力学学报

The effect of curvature on the swept wing boundary layer secondary instability

Using the Parabolized Stability Equations (PSE), the nonlinearevolution of Stationary crossflow vortices over a swept NLF0415(2) airfoilis studied, then Floquet theory is employed to systematically study thedependence of the secondary, high-frequency instabilities on the curvatureat different conditions. Haynes (2000) shows that the curvature has astabilizing effect for linear stability theory and nonlinear ParabolizedStability Equations, and the results show that the curvature has no effectfor secondary linear stablity equations.

2010, 42(6): 995-1005. doi: 10.6052/0459-1879-2010-6-lxxb2009-361

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Experimental study on the frictional pressure drop of water flow in mini-channels with circular cylinder disturbed flow

Liu Dong Wang Yaqing Xu Kan

Using water as working fluid, the pressure drops formini-channel radiator with different height/width ratios involved withcircular disturbed flow before or behind the mini-channels wereexperimentally studied. It is found that the pressure drop increaseslinearly with the Reynolds Number. A general empirical formula was proposedto consider pressure drop as function of Reynolds Number, hydrodynamicdiameter and height/width ratio. The formula can predict flow friction ofthe similar system well. For line-wear mini-channels, the flow frictioncoefficient is inversely proportional to Reynolds number, and the value islarger than that of circle tube. The experimental results indicate that thesurface roughness is the main impact factor for pressure drop. However, thecircular cylinder disturbed flow has little influence on it. It is foundthat the circular cylinder disturbed flow which set in the front ofmini-channel can enlarge the heat dissipation.

2010, 42(6): 1006-1012. doi: 10.6052/0459-1879-2010-6-lxxb2009-222

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A class of discontinuous galerkin/finite volume hybrid schemes based on the ``static re-construction'' and ``dynamic re-construction''

He Lixin

By comparing the compact finite difference schemes and discontinuousGalerkin (DG) methods, the concepts of ``static re-construction'' and ``dynamicre-construction'' are proposed for high-order numerical schemes. Based on thenew concept of ``hybrid re-construction'', a novel class of DG/finite volumehybrid schemes (DG/FV schemes) is presented. In our DG/FV schemes, thelower-order derivatives are computed locally in a cell by traditional DGschemes (called as ``dynamic re-construction''), while the higher-orderderivatives are constructed by the ``static re-construction'' of finite volumeschemes, using the known lower-order derivatives in the cell itself and inthe neighbor cells. The DG/FV hybrid schemes can reduce the CPU time andstorage memory greatly than the traditional DG schemes with the same orderof accuracy, and can be extended directly for unstructured and hybrid gridsas the DG and/or FV methods. The DG/FV hybrid schemes are applied for1D and 2D scalar conservation law. The numerical results demonstrate the accuracy,the efficiency, and the super-convergence property in our third-order DG/FVhybrid schemes.

2010, 42(6): 1013-1022. doi: 10.6052/0459-1879-2010-6-lxxb2009-514

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High efficient numerical method for lco analysis in transonic flow

Zhengyin Ye

Non-linearities can be present in an aeroelastic systemdue to some aerodynamic phenomena that occur in transonic flight regime orat large angles of attack. The candidate sources are motions of shock waveand separated flow. With the recently well-developed software and hardwaretechnologies, numerical simulation of complex aeroelasticity phenomenabecomes possible, such as limit cycle oscillations (LCOs) due to theaerodynamic nonlinearity. However, the computational cost of solvingaeroelastic problem in nonlinear flow field is very high, so it is aconvenient method to solve this kind of problem by constructing a properunsteady aerodynamic model previously. Many research works are carried outin reduced order modeling (ROM) for aeroelastic analysis. Most of thereduced order aerodynamic models are dynamic linear models and in proportionto the structural motions. In this study, by using Radial Basis Function(RBF) neural network model, the nonlinear unsteady reduced order aerodynamicmodel is constructed. The ROM is used to analyze LCOs behaviors for twolinear structural models with large shock motion in transonic flow.Different from the traditional design method of the input signals, signalsof self-excited vibration of the aeroelastic system are designed as theinput signals in this paper. Coupled the structural equations of motion andnonlinear aerodynamic ROM, the system responses are determined by timemarching of the governing equations using a kind of hybrid linear multi-stepalgorithm and the limit cycle behaviors changing with velocities (dynamicpressure) can be analyzed. Two transonic aeroelastic examples show that boththe structural responses and the limit cycle oscillation (LCO)characteristics simulated by ROM agree well with those obtained by directCFD method, and the computational efficiency of ROM based method can beimproved by 1-2 orders of magnitude compared with the direct CFD method.

