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2011 Vol. 43, No. 2

Display Method:
Effects of centrifugal force and glide distance on the flight performance of HCV
Jing Fan
The flight performance of hypersonic cruise vehicles (HCVs), a competitive focus of international aerospace technologies in the 21st century, can be measured by a ratio of the initial boost mass to the generalized payload. A coupling frame to analyze the performance was established in Ref.[1]. Under the frame, two important effects, namely the centrifugal force and glide distance, have been further taken into account in this article. It was shown quantitatively that for a given distance, the first important factor to affect the flight performance of HCVs is the cruise speed, the second is the lift-to-drag ratio, and the third is the specific impulse of the cruise engine. As a flight distance increases, the performance of a rocket-based HCV, greatly improved due to the centrifugal force and glide distance taken into account, is significantly superior to the classical minimum-energy trajectory from short-middle to long range. A hypersonic air-breathing ramjet, though its specific impulse much higher than that of a rocket engine, is not so good as the latter in terms of the cruise speed range and lift-to-drag ratio. It is concluded that rocket-based HCVs flying at the optimal speed are a very competitive choice at the current stage.
2011, 43(2): 249-254. doi: 10.6052/0459-1879-2011-2-lxxb2010-607
Sensitivity analysis of similarity criterion number and its applications
Ben Xu Jiachun Li
Based on the theoretical formula and numerical simulation,the sensitivity analysis of scaling law are performed in complex flows, suchas the resistance of Wigley ship, the lift of symmetrical Joukowski airfoilin shear flow, and the oscillating flow and heat transfer in Pulse-TubeCryocooler (PTC). The computational results are well compared with those ofexperiments. The sensitivity analysis facilitates us to identify whichfactors in terms of dimensionless form are more important and should be paidmore attention to. These conclusions can be referred to engineeringapplications.
2011, 43(2): 255-266. doi: 10.6052/0459-1879-2011-2-lxxb2010-313
Scaling law of resolved-scale isotropic turbulence
Ma Wei Fang Le Shao Liang
In large-eddy simulation (LES), EDQNM theory is employed tocalculate the scaling laws of second- and third-order structure functions,and the skewness of velocity increment, in resolved-scale isotropicturbulence with three different filters, respectively. The scaling law andskewness are affected by several factors, such as the ratio of two-pointdistance to filter size, the LES Reynolds number, and the type of filter.Results show that, when two-point distance is the same magnitude as filtersize, or LES Reynolds number is small, both the scaling law and skewness ofresolved-scale turbulence are far from those of full-scale turbulence andshould be corrected. Three examples of subgrid modeling using these resultsare then introduced.
2011, 43(2): 267-276. doi: 10.6052/0459-1879-2011-2-lxxb2010-079
Turbulent drag reduction via a streamwise traveling wave induced by spanwise wall oscillation
Huang Leping Fan Baochun Dong Gang
The flow control and drag reduction in turbulent channelflow via streamwise traveling wave induced by spanwise-wall oscillation areinvestigated by direct numerical simulation (DNS). The effects of streamwisecontrol parameter $k_{x}$ on the Stokes layer, the near-wall flow structure,turbulent burst events, as well as the skin-friction drag are discussed. Inaddition, the mechanisms of turbulence suppression and drag reduction viastreamwise traveling wave induced by spanwise-wall oscillation are alsodiscussed. The results suggest that only the low-frequency waves have thesignificant influence on the flow field which induces the great variationsof frequency and the intensity of the burst which can be detected by thevariable-interval time averaging (VITA) detective technique. The variationsof the frequency and the intensity of the burst are unsynchronized as the$k_{x}$ increases, and there exists an optimal parameter, k_{x}, in whichthe influence of the intrinsic flow on the induced flow is weakest, and onthe contrary, the intrinsic turbulent flow is modified strongly by theinduced flow, and the largest amount of drag reduction is obtained.
