力学学报

2010, 42(1) doi: 10.6052/0459-1879-2010-1-2010-030

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Model of inflatable structure/fluid interaction for variable leading edge

Yuewen Jiang, Zhengyin Ye, Zhengke Zhang

The paper presents the interactive motion equation ofinflatable structure in flow. The inflatable structure is used in thetechnique of a variable leading edge for high lift. The interaction betweenstructure and fluid is a typically aeroelastic problem. The motion equation isobtained through the analytic solution of an infinitesimal element in thediscrete membrane. Coupled with Navier--Stokes equation, the aeroelasticequation was solved with time-marching methods, and the aerodynamiccharacteristics of NACA 63-212 airfoil with the inflatable leading edge(ILE) were obtained. From the results, the ILE technique has been applied tosignificantly increase the stall angle of attack and lift coefficient.The values of stall angle of attack and maximum lift coefficient wereenhanced to be 30 percent and 22 percent, respectively. In addition, thedeformation of ILE greatly influenced the flow around the airfoil while theelastic coefficient of material was low. The inflatable structure near thesuck peak deformed clearly, and this hump could induce the separation inadvance.

2010, 42(1): 1-7. doi: 10.6052/0459-1879-2010-1-2008-386

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Research on statistic characteristic of near-wall turbulence

Honglin Xiao, Jisheng Luo

Channel turbulence is simulated by large eddy simulation(LES), and turbulent databases of channel flows at different Reynoldsnumbers are established. Then, the mean velocity distribution, Reynoldsstress and root-mean-square (RMS) velocity distribution are obtained.Furthermore the problem of the wall law is discussed. Meanwhile, a rule ofReynolds stress, energy of velocity fluctuations and RMS velocity withdifferent Reynolds number is presented along with quantitative formula.

2010, 42(1): 8-14. doi: 10.6052/0459-1879-2010-1-2008-593

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Numerical studies on flows around a flexiblly wiggling hydrofiol

Guoyi He, Xing Zhang, Shuguang Zhang

Fishes often use a wiggling motion to generate propulsion for swimming. The wiggling motion can be modeled by a progressive wave. In the present study, an immersed boundary method is used to simulate the flows around the wiggling hydrofoil NACA 65-010 at low Reynolds numbers, and the effects of Reynolds numbers on the propulsion generation are investigated. It is observed that, as the Reynolds number ranges from 1 to 200, both the thrust coefficient and the propulsion efficiency increase with the increase of the Reynolds number, while the power efficiency decreases. Especially in the ranges of the Reynolds number smaller than 20, the lift, thrust and power coefficients exhibit a large change. With the increase of the Reynolds number, the flow patterns around the wiggling foils become more complex: the vorticity becomes more intensive near the trailing edge and the wiggling foil produces reversed von Karman vortex streets to generate propulsion.

2010, 42(1): 15-22. doi: 10.6052/0459-1879-2010-1-2008-570

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The nonlinear water wave equations with full dispersion

Hong Jin, Zhili Zou

A 2D nonlinear water wave model with full dispersion isdeveloped. The model is based on the nonlinear kinematic and dynamic freesurface boundary conditions and is expressed in terms of free surfaceelevation $\eta $ and the velocity potential $\phi _\eta $ at the freesurface. The derivation of the equations is accurate to third order innonlinearity and keeps exact dispersion. The mild slope assumption isadopted and the derived equations can be seen as the extention of the mildslope equation of Berkhoff (1972) to the nonlinear and irregular wave case.The corresponding numerical scheme is presented, and the special attentionis paid on the treatment of the integration terms in the equations. Thevalidation of the model is made by simulating the first and second orderStokes waves and the nonlinear evolution of wave groups, the advantage ofthe model is shown by the good prediction of amplitude dispersion andfour-wave resonant interaction for the wave group evolution.

2010, 42(1): 23-34. doi: 10.6052/0459-1879-2010-1-2008-080

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Experimental study of crescent wave without wind driving

Yalong Zhou, Zhili Zou

Experiment study on crescent waves was performed withoutwind driving. L2-type crescent waves wereobtained in the experiment, aswell as other two new types of three-dimensional wave patterns. The timeseries and amplitude spectra characteristics of generated crescent waveswere analysized, and wave lengths of transverse waves and wave heights ofL2-type crescent waves were discussed.