2010, 42(6): 1023-1033. doi: 10.6052/0459-1879-2010-6-lxxb2009-568

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Anisotropic second-order moment method of particles for dense gas-solid flow

A second-order moment model of particles is proposed inthe dense gas-solid flow based on the kinetic theory of granular flow andkinetic theory of gases. The constitutive model of solid phase is closedwith the approximated third-order moment enclosure equation of particlevelocity from the elementary transport theory. The boundary conditions ofvelocity and fluctuating velocity energy of particles are proposed with theconsideration of the energy transfer and dissipations by collisions betweenthe wall and particles. Interaction between gas phase and solid phase ismodeled by Koch (1999) mode. Flow behavior of particles is simulated in ariser. Numerical simulations indicate the distinct anisotropy behavior ofthe turbulent particles in the riser. Simulated particle velocities,concentration and second-order moments are in agreement with measurements byTartan and Gidaspow (2004) in a riser. Predicted axial fluctuating energy ofparticles is on average 1.5 times the mean fluctuating energy of particles,and the axial fluctuating energy is 3.0 times the lateral fluctuating energyof particles.

2010, 42(6): 1034-1041. doi: 10.6052/0459-1879-2010-6-lxxb2009-424

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Three dimensional numerical simulation study on the flow of the explosion shock wave around the wall

Ma Tianbao

The partial differential conservation equations for mass,momentum and energy are applied by adopting the compressible fluid model forthe explosion flow field. Based on the Eulerian algorithm of multi-materialin cell (MMIC), the operator splitting scheme is used, and the movinginterface is treated by volume ratio method. The development of the shockwave near the explosion source and in the explosion field caused bythree-dimensional air explosion are simulated using three-dimensionalnumerical simulation code MMIC3D compiled by authors. The formation andchange of the flow field around the corner wall are studied. Furthermore theeffects of the explosion shock wave are analyzed and compared with theempirical formula because of different locations and different shapes of theprotective wall. The simulation results turn out to be in full agreementwith the principle of physics. It also indicates that the model andalgorithm presented in this paper are proper, thus the numerical simulationcan be used for engineering design of decompression facilities.

2010, 42(6): 1042-1049. doi: 10.6052/0459-1879-2010-6-lxxb2009-459

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The nonlinear oscillation of bubbles in the ultrasonic field

Chenghui Wang

The nonlinear oscillation can be described by FlynnEquation when considering the compressibility of inner gas of bubbles. Basedon the model the displacement/the time relation and phase-trajectory ofvibrating bubbles of different initial radii are simulated numerically,which shows that the movements of bubbles depend strongly on the initialconditions in the same sound field. When the driving frequency of 26.5kHzand intensity of 1.35atm is adopted, the bubbles oscillate forcedly withinitial radii are smaller than 1\mu m, while oscillate quasi-intrinsicallywith initial radii larger than 200\mu m. The two kinds of bubbles are notcavitation ones. The changes of smaller bubbles are more intense to thesound intensity. If the sound intensity increases, a restricted range ofbubbles smaller than 1\mu m can become cavitation ones. Furthermore, thesmaller the initial radius is, the larger the increase of maximumdisplacement is. In addition, the driving frequency also affects themovement of bubbles. With the increase of driving frequency, the initialradii range of cavitation bubbles decrease, and the oscillation intensityreduces. The results present that there are three types of bubbles in theultrasonic field: big bubbles oscillated quasi-intrinsically, cavitationbubbles and micro-bubbles oscillated forcedly at the driving frequency. Thesize range of cavitation bubbles is influenced jointly by driving frequencyand pressure amplitude. At the same time, we researched the bubbles field intap water by high speed photography when the ultrasonic transducer isworking. The results show that there is a mixed field, where many bubbleswith different radius are vibrating and moving. Not only cavitation bubblesbut also bubbles with the millimeter scales coexist in the radiation fieldof ultrasonic transducer. The movements of bubbles can affect the intensityof cavitation directly. There is a complex physical field when cavitationcomes into being in the liquid, where bubbles are vibrating, colliding andcombining.