2011, 43(2): 277-283. doi: 10.6052/0459-1879-2011-2-lxxb2009-041
ynamics model of statistical fractal structure of ideal gas under gravity
Lai Xiaoming Bian Baimin Yang Ling Yang Juan Li Zhenhua He Anzhi
Differential equations of ideal gas under gravity are madedimensionless by choosing statistical quantities \rho (R), p(R),u(R) as the unit with respect toscale factor R (t) and substituting time t with spatial scalefactor R (t). The equations that have separable variables areobtained based on {\it\Pi} theory, then a serial of differential equationshaving fractal structure characteristics are obtained. Statisticalquantities of ideal gas under gravity Y(R) have generalizedfractal characteristics. This result shows that the local differentialequations of fluid can be the fundamental equations of the dynamics ofstatistical fractal structures.
2011, 43(2): 284-288. doi: 10.6052/0459-1879-2011-2-lxxb2009-642
Integrated optimization design of light-weight multilayer thermal protection structures
Chen Liming Dai Zheng Gu Yu Fang Daining
The large-area thermal protection structure is widely used in aerial and aerospace fields, in which creative structural design is one of the key technologies. The work conditions of the aerospace structures demand the thermal protection materials and structures should have combined features of light-weight, high thermal resistance and anti-collision stiffness. Thus the thermal protection materials and structures are in the trend of integration. Based on this trend, this paper brings forward a design of the light-weight integrated multilayer thermal protection structures. The heat transfer of integrated multilayer thermal protection structures during the re-entry process of space shuttle is investigated. Based on the assumption of one dimension heat transfer of the large-area thermal protection structures and the temperature conditions of the re-entry process for space shuttle, one-dimension transient heat transfer model and closed equations are established. A numerical difference method is used to solve the equations, and finite element analysis using the commercial software ABAQUS is carried out to identify the validity of the difference method. The temperature distribution of multilayer thermal protection structures is obtained. The integrated optimization design method of light-weight multilayer thermal protection structures is presented aiming at the lightest weight of the structures under given certain thermal constrains. The optimal geometry parameters of the multilayer structures are obtained.
2011, 43(2): 289-295. doi: 10.6052/0459-1879-2011-2-lxxb2009-500
Topology optimization of structures designed with multiphase materials: volume constraint or mass constraint?
Gao Tong Zhang Weihong Pierre Duysinx
Instead of adopting the common idea of using volumeconstraint in topology optimization, this work is focused on the topologyoptimization of structures designed with multiphase materials and massconstraint. Related structural optimization models involving mass constraintand material interpolation model are proposed. Based on the study of twotypes of material interpolation models, i.e. GSIMP and UIM, the former isfound to introduce the nonlinearity into the mass constraint which bringsnumerical difficulties in searching the global optimum of the optimizationproblem. The adopted UIM model, however, makes the mass constraint linearand design variable separable, which favors the mathematical programmingapproaches, especially the convex programming methods. Numerical examplesshow that the presented scheme is reliable and efficient to deal with thestructural topology design problems of multiple materials with massconstraint. The mass constraint is proved to be more significant andimportant than the volume constraint in structural topology optimization.
2011, 43(2): 296-305. doi: 10.6052/0459-1879-2011-2-lxxb2010-303
esign of material distribution of acoustic structure using topology optimization
Jianbin Du Song Xiankai Dong Lili
Analysis and design of the acoustic structure arestudied in the present paper. The sound pressure on a prescribed referenceplane/domain in the acoustic field that is generated by the vibratingstructure is minimized by two-phase damping material distributionoptimization over the structural domain. The Finite element method-Boundaryelement method (FEM-BEM) based structural-acoustic coupling topologyoptimization model is established. The sensitivities of the couplingvariables with respect to the design variables are derived by using thedirect differentiation method as well as the adjoint method. It is pointedout that the adjoint method provides the more efficient formulation forsensitivity analysis when the amount of the reference field points on thereference surface for sound pressure calculation is much less than the totalamount of the design variables. The proposed methods are validated bynumerical examples of the designs of the traveling wave tube and the motorcover. Some interesting features on optimum topologies obtained from thestructural-acoustic coupling designs are revealed and discussed.