2010, 42(1): 35-43. doi: 10.6052/0459-1879-2010-1-2008-143

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Dynamic interaction between waves and poroelastic seabed with boundary layer effects

Dynamic interaction between waves and poroelastic seabedis investigated in relation to the boundary layer near the seabed. Potentialtheory is applied to describe the wave field and a boundary layermodification is considered. The deformation of the seabed is governed byBiot's consolidation theory. Stress and velocity continuity at the interfacewill be coupled with the wave motion and the relevant seabed response. Underthe assumptions of small amplitude waves and small deformation of theseabed, an analytical solution is obtained and shown to be in good agreementwith field data. The conditions under which wave-seabed interaction becomessignificant are also discussed.

2010, 42(1): 44-50. doi: 10.6052/0459-1879-2010-1-2008-227

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Leaky rayleigh wave at the interface between inviscid fluid and solid

Xiao Chen

The leaky Rayleigh wave, an inhomogeneous surface wave,exists at the interface between a fluid half space and a solid half space.The secular equation of leaky Rayleigh wave is derived and the formulas ofparticle displacement and stress distributions in the inviscid fluid and theisotropic solid are presented. The characteristics of leaky Rayleigh waves,the particle displacement and stress distributions in the fluid and solidare investigated with numerical results using those equations. The effect ofthe fluid-solid density ratio on the velocity and attenuation of leakyRayleigh wave and its particle displacement and stress distributions in thefluid and the solid is analyzed numerically. The leaky Rayleigh wave isnon-dispersive and attenuate with propagetion distance. Its velocity andattenuation increase with the fluid-solid density ratio. The fluid-soliddensity ratio has significant effect on the vertical displacement but littleon horizontal displacement in the solid half space. The fluid-solid densityratio also dramatically effects on the vertical normal stress and shearstress but little on horizontal normal stress in the solid half space. Thetheory is promising to be explored to nondestructive testing and evaluationwith leaky Rayleigh wave.

2010, 42(1): 51-55. doi: 10.6052/0459-1879-2010-1-2007-563

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he analytical solutions of thick-walled cylinder of softening material and its stability

Youquan Yin

The constitutive law of elastoplastic material beingsimplified to three-line model (elastic-linear softening plastic-residualideal plastic model), and the material obeying Tresca yield criteria andassociated flow rule, the analytical solutions of thick-walled cylindersubject to internal pressure $p$ were derived in the paper. The result showsthat the yield stress in the softening plastic region is the inverse squareof radial coordinate $r$.Firstly, the pressure $p$ was taken as generalized force, the displacement $u$taken as generalized displacement, and the thick-walled cylinder taken as awhole system. On the basis of the solutions the stability problem ofthick-walled cylinder was then discussed. The $p$-$u$ curve of balance path wasdrawn, on which each point denotes a balance state. The slope of the tangentline for each point can be considered the stiffness of thick-walledcylinder. The extreme value of generalized force is the critical point onthe curve, and the critical point separates the curve into two sections: thesection before the critical point is stable, and the stiffness is positive;the section after the point is unstable, and the stiffness is negative. Whenthe generalized force reaches the critical point, the displacement increasesquickly and the system loses its stability, while ideal plastic thick-walledcylinder loses its stability only when the plastic region penetrates throughthe whole cylinder. Therefore, the failure mechanism is completelydifferent: the former belongs to extreme value point destabilization, andthe latter belongs to strength failure. That is to say, the bearing capacityhas different mechanical meanings.