2010, 42(6): 1050-1059. doi: 10.6052/0459-1879-2010-6-lxxb2009-544

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The models by considering magnetic field and convection of chemical mechanical polishing and their numerical simulations

Zheng Qiuyun

Chemical mechanical polishing (CMP) is one of the mosteffective technologies in modern ultra-precision processing. In this paper,firstly, we deduce the model of CMP with convection effects, and researchthe pressure distribution by changing different parameters. Then, weconsider the model of CMP under the magnetic fluid slurry and externalmagnetic field, and research the pressure distribution in the externalmagnetic field. The numerical results show that pressure distribution of themodel with convection is more consistent with the known empirical results,and more efficiently explain the sub-ambient pressure in the CMP. Theresults also show that we can efficiently change the distribution ofpressure by external magnetic field, so these technologies can provide a newreferenced way for the wafer's global planarization.

2010, 42(6): 1060-1067. doi: 10.6052/0459-1879-2010-6-lxxb2009-423

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Calculation and analysis of the Mg-W GDI complex loading experiment

Bai Jinsong Da Chengda

A Mg-W material system graded density impactor (GDI) forthe complexity loading experiment was designed by means of numericalsimulation with elastic-plastic fluid dynamics calculation method. Byconsidering the technical restriction of minimum thickness of a discretelayer and the limitation of compact condition in maximum mixing rate betweenthe two individual constituents in the actual material fabrication, a set ofpreparation parameters for twelve-different-constituent Mg-W system GDI aregiven. One experiment of shock loading and quasi-isentropic compression forthe presented GDI on a gas gun was performed. And the velocity of interfacebetween the flyer and LiF window was provided by VISAR or DISAR technology.Through the comparison between the computational results and theexperimental data, analysis and verification are implemented for singularphenomena. As a result, a proposal using Mg-Cu material system to fabricatethe flyer is put forward. The project is helpful for the furtherexperimental study with loading/unloading controllable path and controllablerate.

2010, 42(6): 1068-1073. doi: 10.6052/0459-1879-2010-6-lxxb2009-351

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Extreme wind pressure estimation based on the r largest order statistics mode

This paper presents a procedure for statisticalestimation of extreme wind pressures using the r largest order statistics(r-LOS) model, which includes a joint generalized extreme value (GEV) modeland joint Gumbel model. Methods are devised to extract r-LOS vectors ofindependent peaks from individual time histories, choose optimum r, anddiscriminate between the r-LOS GEV model and r-LOS Gumbel model, respectively.The procedure is applied to analyze the pressure data obtained on the rigidmodel of a low-rise industrial building. When multiple pressure timehistories are used to estimate the extreme pressure coefficients, ther-LOS Gumbel model is superior to the r-LOS GEV model and the classical Gumbelmodel. When a single time history is used, the r-LOS Gumbel model usuallyestimates the extreme pressure coefficients more accurately than the peakfactor method based on the Modified Hermite Model and Sadek-Simiu procedure,and it is applicable when the wind pressure is non-Gaussian; furthermore,the r-LOS Gumbel model gives an analytical solution to the quantiles ofextreme pressure coefficients. The paper concludes that the procedure basedon the r-LOS Gumbel model is an effective alternative for the estimation ofextreme wind pressures when either multiple pressure time histories or asingle time history is available.

2010, 42(6): 1074-1082. doi: 10.6052/0459-1879-2010-6-lxxb2009-700

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A wall grid scale criterion based on the molecule mean free path for the wall heat flux computations by the navier-stokes equations

Cheng Xiaoli

The wall heat flux is a very important physical parameterfor the heat protection system design of high-speed vehicles, and itsaccurate prediction is one of difficult problems in computational fluiddynamics. In this paper, the wall normal grid scale is discussed for theaccurate computation of wall heat flux by the Navier-Stokes equations.Firstly, the wall heat flux is analyzed using the micro statistical approachin gas molecule physics, and the analysis shows that the coherent relationbetween the wall heat flux and the gas molecule mean free path results inthe optimal critical limit of the wall normal grid scale. Secondly, a newwall normal grid scale criterion, called MFP (mean free path) criterion forshort, is given based on the foregoing theoretical analysis. This criterionwith clear thermodynamics sense is simple and easy to be applied, and itonly depends on the wall local parameters. Finally, a few differentnumerical examples are chosen for comparisons to validate the accuracy andthe validity of the MFP criterion, namely, a hypersonic flow around a bluntcone at zero angle-of-attack, a hypersonic flow around a blunt bi-cone withand without angle-of-attack, and a hypersonic flow around a doubleellipsoid at different angle-of-attacks. The considered numerical methodsare finite difference, finite volume, and finite element, and the considerednumerical schemes are TVD, WENO, NND, and AUSM-DV. The wall heat fluxesbased on the MFP criterion are in well agreement with the relevantexperiment data for all of the numerical methods and numerical schemes.