2011, 43(2): 306-315. doi: 10.6052/0459-1879-2011-2-lxxb2009-594
Analysis and design of two dimensional lattice materials with band-gap characteristics
Huang Yu Liu Shutian
Periodic materials or structures own the capability ofattenuating wave propagation over certain frequency bands, which is calledband-gap characteristics, and the materials can be reasonably designed toadjust the location and width of band gaps. With the great potentialapplications such as filters, wave guides and sound or vibration isolation,the effect of the configuration in microstructure on the band-gapcharacteristics is investigated. First,the band-gap behaviors of elastic wave and the attenuationcharacteristics in localization in seven 2D periodiclattice topologies, namely triangular honeycomb, square honeycomb, groundhoneycomb, hexagonal honeycomb, auxetic honeycomb, Kagome honeycomb anddiamond honeycomb, are analyzed and compared. Objective function to measurelow and wide band-gap character is proposed, and the optimal band-gapmaterial is then selected. Furthermore, the laws of geometry configurationparameters affecting on the band-gap characteristics are obtained andnumerically demonstrated. The techniques developed in this work can beapplied in design periodic band-gap materials by adjusting geometryconfigurations in the microstructure.
2011, 43(2): 316-329. doi: 10.6052/0459-1879-2011-2-lxxb2010-047
Uniaxial tensile stress-strain behavior and strength of plain woven C/SiC composite
Yang Chengpeng Jiao Guiqiong Wang Bo
Fiber reinforced ceramic matrix composites (CMCs) are widely investigated inrecent years in order to obtain their damage mechanisms, failure modes andmechanical properties. A well-accepted fact is that the interface betweenthe fibers and the ceramic matrix has great effects on the mechanicalbehavior of CMCs. The tough and nonlinear stress-strain behavior of CMCs canmainly be attributed to matrix cracking and interface debonding. Therefore,how these two factors affect the stress-strain relationship and the finalstrength of CMCs needs to be deeply studied.In this paper, the damage evolution and the tensile stress-strain behaviorof 2D-C/SiC composite were investigated under monotonic and stepwiseincremental loadings and unloadings. The strain is measured by 25 mmextensometer. The experimental results show that the stress-strain behaviorof the material is obviously nonlinear; the unloading modulus decreaseswhile the inelastic strain increases with increasing of the unloadingstress; the relational curves of residual strain and unloading modulusversus the applied stress have analogous form with the tensile stress-straincurve; the fracture of the composite is quasi-brittle, i.e. catastrophic.Based on the shear-lag theory and the rule of mixture, a conciseconstitutive equation and a tensile strength calculation model of thedamaged material were established. The simulated stress-strain curve is ingood agreement with the experimental data when the applied stress is lowerthan 100 MPa. The difference between the theoretical curve and theexperimental data when the applied stress is higher than 100 MPa mainly comesfrom the local strain concentrations within the seriously damaged zone,because large crack openings usually appear in this region from theexperimental view. The analysis results reveal that the residual strainmainly depends on the crack opening displacement and the crack spacing,while the unloading modulus is significantly dependent on the interfacedebonding rate. Moreover, the uniaxial tensile behavior of 2D-C/SiCcomposite is mostly dominated by the longitudinal fiber bundles; thecontributions of transverse fibers to the material's modulus and strengthare obviously small.In the strength model, the failure criteria proposed by Tsai-Hill wasapplied to obtain the off-axes strength, and then the curved fiber bundle inthe real material structure was equivalent to the straight. Furthermore, therule of mixture was modified and the expression for strength calculation waspresented. And, the predicted tension strength ranges from 210.5 MPa to265.6 MPa for the 2D-C/SiC composite with 0.15 \mu m thick carboninterphase, which is also in good agreement with the experimental data.
2011, 43(2): 330-337. doi: 10.6052/0459-1879-2011-2-lxxb2009-717
An evolution model of delamination for composite laminates under external impact
Zhang Sijin Wen Guilin
The evolution of delamination is studied by usingdouble-linear characteristic model of damage. With a representation ofdamage parameters for elastic/shear moduli, a series of differentialequations of damage parameters with respect to strain are derived, and therelations of cracking dissipated work with respect to damage parameters arealso obtained. By computing the evolution of strain, strain rate and damageparameters in a certain interface of composite laminates under impact withvariety of initial velocities, delamination in the interface and its effectto shear moduli are yielded. Then the delamination regions between the firstand the second layer after impact are evaluated by checking whether one ofdamage parameters is changed at each point in interface. The result showsthat the shear moduli start to decay in the point where shear stress reachesthe shear strength. The decaying amplitude increases as the initial impactvelocity of iron ball being raised, while it decreases outwards from theimpact point nearby. With all boundaries simply supported, the delaminationregion appears firstly in the center of one interface, and they expand asthe initial impact velocity being raised. Several independent delaminationregions will appear along two symmetric axes of interface plane between thefirst and the second layer of composite laminates if the initial impactvelocity is higher enough.