2010, 42(1): 56-64. doi: 10.6052/0459-1879-2010-1-2008-440

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Equivalences of the generalized viscoelastic models and their inherent properties

Xiaohua Huang, Xiating Feng, Bingrui Chen

The equivalences of generalized viscoelastic models andtheir inherent properties are investigated. The creep compliance of thegeneralized Maxwell model is difficult to obtain due to its parallelconnection. However, a method by using Laplace transform is proposed in thepresent paper to solve this problem and a theoretical expression isobtained. The equivalence of the generalized Maxwell model and the Kelvinchain is proved and the conversion relations of the parameters between thesetwo models are also derived. Moreover, an inherent property of thegeneralized viscoelastic model proved here is that relaxation times anddelay times are mutually interlaced, and the former is always greater thanthe latter when the spectrums of relaxation time and delay time are placedin order. This property is also the imperative condition when thegeneralized viscoelastic model is applied to describe the rheologicalbehavior of materials in engineering. As special instances of theequivalence of the generalized Maxwell model and the Kelvin chain, there arethe equivalence between the Wiechert model and the generalized Zhong-cunmodel, the Generalized Jeffreys model and the Generalized N-K model, theMaxwell chain and the Generalized Kelvin model. Finally, the proposed methodis demonstrated by an example.

2010, 42(1): 65-73. doi: 10.6052/0459-1879-2010-1-2008-128

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discontinuous galerkin method for discontinuous temperature field problems

Donghuan Liu, Xiaoping Zheng, Yinghua Liu

A discontinuous Galerkin (DG) finite element method forthe discontinuous temperature field problems is presented. The DG methoduses discontinuous interpolation functions on the element boundaries, andthe discontinuous effect is considered by the penalty function techniques,in which the numerical flux and the stabilization term are adopted at theinterface. By substituting the numerical flux at the imperfect contactinterface with the definition of the thermal contact resistance, andeliminating the stabilization term, the present DG method can easily andaccurately capture the temperature jump caused by thermal contactresistance. Compared with the continuous Galerkin method, the present DGmethod also has higher computational efficiency in capturing the peak valueof the heat flux of the local high gradient temperature field. Numericalexamples also show that the present DG method is a novel numerical methodfor solving the coupling problems between the temperature and stress fieldcaused by thermal contact resistance.

2010, 42(1): 74-82. doi: 10.6052/0459-1879-2010-1-2009-003

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Area coordinates and b-net method for quadrilateral spline elements

Juan Chen, Chongjun Li, Wanji Chen

In general, there are two types of quadrilateralisoparametric elements, Serendipity type and Lagrangian type. The S-typeelements only possess low order completeness, and are sensitive to meshdistortions. The L-type elements possess high order completeness, butinclude interior nodes. By using numerical integrations due to isoparametrictransformation, the overall stiffness matrix may remain singular. In thispaper, a kind of quadrilateral spline elements are constructed by usingtriangular area coordinates interpolation and B-net method. These splineelements have property of conformality, and are insensitive to meshdistortions. The 8 and 12-node quadrilateral elements are represented bybivariate splines of degree 2 and 3, respectively. The two elements possess2 and 3 order completeness in Cartesian coordinates, higher than thecorresponding isoparametric elements with the same nodes. Some numericalexamples are employed to evaluate the performance of the proposed elements.The results show that the new spline elements present higher precision andefficiency in comparison with other quadrilateral elements.

2010, 42(1): 83-92. doi: 10.6052/0459-1879-2010-1-2008-501

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Influence of the stress path on dilatancy of soils and its modeling

Ding Luo, Zhiwei Gao, Yangping Yao

One of the most important characteristics of soil is itsdilatancy in which plastic volumetric strain occurs during shearing. Theinfluence of stress path on the dilatancy of soils is systematicallyanalyzed in this paper with the asymptote state model proposed by authors etal (Luo et al, 2009), in which the part coupling effect between the plasticvolumetric strain and plastic shear strain is assumed firstly. Thecomparisons are carried out between the test results of the dilatancy andthe model predictions of the original Cam-Clay model, the modified Cam-Claymodel, the unified hardening model (Yao et al, 2008) and our proposed model.The comparisons results demonstrate that the asymptote state model candescribe the effect of the stress path on the dilatancy of soils in a betterway in the stress-strain and strength behaviors of soils.