2010, 42(6): 1083-1089. doi: 10.6052/0459-1879-2010-6-lxxb2009-416

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Implementation of reduced chemical kinetics for kerosene combustion and in situ adaptive tabulation in parallel computations of scramjet

Yang Shunhua

A detailed chemical kinetics model including 109 speciesand 946 elementary reactions for kerosene combustion was obtained. Then,using the software SPARCK (Software PAckage for Reduction of ChemicalKinetics) which is based on quasi-stationary state approximation andspecifically developed for chemical reaction kinetics reduction, a reducedmodel with 22 species and 18 global reactions was achieved. The calculatedignition delay with this reduced model gives a good agreement with referenceand experimental results to verify the reliability of the model. The 2-Dparallel numerical simulation of scramjet was performed using in situadaptive tabulation (ISAT) and the reduced model. The calculated results show thatthe distribution of wall pressure agrees well with the experimentalmeasurements, and the reduced model can simulate well the complex combustionphenomena in a kerosene-fueled scramjet. Compared with that of the directintegration method, the results show that ISAT method can reduce the CPUtime up to 3.73 times under the present parallel environment and thecomputational efficiency can be dramatically enhanced.

2010, 42(6): 1090-1097. doi: 10.6052/0459-1879-2010-6-lxxb2009-490

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Contrast of movement law of saline intrusion in modaomen waterway in the wet year and the dry year

The movement law of saline intrusion in the Modaomenwaterway in the wet and dry years is obtained by the method of the figuresof salinity borderline distribution (SBD). The effect of different runoffsin two years on the movement saline intrusion in the Modaomen waterway iscontrasted. The different runoffs in the wet year and the dry year changethe distance and the speed of the saline water movement, and cause thedifferent saline intrusion disaster. The period law of the half-month forthe saline water movement, which is that the saline water moves oscillatingup during the neap tide and down during spring tide, is not affected by thedifferent runoffs in the wet year and the dry year. The magnitude ofupstream runoff only affects the distance and the speed of the saline watermovement in the Modaomen waterway, but does not change the period law of thehalf-month for the saline water movement.

2010, 42(6): 1098-1103. doi: 10.6052/0459-1879-2010-6-lxxb2009-505

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An explicit method for numerical simulation of wave motion---2-D wave motion

For numericalsimulation of wave motion, this paper generalizes the explicitmethod for 1-D wave equation to 2-D case, and develops thecorresponding recursion formulas for an irregular grid for 2-Dwave equations. For uniform quadrate grids, an approach toconstruct 2M-order stable formulas is discussed in detail, withM being a positive integer, which is illustrated by constructingsecond-order (M=1) and fourth-order (M=2) formulas. Bynumerical tests, the theoretical results presented in the paperare demonstrated, in which the effect of highly accurate recursionformulas in improving calculation efficiency is emphasized.

2010, 42(6): 1104-1116. doi: 10.6052/0459-1879-2010-6-lxxb2008-590

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Numerical analysis on impact safety of fuel air explosive

Fuel air explosive (FAE), different from high energyexplosive is a three-phase medium consisting of metal solid particles, waterand gas. Its mechanical behavior is affected by initial condition andloading condition. In this paper a three-phase material model for FAEexplosive subjected to shock loading was presented. In the model the FAEexplosive was modeled as a three-phase mixture which contains solid metalparticles, water and gas. The solid metal particles formed a skeletonstructure. The liquid and gas were filled in the void of the skeletonstructure. In addition, the gas adiabatic compression model was introduced.The profiles of stress and temperature of individual phases could be showedin the material model. Hence it could be a way to reasonably validate thesafety of fuel. This material model was embedded into dynamic softwareAUTODYN as user subroutines. Finally, the model was applied to analyze theresponse of the FAE charge when the FAE warhead was dropped from 20m highdown to steel plate vertically. Based on the stress status and temperaturedistribution in the charge, the safety of FAE charge was discussed.

2010, 42(6): 1117-1124. doi: 10.6052/0459-1879-2010-6-lxxb2009-463

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Penetration and perforation performance of three pyramidal lattice-cored sandwich plates: numerical simulations

Jin Feng

The ballistic performances of three different kinds of sandwich plates with pyramidal lattice cores are numerically evaluated with the method of finite elements, including empty lattice--cored sandwich without any insertion, ceramic filled sandwich, and ceramic and epoxy resin filled sandwich. As the complexity of the sandwich structure and material composition increase, the energy absorption performance of the sub-structures and the sandwich plate as a whole is quantified. Both the incidence and exit velocities of the projectile are considered to establish the ballistic limit as well as the ballistic performance of the sandwich plates. Obtained results reveal that ceramic insertions lead to enhanced penetration resistance of the sandwich due to their high-strength and high-hardness characteristics, whereas the use of epoxy resin improves the integrity of the sandwich so that more energy of the projectile can be absorbed. Therefore, the third type of sandwich (ceramic and epoxy resin filled) achieves the highest ballistic limit velocity and the best ballistic performance mainly due to its structural integrity.