2011, 43(2): 338-345. doi: 10.6052/0459-1879-2011-2-lxxb2010-448
Constitutive Theory and Experiment Analysis of Hot Forming for High Strength Steel
Ma Ning Hu Ping Wu Wenhua Shen Guozhe Guo Wei
Thermal-mechanical-transformation coupled relations ofboron steel are investigated in the hot forming (HFS, hot stamping) processby tensile and quenching experiments at high temperature. In theexperiments, plate specimens of boron steel are austenitized for fiveminutes at 950℃, then formed in tension and quenched. The force,displacement, expansion and temperature in the experimental process aremeasured. Based on the analysis of the above physical quantities variationand the specimen's microstructure, thermal-mechanical-transformation coupledrelations of boron steel are researched and thethermal-mechanical-transformation coupled constitutive models are developed.The multi-phase mixed relationship is introduced to analyze the effectivethermo-mechanical parameters and mechanical properties of multi phasesduring the hot forming. The components of strain and their evolved mechanismfor hot forming are investigated. The phase-transformation volume stress andphase-transformation plastic stress are defined and expressed to explain themechanism of thermal-mechanical-transformation coupled relations. Themodified Norton-Hoff flow stress is applied to describe the flow propertiesof boron steel at high temperatures and the material parameters is obtainedby analyzing the measured data of high-temperature tensile tests. Based onthe above research, the thermal-mechanical-transformation coupled models areintroduced into the constitutive equations of hot forming, and theintegrated and incremental constitutive equations are developed,respectively. Numerical simulation of U-shaped hot forming process isimplemented and compared with the experimental results. The results provethe validity of the developed constitutive equations.
2011, 43(2): 346-354. doi: 10.6052/0459-1879-2011-2-lxxb2010-004
Static reanalysis methods for large-scale structrues with large modifications
Jizhuo Huang Wang Zhan
This study presents three static reanalysis methods forlarge-scale structures with large modifications of structural parametersbased on the Combined Approximation (CA) method. For large-scale structureswith large changes in the design, the Combined Approximation method can notprovide enough accurate results. To improve the accuracy of the results inreanalysis of the modified structure, three CA-based static reanalysismethods are presented by introducing several strategies, such asdisplacement iterative correction and stiffness progressive approximation.Two numerical examples are presented to demonstrate the validity and theimprovement of the proposed methods, and the results show that the methodsgiven can provide accurate approximations and can significantly reduce thecomputational effort involved in reanalysis of large-scale structures withlarge modifications. Comparisons of the computational costs of these threepresented methods are made.
2011, 43(2): 355-361. doi: 10.6052/0459-1879-2011-2-lxxb2009-718
Symplectic system for analytical solutions of orthotropic foundation beam
Yang Youzhen Ge Xiurun
Based on the two-dimensional theory of elasticity (2DET),Hamiltonian system is introduced to solve the bending of orthotropic BeamsResting on Pasternak Elastic Foundations and the original problems come downto solve the eigensolutions of zero eigenvalue and non-zeroes eigenvalue.Elastic foundation is treated as the side boundary conditions similar to theapplied load and their contributions to the solutions of beams areapproximated by linear expansion of all eigensolutions of zero. Thesymplectic concept makes no hypothesis of deformation along the thicknessdirection and shows a rational derivation. Thus, the current method canprecisely analyze foundation beams with arbitrary depth-to-length ratio, andcan deal with arbitrary end conditions. In additional, a new improvedboundary condition for fixed ends beam is presented. Numerical examples incomparison with other methods are given to illustrate the accuracy of thepresent symplectic approach.
