The power series solution of this problem has been reached in theory iwth the power series approach.The buckling criterion of this problem is proposed by analyzing the characteristics of the solution.The relationship among critical velocity and impact mass,critical buckling length,hardening modulus is given by using theoretical analysis and numerical computation.

Method Based on Dual-Quadratic Programming for Frame Structural Optimization With Large Scale

SUI Yun-kang, DU Jia-zheng, GUO Ying-qiao

2006, 27(3): 342-350.

Abstract(2766) PDF(657)

Abstract:
The optimality criteria(OC) method and mathematical programming(MP)were combined to found the sectional optimization model of frame structures.Different methods were adopted to deal with the different constraints.The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion.The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method.Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints.To improve the resolution efficiency,the Dual-Quadratic Programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space.A method called approximate scaling step was adopted to reduce computations and smooth the iterative process.Negative constraints were deleted to reduce the size of the optimization model.With MSC/Nastran software as structural solver and MSC/Patran software as developing platform,the sectional optimization software of frame structures was accomplished,considering stress and displacement constraints.The examples show that the efficiency and accuracy are improved.

Difference Discrete System of the Euler-Beam With Arbitrary Supports and Sign-Oscillatory Property of Stiffness Matrices

WANG Qi-shen, WANG Da-jun

2006, 27(3): 351-356.

Abstract(3062) PDF(676)

Abstract:
The difference discrete system of Euler beam with arbitrary supports was constructed by using the two order central difference formulas.This system is equivalent to the spring-mass point-rigid rod model.By using the theory about oscillatory matrix,the sign-oscillatory property of stiffness matrices of this system was proved,and necessary and sufficient condition for the system to be positive is obtained completely.

Research on Method to Calculate Velocities of Solid Phase and Liquid Phase in Debris Flow

CHEN Hong-kai, TANG Hong-mei, CHEN Ye-ying

2006, 27(3): 357-364.

Abstract(2696) PDF(704)

Abstract:
Velocity of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow.Debris flow was simplified two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features.Assuming debris flow is one dimension two-phase liquid moving to one direction,then general equations of velocities of solid phase and liquid phase were founded in two-phase theory.Methods to calculate average pressures,volume forces and surface forces of debris flow control volume were established.Especially,surface forces were ascertained using Bingham's rheology equation of liquid phase and Bagnold's testing results about interaction between particles of solid phase.Proportional coefficient of velocities between liquid phase and solid phase was put forwarded,meanwhile,divergent coefficient between theoretical velocity and real velocity of solid phase was provided too.To state succinctly before,method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations.The method is suitable for both viscous debris flow and thin debris flow.Additionally,velocities every phase can beidentified through analyzing deposits in-situ after occurring of debris flow.It is obvious from engineering case that in the method it is consistent to that in real-time field observation.

Effects of the Varying Bottom on Nonlinear Surface Waves

WU Zheng-ren, CHENG You-liang, WANG Song-ling, LÜ Yu-kun

2006, 27(3): 365-371.

Abstract(2993) PDF(570)

Abstract:
The resonant flow of an incompressible,inviscid fluid with surface tension on varying bottoms was researched.The effects of different bottoms on the nonlinear surface waves were analyzed.The waterfall plots of the wave were drawn with Matlab according to the numerical simulation of the fKdV equation with the pseudo-spectral method.From the waterfall plots,the results are obtained as follows:for the convex bottom,the waves system can be viewed as a combination of the effects of forward-step forcing and backward-step forcing,and these two wave systems respectively radiate upstream and downstream without mutual interaction.Nevertheless,the result for the concave bottom is contrary to the convex one.For some combined bottoms,the wave systems can be considered as the combination of positive forcing and negative forcing.

Damping of Vertically Excited Surface Wave in a Weakly Viscous Fluid

JIAN Yong-jun, E Xue-quan, ZHANG Jie

2006, 27(3): 372-378.

Abstract(2524) PDF(412)

Abstract:
In a vertically oscillating circular cylindrical container,singular perturbation theory of two-time scale expansions was developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation.The fluid field was divided into an outer potential flow region and an inner boundary layer region.The solutions of both two regions were obtained and a linear amplitude equation incorporating damping term and external excitation was derived.The condition to appear stable surface wave was obtained and the critical curve was determined.In addition,an analytical expression of damping coefficient was determined.Finally,the dispersion relation,which has been derived from the inviscid fluid approximation,is modified by adding linear damping.It is found that the modified results are more reasonably close to experimental results.Result shows that when forcing frequency is low,the viscosity of the fluid is prominent for the mode selection.However,when forcing frequency is high,the surface tension of the fluid is prominent.

2006 Vol. 27, No. 3