2010, 42(6): 1125-1137. doi: 10.6052/0459-1879-2010-6-lxxb2009-400

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Numerical study on porous materials under shock

Shock responses ofporous materials are studied using the material-point method. Theeffects of porosity, mean-cavity-size, shock strength, localdivergence and vorticity are investigated. In materials with verysmall porosity, the shocked portion may arrive at a nearly steadystate; the mean pressure and density oscillate slightly due to thetension waves reflected back from the cavities in the downstreamportion. In materials with larger porosity, the shockcompressibility decreases and the attenuation of shock wavesbecomes more evident. Under fixed porosity, a highermean-cavity-size results in a higher mean temperature. Theattenuation of shock waves depends on the porosity,mean-cavity-size, and shock strength. Local turbulence mixing andvolume dissipation are two important mechanisms for transformationof kinetic energy to heat. The stronger the loaded shock, thestronger the porous effects. The pressure, density, temperatureand particle speed do not approach their equilibriums at the samerate.

2010, 42(6): 1138-1148. doi: 10.6052/0459-1879-2010-6-lxxb2009-464

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Mechanical property and numerical simulation on W-Ni-Fe alloys

Ning Jianguo

Tungsten alloy is a type of particulate reinforced composites and has wide military and civilian applications. It can be used as kinetic energy penetrator, radiation shielding material, balance mass in aerospace, vibrating material in cell phones, etc. These alloys are characterized by the high strength, high density and high toughness resulting from their special microstructural features. Because of their good strength as well as ductility, these alloys have been extensively studied for a variety of promising applications. So far, most studies mainly focused on the understanding of their densification mechanism, the two-phase microstructure evolution mechanism during sintering, and the relationship between the microstructure and mechanical properties. The two-phase composite structure of tungsten alloy determines that the macroscopic deformation and fracture behavior have close relation with the microstructure of the composites. Therefore, it is important to investigate the relationship between the microstructure and the mechanical properties of the composites under different loadings, which provides practical values for the improvement of the mechanical properties and the optimization of tungsten alloys. In the current paper, MTS and SHPB techniques are used to investigate the mechanical properties of 91wt.% tungsten alloys. Based on the experimental results, finite element models of unit cells with typical structures of tungsten alloys are established. Fixed point iteration method is adopted to provide real displacement conditions for the finite element models. The effects of the microstructure parameters, such as particle size and volume fraction, on the mechanical characteristics of tungsten alloys under different tensile loadings, are examined and the corresponding stress-strain relations are obtained. The comparison of numerical predictions and the experimental results shows a good agreement. The numerical simulations demonstrate that tungsten alloys are rate-independent materials. The aspect ratios of tungsten particle have no obvious influence on the mechanical behavior of tungsten alloys, and the yield stress increase with the mass fraction of tungsten particles.

2010, 42(6): 1149-1155. doi: 10.6052/0459-1879-2010-6-lxxb2009-461

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Effects of surface curvature on cavitation evolution and reloading

Renzhong Renzhong

In this work,effects of surface curvature on cavitation evolution and structureloadings are investigated. We extended the latest techniques offluid-structure Riemann problem and the modified ghost fluidmethod to treat the flow-structure nonlinear interaction. Resultsdisclosed that a concave shape can strongly lead to not only shockfocus but also rarefaction wave intensification; suchintensification subsequently enhances local cavitation collapseand thus cavitation reloading. The magnitude of such enhancementincreases nonlinearly with the increase of surface curvature. Aconvex shape can weaken the shock impact and subsequent cavitationcollapse. However, such effect is well limited.