2011, 43(2): 362-271. doi: 10.6052/0459-1879-2011-2-lxxb2009-440
Numerical investigation of drag-reducing property for a high-rise building by subsection suction control
Chao-Rong ZHENG Zhang Yaochun
As a result of theextensive utility of high-strength and light-weight materialsin construction, high-rise buildings tend to be very vulnerable tothe wind loads, and the wind-resistance design has graduallybecome the dominate factor in structural designs. To reducethe wind-induced drag force and improve the wind-resistanceperformance of a high-rise building, the active suction controlis proposed to investigate the drag-reduction property vianumerical simulation. Effects of the slot locations along theheight, the suction heights and suction velocities on thedrag-reduction property are analyzed. Moreover, the detailed flowfield is presented to discuss the mechanism of the suction control. Theresults indicate that, as the suction height increases,coefficient of pressure reduction, coefficient of drag reductionand coefficient of along-wind base moment reduction will increaseunder the same suction velocity, and their efficiencies(efficiency of pressure coefficient reduction $\eta_{\rm{PR}}$,efficiency of drag reduction $\eta_{\rm{DR}}$ and efficiency ofalong-wind base moment reduction $\eta_{\rm{MR}})$ will decreaseuntil 1.0. On the other hand, the $\eta_{\rm{PR}}$ ($\eta_{\rm{DR}}$ or $\eta_{\rm{MR}}$) will increase along with theincrement of suction height under the same flux coefficient, andonly the $\eta_{\rm{MR}}$ will be greater than 1.0 at largersuction height. Based on the analysis above, formulae of the$\eta_{\rm{DR}}$ and $\eta_{\rm{MR}}$ versus the slot location,suction height and suction velocity are regressed to be referredfor practical application of subsection suction on the high-risebuilding. Lastly, comparison of the drag-reduction property of thesubsection suction models and all-height suction model areperformed based on the maximal drag-reduction efficiencies and theminimal power consumed, and the latter is superior to the formers.However, the subsection suction is still practical, as it canbe used on upside of high-rise buildings to reduce the basemoment or improve the local wind pressure characteristics.
2011, 43(2): 372-380. doi: 10.6052/0459-1879-2011-2-lxxb2009-577
Finite element analysis on lumbar interbody fusion
Peng Xiongqi
The aim of this paper is to evaluate the effect ofinterbody fusion on lumbar spine via finite element (FE) method. Based on CTscanning images and CAD three-dimensional reconstruction technique, detailedand anatomically accurate normal and fused human lumbar spine FE models forthe L2-L4 motion segment with or without L3-L4 fusion are built. The lumberspine models include vertebrae, intervertebral disc and various ligaments. Apreviously developed hyperelastic fiber reinforced constitutive model isused to characterize the nonlinear anisotropic material property ofintervertebral disc annulus fibrosus. The proposed FE model is validated bycomparing numerical results of axial compressive load-displacement withexperimental data available in literature. Commercial FE analysis softwarepackage ABAQUS/Standard is used to simulate the normal and fused lumberspine segment under flexion, extension and axial rotation. The lumbar spinemotion range and stress distribution of two models under different loadingconditions are obtained and compared. Numerical simulation results show thatunder the same loading condition, the fused model has a much smaller bodymotion range compared the normal one. Interbody fusion brings out obviouslydifferent stress distribution in adjacent vertebral bodies, but has minorimpact on adjacent intervertebral disc. The results also suggest that facetjoints play an important role in maintaining normal physiological functionof spine. The analysis results can provide references and guidelines forhuman lumbar fusion neurosurgical operation in clinic.
2011, 43(2): 381-389. doi: 10.6052/0459-1879-2011-2-lxxb2009-697
Study on redundant constraints in multibody systems
Qi Zhaohui Fang Huiqing
Being resulted from singular configuration and cut jointconstraint equations generated in a programmed way, redundant constraints inmultibody systems exert great influence on the methods for modeling andsolving multibody systems. It is necessary to select a group of independentequations from whole constraint equations in order to keep the systemcontrol equation solvable. It is observed that results of numerical analysisusually being changed by different choices. However it is not true intheory, as proven rigorously in this paper. Due to constraints violation,many methods for solving DAE lose their effectiveness near by the positioncorresponding to the singular configuration of multibody systems. Based onthe combination of constraints stabilization and elimination of constraintviolation, we present a method to overcome such difficulties and testify itsvalidness by an example. It is the greatest negative effect brought byredundant constraints that forces of interaction between bodies may be notunique. A criterion to certify which and when a constraint force would bedefinite is given. It is known that when a pair of bodies is linked by morethan one joint, the reaction forces in those joints would be ambiguous. Thispaper present a method of making the reaction forces definite in such caseby replacing those joints with a single composed one.