2010, 42(1): 93-101. doi: 10.6052/0459-1879-2010-1-2008-484

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The biomechanical study of the subsequent injury of an acl deficient knee

Jie Yao, Yubo Fan, Ming Zhang, Deyu Li, He Gong

Meniscus and ligament ruptures are common in anteriorcruciate ligament (ACL) deficient knee. The mechanism of injuries is stillunclear, and was mainly inferred from ex vivo experiments and clinicalstudies. In this study, a three dimensional finite element model of kneejoint was reconstructed from magnetic resonance images. The geometry data ofthe knee from literature was used to validate the model. Tibial displacementand in situ force in ACL in response to the anterior tibial loads werecalculated and coincided with the published experimental data. Thesimulations of the models with and without ACL were performed under anteriortibial loads and axial tibial loads at 0$^\circ$ and 30$^\circ$ flexion. Our resultssuggest that ACL deficiency could lead to abnormal stress distribution: thestress near the posterior insertion of the medial meniscus increasedsignificantly; the changes of the stress in the lateral meniscus, posteriorcruciate ligament and collateral ligaments depended on the loads and theflexion angles. This study may help to explain the higher subsequent injuryrate of ACL-deficient knee, and to predict the injury risk positions in thejoint. Furthermore, this model could shed some light on the mechanism of ACLinjuries and the treatments.

2010, 42(1): 102-108. doi: 10.6052/0459-1879-2010-1-2008-526

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Numerical study on the effect of the floating mass transducer on middle ear sound transmission

Houguang Liu, Na Ta, Zhushi Rao

To overcome some inherent problems in conventional hearingaids, such as low gain at high frequencies, discomfort, and acousticfeedback, floating mass type for middle ear implant system are currentlyunder development. The floating mass transducer (FMT) is the most importantcomponent of these devices. For the purpose of investigating the effect ofthe FMT to middle ear sound transmission, a middle ear finite element modelwith FMT clamped was constructed. This model was built based on a completeset of computerized tomography section images of a healthy volunteer's leftear by reverse engineering technology. The validity of this model wasconfirmed by comparing the motion of the tympanic membrane and stapesfootplate obtained by this model with published experimental measurements onhuman temporal bones. The result shows that FMT produces mass loading effectprominently at high frequencies, the force required to drive the incus tothe equivalent of 100\,dB SPL is about 8.9 dynes, and placing the clamp pointof the FMT close to the incudostapedial joint enhances the driving effect.

2010, 42(1): 109-114. doi: 10.6052/0459-1879-2010-1-2008-519

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Experimental and theoretical analysis of intelligent control for structural nonlinear vibration

Luyu Li, Gangbing Song, Jinping Ou

Experimental verification of structural dynamics andcontrol strategies is essential for theoretical and numerical study, butonly the linearity of the structures was studied in the existing modeltests. Therefore, recently there has been an increasing interest in researchof establishing experimental model for structural nonlinear vibration. Inthis paper, MagnetoRheological (MR) rotary brake is used to mimic theplastic hinge of structure so as to analyze structural nonlinear vibration.By means of adjusting the input voltage to MR rotary brakes, differentnonlinear behaviors can be detected. Moreover, the dynamical neural networkand adaptive fuzzy sliding mode control have been experimentally verifiedunder different nonlinear behaviors by incorporating MR damper into thisexperimental model. Experimental results show that the structural nonlinearvibration model which is established in this paper can be recovered toinitial state without any cost after nonlinear vibration tests. In addition,different nonlinear behaviors can be achieved by changing the input voltageto MR rotary brakes. The intelligent control algorithms are experimentallyverified to be suitable for control of structural nonlinear vibration.

2010, 42(1): 115-121. doi: 10.6052/0459-1879-2010-1-2008-355

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xistence condition of one-dimensional self-similar motion of ideal gas

Xiaoming Lai, Baomin Bian, Ling Yang, Anzhi He

The extension criterion of ideal gas self-similarity motion is not verycomplete. Hydrodynamic equations are made dimensionless, and then we obtainthe basic characteristic quantities solutions of ideal gas one-dimensionalself-similarity differential equations described by relative coordinate \xi and distance r. All of them have the same form Y ( \xi ,r ) =y ( \xi ) r^{C_Y }, which means that characteristic quantities forevery certain \xi are spatial scale-invariant according to r. It is provedthat the spatial scale-invariant is the existence condition ofone-dimensional ideal gas self-similarity motion.