2010, 42(6): 1156-1163. doi: 10.6052/0459-1879-2010-6-lxxb2009-460

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An experimental approach on fracture behavior of cortical bones

The transverse and longitudinal crack propagationbehaviors in bovine cortical bone were studied using stable crack growth andfatigue test methods. Twenty five Compact Tension (CT) specimens of corticalbone were prepared in specific directions. In stable crack growthexperiment, the ASTM standard is no longer applicable due to the geometry ofthe CT specimens and anisotropy of the materials. The relationship betweenthe stress intensity factor and crack length was established by means ofnumerical method. In order to identify the location of crack tip duringcrack propagation, Digital Image Correlation (DIC) method was used. As thecrack deflected largely when propagating in the transverse direction, thetransverse fracture toughness was analyzed with J integral. The results showthat the fracture toughness of cortical bone increases with crack extensionin a certain range, i.e. cortical bone exhibits rising resistance curve(R-curve). And the fracture toughness in the transverse direction is muchhigher than that in longitudinal direction, which indicates that the R-curveis anisotropic. The fatigue test shows that fatigue crack propagationbehavior in cortical bone is also anisotropic. Crack grow rate in thelongitudinal direction is greater than that in transverse direction. It isalso found that the fatigue crack growth rate decreases with the increase ofstress intensity factor range at the initial stage of crack extension.

2010, 42(6): 1164-1171. doi: 10.6052/0459-1879-2010-6-lxxb2009-604

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Elastic stability of circular cylindrical shells with FGMS layers under end torsion force

By usingsemi-analytical method, elastic stability of a simply supportedFGM sandwich circular cylindrical shell under torsion loading wasstudied. The inner and outer layers of the shell are comprised ofthe same homogeneous and isotropic material, and the middle layeris made of an isotropic functionally graded material whoseproperties varies continuously in the thickness direction from theinner layer to the outer layer, and keeps continuation in thematerial properties of the interface. Firstly, based on theFlügge thin shell theory, the governing equations for staticbuckling of the structure in terms of displacements wereformulated. Secondly, by introducing the displacements in terms oftrigonometric functions that identically satisfy the boundaryconditions, an eigenvalue problem for linear algebraic equationsincluding the torsion force parameter is obtained. Finally,critical buckling load characterizing the features of instabilityof the structure were obtained by numerical method. The numericalresults show that the buckling load decreases with an increases inthe radius to thickness ratio, and increases with an increase inthe average value of Young's modulus of the FGM middle layer.

2010, 42(6): 1172-1179. doi: 10.6052/0459-1879-2010-6-lxxb2009-425

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Calculation of tensile membrane effects of concrete slabs

Dong Yuli

Significantexperimental and theoretical research work showed that, concreteslabs at large vertical displacements could support loadsconsiderably greater than those calculated by the well-establishedyield-line approach. The mechanism for supporting the load wasshown to be tensile membrane action, which could form within theslab irrespective of whether it was restrained or unrestrainedhorizontally at its boundaries. Most of these research works werebased on work method. Combining of previous research work andsegment equilibrium method, Bailey (2001) proposed a simplifieddesign method, which took account the membrane action of compositefloor slabs at large displacements. This model considered the slabwith no in-plane horizontal restraint at its edges, can carry aload greater than that calculated using normal yield-line theory,is partly due to in-plane tensile stresses developing at thecentre of the slab and partly due to the increase in yield momentin the outer regions of the slab, where compressive stressesoccur. The enhancement included two parts, one is due to membraneaction and another is due to membrane forces, of yield line loadfor each element. Typically the enhancements of 2 elements are notequal, and the difference was explained by the effects of verticalshear or the in-plane shear. Because Bailey's theoreticalderivation was based on in-plane resultant moment equilibriumequations, and assumed the fracture failure model ofreinforcements occurred through the depth of the slab across theshort span at first, so it is not unified with the yield-linetheory, and may lead to tedious calculations.Based on the additive decomposition theory of deformationgradients, this paper presents an energy-based model to determinethe limit carrying capacity of concrete slab at largedisplacement, which considered the membrane effects and unifiedwith the conventional plastic line theory. The model could predictthe load-carrying capacity of either rectangular or squareconcrete slabs with both orthotropic and isotropic reinforcement,and could interpret why for similar reinforcement the square slabsalways fail at a lower vertical displacement compared to therectangular slabs, and the reason of fracture of reinforcementalong the short span of rectangular slab. Comparison between thedeveloped model and test results shows good correlation.