2011, 43(2): 390-399. doi: 10.6052/0459-1879-2011-2-lxxb2009-596
DAE-LCP mixed method for multibody system dynamics with frictional contacts
Fu Li Yue Yuefengtong
Presently, dynamics of nonsmooth multibody systems is a hot research topic.The usual approach in treating such systems is to derive basic system fromthe original system by removing the nonsmooth constraints firstly. TheLagrange equations of the second kind of basic system combine with thecomplementarity condition of the nonsmooth constraints to set up at eachdiscrete moment in time a Linear Complementarity Problem (LCP).This article focuses on the problem of dynamic modeling and numericalsimulating of multibody systems with friction contacts. By neglecting theclearance and the effect of impact between rigid bodies and constraints, thestate variables in the differential equations are continuous. Due to theset-value mapping characteristic of dry friction forces, the differentialequations of motion have discontinuous right-hand vector fields, thereforeto allow our system to be classified as a Filippov system. In addition tothe friction constraints, our model also incorporates frictionless bilateralones. If the simulation has only friction constraints, then the problem isan ODE-LCP model. Combining friction contacts with frictionless bilateralconstaints, the ODE-LCP model has to be extended to DAE-LCP (DAE,Differential Algebra Equation) mixed model. In order to obtain the model,the basic system is derived from the original system by removing thefriction constraints firstly. Because the equality constraints are retainedin the basic system, the dynamic model of basic system is a set of DAE. Withthe aid of constraint Jacobian matrix, the normal contact forces andtangential friction forces of nonsmooth constraints, which obey thecomplementarity contact laws, are added to the DAE of the basic system toobtain the DAE-LCP mixed model.Approaches used in the past for simulating rigid multibody dynamics withfriction contacts include piecewise DAE approaches, acceleration-force LCPapproaches, and velocity-impulse LCP-based time-stepping methods.Recognizing that the nature of the frictional constraint can inducesick-slip motion, the last approach is used in this work, which has theadvantage that it does not suffer from the detection for stick-sliptransition that could appear in the first two approaches. This framework isbased on a LCP, but it is different from acceleration-force LCP approachesthat attempt to find the accelerations of the bodies.Our approach considersimpulses and velocities as the fundamental unknowns. Acceleration-force LCPapproaches solve for accelerations from the dynamics equations and then usethe accelerations in an integration procedure. Because the complementaritylaw between acceleration and friction surplus is valid only when therelative tangential velocity is zero, zero crossing detection for velocityis required. However the complementarity law between velocity and frictionsurplus remains valid through a full-range of motion, so in contrast toacceleration-force schemes, the velocity-impulse methods need noevent-detection. In the new framework, the integration and dynamicalresolution steps are combined. The main achievement of this approach is thatit has solutions for any configuration. As the time-step tends to zero, asubsequence of the numerical solutions approaches the solution of adifferential inclusion.Our method is carried out in a numerical example, and the simulation resultsindicate that this method is effective.
2011, 43(2): 400-407. doi: 10.6052/0459-1879-2011-2-lxxb2009-574
Correction methods analysis of double lunar-swingby trajectory
Zong-Fu Luo Meng Yunhe Tang Guojian
Double Lunar-Swingby (DLS) trajectory is a type ofnon-linear orbit which has potential applications in the deep-spaceexploration. A nominal trajectory is given under CR3BP model, and itsdynamic characteristic is analyzed. According to the error dispersion of thenominal trajectory, several correction principles are established.Considering the solar gravitational perturbation, the R4BP model isestablished. A method of explicit guidance at the ``key node'' is developed,and the correction maneuver results of the initial error, navigation error,maneuver error and the solar gravitational perturbation are obtained. Thestatistical dispersion analysis is carried out with Monte-Carlo simulation.Based on these works, a new method of initial velocity supplement combinedwith explicit guidance is proposed to correct the initial error, navigationerror, maneuver error and the solar gravitational influence, and theparameters including the magnitude of supplement velocity and time of TCMare optimized. The simulation results show that this method can reduce thecorrection maneuver obviously. The results and conclusions of this paper canprovide a reference for the engineering applications of DLS trajectory.