2010, 42(1): 122-126. doi: 10.6052/0459-1879-2010-1-2008-576

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A new method for location leak in long-distance pipeline

Junhua Li, Wenbai Liu, Li Cui, Zhaochen Sun

For the long-distance pipeline based mainly on frictionalhead loss, it is necessary to locate the leak point after the leak appears.The researchers have developed many methods for position leak during thepast of a few years, such as pressure gradient method, inverse transientmethod, etc. These methods have their respective advantages anddisadvantages for long-distance pipeline. The pressure gradient method issuitable to the pipeline of hydraulic grade line varied linearly. The leaklocation in the inverse transient method is firstly assumed. Therefore, anew method for location of the leakage points has been developed with thecombination of the pressure gradient method and the inverse transient methodin this paper. In this scheme, the coefficients of the friction resistancebefore and after the leakage points, and the coefficients of the leakageflow, are taken as the optimizing control variables, and the difference ofwater head between the calculated values by waterhammer equations and themeasured values at measured sites are utilized as the objective function.The coefficients of the friction resistance before and after the leakagepoints are optimized through the genetic algorithm, based on which theiterative method is used to locate the leakage points.To verify the new method, the experiment in a water pipe with a length of48.775m and a diameter of 53mm was set up in the hydraulics laboratory ofDalian University of Technology. The pipeline is made of iron pipe, and isconnected to the pump at the upstream end and the water flume at thedownstream end. The error value of mean location in this method is about4%, compared with the experimental data. The experimental results showthat the method is quite feasible and efficient to locate the leak inlong-distance pipeline.

2010, 42(1): 127-131. doi: 10.6052/0459-1879-2010-1-2008-222

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Tensile fatigue damage and its mechanism of stitched composite laminates

Xiaoquan Cheng, Kun Yang, Renwei Hu, Jian Zou

Stitched laminate is a new kind of composite structure toimprove the interface strength of composite. But the in-plane properties ofthe laminate may reduce because there are local fiber bending in thelaminate plane and in the thickness direction, and the damage induced by thestitching threads. A lot of researches have been carried out on theproperties of laminates to push this material into engineering applications,such as in-plane tension and compression, compression after impact,hygrothermal properties, etc. But few studies have been performed onstitched composite fatigue properties. The aim of this paper is tocomprehend the fatigue damage development and mechanism of stitchedlaminates under tensile loads. The material of the laminates was uni-weaveT300/QY9512 stitched in 0^\circ direction. Un-stitched laminates were studiedfor comparison with the stitched laminates.Experimental study was carried out on the fatigue performance of stitchedand non-stitched composite laminate. The finite element models wereestablished to obtain the stress or strain distributions in the laminates.The mechanism of tensile fatigue damage origination and propagation ofstitched laminates was analyzed. The results show that the tensile fatiguedamage origination and propagation mechanisms of laminates have been changedby stitching. The stress concentration of in-plane stress \sigma_{x} andinterlaminar shear stress near the stitching node plays an important role indamage origination and propagation. Stress concentration of interlaminarstress at the free sides has effect on fatigue performance of stitchedlaminates. The stress concentration of interlaminar stress at the free sidesis the main reason that causes fatigue damage and its propagation ofnon-stitched laminates.

2010, 42(1): 132-137. doi: 10.6052/0459-1879-2010-1-2009-028

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A study on the two second-order strain gradient theories

Jie Zhao, Wanji Chen, Bin Ji

There are various strain gradient theories derived fromphenomenal theory and nonlocal continuum mechanics. Meanwhile, there are twopopular second-order strain gradient theories in which strain gradient termwas introduced into the constitutive law with positive and negative signsrespectively. In this paper, these two theories are discussed in the aspectof formula derivation, energy expression, and application fields. By usingthe 18-DOF triangle strain gradient plan element (RCT9+RT9) and axisymmetricelement (BCIZ+ART9) which can pass C^{0\hbox{-}1} patch test, the elasticpull-out processes of the reinforced concrete bond specimen and thedeformation of a cantilever beam are simulated to compare the limitation ofthe two theories in the analysis of microstructures.

2010, 42(1): 138-145. doi: 10.6052/0459-1879-2010-1-2008-517

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2010, 42(1): 146-149. doi: 10.6052/0459-1879-2010-1-2009-794

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2010, 42(1): 150-150. doi: 10.6052/0459-1879-2010-1-2009-795

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