2010, 42(6): 1180-1187. doi: 10.6052/0459-1879-2010-6-lxxb2009-533

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Unified displacement calculation theory of generalized structure with double resistances to lateral force

The building structure is considered as a structure withdouble resistance to lateral force and consists of two substructures ingeneralized concept. Horizontal deformation of the substructure consists ofbending deformation and shear deformation. Unified displacement calculationmethod of the dual structure in elastic stage will be proposed in thispaper. The basic regulation between internal force and deformation of everysubstructure obeys Timoshenko beam theory. Based on cooperative workmechanism of two substructures, the unified displacement differentialequation of generalized structure with double resistance to lateral force isestablished by deformation continuation approach. Taking uniform load as asample, the unified displacement analytical solutions of the dual structureare deduced which include bending deformation solution, shear deformationsolution and the total deformation solution. The displacement differentialequation, special solution and displacement analytical expressions arecompared between frame-shear wall structure and generalized structure withdouble resistances to lateral force. Frame-shear wall structure can beregarded as one of the concrete expression forms of the double structure.Numerical example results indicate that calculation accuracy by analyticalmethod can meet the requirement to the middle-high dual structures. Theunified displacement theory of generalized dual structure makes structureswith different deformation characteristics to connect together essentially,and it has important theoretical significance for us to understanddeformation mechanism and internal relations of the building structuresdeeply.

2010, 42(6): 1188-1196. doi: 10.6052/0459-1879-2010-6-lxxb2010-029

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Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate

The absolute nodal coordinate method has been widely usedto study the dynamics of flexible multibody systems. The computationalefficiency of this method, however, has much room to be improved. Generally,the second kind of Piola-Kirchhoff stress tensor is used to derive theelastic forces and corresponding Jacobians, namely, the partial derivativematrix of the elastic forces with respect to the generalized coordinates.Nevertheless, this method is inefficient enough. Based on the principle ofvirtual work, the analytical formulations for the elastic forces and theirJacobians are deducted directly by using the first kind of Piola-Kirchhoffstress tensor. Numerical example results based on different methods showthat the proposed approach is able to enhance the computational efficiencysignificantly.

2010, 42(6): 1197-1205. doi: 10.6052/0459-1879-2010-6-lxxb2009-543

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Experiments on the relationship between bulging and back-attack of submerged supersonic gas jets

The paper presents an experimental study on dynamicinstability of submerged supersonic gas jets. The gas-jet flow patterns arerecorded at real time by a high-speed camera. The development process ofsupersonic and subsonic gas jets and the process of the unstable flowpattern are visualized clearly. The patterns of the unstable jet flow areanalyzed in detail. The frequencies of bulging and back-attack of the jetare calculated from the experiment data. The experimental results indicatethat the frequency of the back-attack increases with increasing the bulgingfrequency, and the frequency of the bulging increases with increasing thestagnation pressure ratio P_{0}/P_{b}. Comparison of the data from the twokind of unstable patterns indicates a certain relevance between bulging andback-attack: Both the bulging and back-attack are all initiated by pressureoscillation inside of the gas jets and have a strong randomness, and thebulging is a kind of representation of energy storage before back-attackhappens. In addition, when the energy storage gets to a certain limit, aback-attack event will be occurring.

2010, 42(6): 1206-1210. doi: 10.6052/0459-1879-2010-6-lxxb2009-328

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Relation of load and displacement for the metal foam-filled tube during the axial compression

The energy absorption of metal foam-filled tube wasregarded as the sum of that of metal foam and tube. Based on the straightchain plastic hinge model including the effect of eccentricity and theimproving results of Alexander model by Reddy and Wall, the deformation modeof tube was modified to reflect the effect of interaction between tube walland metal foam. Then, the expressions for the mean crushing force of staticand dynamic axial compression of metal foam-filled tube were derived. By thecomparison between theoretical prediction and experiments, the resultspredicted theoretically were found to be lower than experimental curve butagree well in the tendency, and slightly higher than the sum of averageloads of tube and metal foams. In addition, as the plateau stress of thefilling foam increases, the average compressive load of foam-filled tubeimproves linearly. This is consistent with the existed results and actualsituation, proving the rationality of the model in this paper.

2010, 42(6): 1211-1218. doi: 10.6052/0459-1879-2010-6-lxxb2009-190

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Dynamic stress intensity factor for interfacial cracks of mode III on a circular cavity in piezoelectric bimaterials

Song Tianshu Li Dong

Based on the method of Green's function, the problem ofSH-wave scattering by interface radial cracks with arbitrary finite lengthson a circular cavity in piezoelectric bimaterials was investigated in thepresent paper, and the solution of dynamic stress intensity factor at thecrack tip was given. Firstly, a pair of coupled Green functions on theelastic displacement and the electric potential which were suitable for thepresent problem was constructed. Secondly, the infinite piezoelectricbimaterials were divided into two semi-infinite media. Based on thecrack-division technique and the continiuty condition at the interface, twohalf spaces were bonded to infinite whole space. Thirdly, integral equationsfor the solution of the unknown stresses, which were related to dynamicstress intensity factor at the crack tip, were established. Finally, someexamples and results for dynamic stress intensity factor (DSIF) of theradial cracks on a circular cavity were given, and the influence of acircular cavity on DSIFs at the crack tip was discussed.