2011, 43(2): 408-416. doi: 10.6052/0459-1879-2011-2-lxxb2010-063
The elastic-viscoplastic field near mode I dynamic propagating crack-tip of interface in double dissimilar materials
Wang Zhengqing Wen-Yan Liang Lv Hongqing
The existence of viscosity effect at the interface ofdouble dissimilar materials has an important impact to the distribution ofinterface crack-tip field and the properties variety of the interfaceitself. The singularity is considered in crack-tip, and theelastic-viscoplastic governing equations of double dissimilar materials atinterface crack-tip field are established. The displacement potentialfunction and boundary condition of interface crack-tip are introduced, andthe numerical analysis of rigid-elastic viscoplastic interface for mode Iwas worked out. The stress-strain fields are obtained at the crack-tip andthe variations of solutions are discussed according to each parameter. Thenumerical results show that the viscosity effect is a main factor ofinterface propagating crack-tip field, and the interface crack-tip iselastic-viscoplastic field that is governed by viscosity coefficient, Machnumber and singular factor.
2011, 43(2): 417-422. doi: 10.6052/0459-1879-2011-2-lxxb2010-018
Thickness-twist waves in the magneto-electro-elastic bi-material plate
Kong Yanping Yang Qian Jin-Xi Liu
This paper is concerned with the thickness-twist wavespropagating in an infinite magneto-electro-elastic bi-material plate. Theupper and lower surfaces of the plate are assumed to be mechanically free,electrically open and magnetically closed. Based on the fully coupledmagneto-electro-elastic constitutive relations, the general solutions of thethickness-twist waves are first derived. Then the frequency equations areobtained by using the boundary conditions and interfacial conditions. As anexample, for the propagation of the thickness-twist waves in the bi-materialplate consisting of BaTiO_{3} and CoFe_{2}O_{4}, the distributions ofthe displacement, electrical potential and magnetic potential are obtained.The dependence of the number of trapped modes on the geometric size is alsogiven. The theoertical results are useful for the design of plateresonators, filters and acoustic wave devices with magneto-electric effect.
2011, 43(2): 423-429. doi: 10.6052/0459-1879-2011-2-lxxb2009-605
A time-stepping method of seismic response analysis for structures using differential quadrature rule
Li Hongjing Wang Tong
A numerical time-stepping method is developed for thesolution of equations governing the motion of a MDOF system subjected toearthquake induced ground acceleration on the basis of the differentialquadrature (DQ) rule. Initially the history of the seismic ground motion andthe structural dynamic responses are divided into a sequence of timeintervals, and the DQ rule is used within each discrete time step, thus thefinal response of velocity and acceleration during the interval may beexpressed as a weighted linear sum of the initial condition and the responseof displacement at the sampling grid points. It is assumed that the groundacceleration over the time step increases linearly with time, and theformulae for the quadrature solution of the differential equations of motionare deduced so that the history of the dynamic response could be calculatedin the time-stepping procedure using the DQ method. A two-story shear framestructure is employed for numerical illustration, and results from numericalanalysis show that the proposed quadrature procedure can still achieve anexcellent analysis for the time history of the seismic response even whenthe length of the time step is selected to be a little larger.
2011, 43(2): 430-435. doi: 10.6052/0459-1879-2011-2-lxxb2009-454
On vortex induced vibration in two-degree-of-freedoms of flexible cylinders
Huang Weiping Cao Jing Zhang Enyong Tang Shizhen
In-line and cross-flow vortex-induced vibration (VIV) offlexible cylinders is studied based on the VIV experiment. The relationshipof two-degree-of-freedom of vortex-induced vibration of flexible cylindersis also investigated. A nonlinear model, with fluid-structure interaction,of two-degree-of-freedom VIV of flexible cylinders is then proposed. It isshown that the ratio of the frequencies and amplitudes of in-line and crossflow VIV of the cylinders changes with current velocity/Reynolds number. Theratio of the VIV frequencies is 1.0 beyond the lock in district and 2.0within the lock in district, respectively. And the ratio of the VIVamplitudes is 1.0 beyond the lock in district and 1/3 to 2/3 within the lockin district.
2011, 43(2): 436-440. doi: 10.6052/0459-1879-2011-2-lxxb2010-500