2010, 42(6): 1219-1224. doi: 10.6052/0459-1879-2010-6-lxxb2009-555

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A new model for life prediction of multiaxial high-cycle fatigue

Several groups of fatigue damage parameters under threetypical loading cases (i.e., fully reversed tensional, fully reversedtorsional and 90$^\circ$ non-proportional loading) are discussed in this paperand a new life prediction model for multiaxial high-cycle fatigue isproposed. The proposed model is based on a nonlinear combination of themaximum shear stress amplitude and maximum normal stress on the criticalplane defined by the plane of maximum shear stress range. A compromisingsolution to correct the mean normal stress acting on the critical plane isalso proposed. The new model also extends the range of metallic materials.The predictions based on the presented model show a good agreement with testdata.

2010, 42(6): 1225-1230. doi: 10.6052/0459-1879-2010-6-lxxb2009-655

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Fatigue paths simulation of a center slant crack in cracked brazilian disk by BEM

Liu Baoliang Hu Zhaohui

This paper presents a prediction model for fatigue growthof multiple crack tips in a plane elastic plate. It mainly involves atheoretical model and a numerical method to investigate the fatigue growthof multiple crack tips under mixed-mode loading. The numerical method wasadopted with a hybrid displacement discontinuity method (HDDM), a kind ofboundary element method. With the boundary element method, a crack growthproblem of multiple crack tips can be solved in a single-region formulation.In the numerical simulation, crack extension is conveniently modeled byadding new boundary elements on the incremental crack extension to theprevious crack boundaries. Menwhile, the element characters of some relatedelements will be adjusted. As an example, the present numerical approach isused to simulate the fatigue growth of a center slant cracked circular disk.The numerical results illustrate the validation of the prediction model andreveal the geometry effect of the cracked circular disk on the fatiguegrowth.

2010, 42(6): 1231-1236. doi: 10.6052/0459-1879-2010-6-lxxb2009-602

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Optimal control for elliptic orbital rendezvous based on line-of-sight dynamic model

Optimal control methods for autonomous rendezvous on theelliptical orbit were discussed in line-of-sight(LOS) coordinate frame. Forthe rendezvous courses with constrained proximity aspects, an LOS dynamicmodel with respect to LOS measurement information was adopted so that LOSangle could be controlled directly. Then the rendezvous problem wasformulated as a nonlinear optimal control problem. The State-DependentRiccati Equation(SDRE) controller and \theta-D controller were derivedrespectively. Also an SDRE approach with the control thrust along the axisof Local Vertical / Local Horizontal(LVLH) frame was discussed for theavailability of control thrust. Numerical simulations demonstrated thefeasibility of the control strategies in constrained-aspect rendezvousmissions. The \theta-D controller got a higher computational efficiencyand lower control accuracy comparing with the SDRE controller. Moreover, theSDRE controller also could be achieved while the control thrust fixed withthe LVLH axis.

2010, 42(6): 1237-1243. doi: 10.6052/0459-1879-2010-6-lxxb2009-751

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Real-time 3D profile measurement and kinematics analysis for carp tail fin

A experimental system based on grid projector andhigh-speed camera was established in order to accurately measure 3Dkinematics of fish fin, and the corresponding analysis method was applied. Afree-swimming carp was used in the experiment. Projecting the sinusoidfringes onto its tail fin, the deformed fringe pattern containing 3Dinformation was produced and varied with the tail fin movement. Thesetime-sequence images were captured by a high speed camera. By Fouriertransform, filter, inverse Fourier transform and 3D phase unwrap, thecomplex 3D movement of tail fin was really reconstructed. And then themovement characteristics and the kinematics parameters of tail fin werestudied. Analysis of tail kinematics suggests that, when the swimming speedof carp is 0.5Ls^{-1} (L is the length of fish body), the tail beatfrequency is about 1.42Hz. The tail movement mainly occurred in the lateraldimension as the tail beat from side to side. The 3D profile of tail variedduring the tail beat cycle. The tail underwent a cyclic vertical expansionand compression. A dorsal-ventral asymmetry was present in the lateralmovements of the tail in which the maximum lateral excursion of the dorsaltail tip underwent a 15.6% greater than did the ventral tail tip. Thepresent study provides a new method to quantify the analysis of kineticcharacteristic of the tail fin during steady swimming.

2010, 42(6): 1244-1249. doi: 10.6052/0459-1879-2010-6-lxxb2009-632

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2010 Vol. 42, No. 6

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