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2011 Vol. 43, No. 6

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Thoughts of Hsue-Shen Tsien on Engineering Sciences---In Memory of Hsue-Shen Tsiens 100th Anniversary
Che-Min Cheng
This article is a brief review of Professor Hsue-Shen Tsien's thoughts on Engineering Sciences from the author's perspective. Topics covered are what are engineering sciences, the importance and role of engineering sciences, the strong emphasis on application, basic trainings of engineering scientists and Tsien's application of these ideas in running the Institute of Mechanics. It is the author's view that the mainstream for the development of mechanics in China should follow the route charted by Tsien.
2011, 43(6): 973-977. doi: 10.6052/0459-1879-2011-6-lxxb2011-323
Development study of detonation driving techniques for a shock tunnel
Hongru Yu
The cause for abnormal increase of shock Mach number in a combustion driven shock tube had been discovered. The experimental results show that the capabilities of gaseous detonation driver are stronger than to combustion driver which bring about a great advance in detonation driving technique. Using a dumping section to eliminate the reflected high pressure of the detonation wave and utilizing double detonation driver to eliminate completely the Taylor wave following the detonation wave makes the backward and forward detonation drivers usefulness. The backward detonation technique is utilized still to prolong the test duration for a shock tunnel.
2011, 43(6): 978-983. doi: 10.6052/0459-1879-2011-6-lxxb2011-331
Exploration of systems science methodology
Dinghua Shi
As everyone knows, systems science is a new discipline for scientificmethodology. Systems science researches the common characteristics of allcomplex systems in nature and human society, exploring the universal laws inthe generation, the evolution and the emergence of systems in general.Classical science pays attention to the reductive analysis while the systemsscience emphasizes holistic grasp, with substantial distinction inmethodology. In this paper we first review our important achievements insystems science methodology, next introduce the results in descriptionmethod using operations research, emphasizing the use of networkmodelling and analysis inthe research methods of systems science.
2011, 43(6): 984-990. doi: 10.6052/0459-1879-2011-6-lxxb2011-318
Interplanetary travel with electric propulsion: technological progress, trajectory design, and comprehensive optimization
Yang Gao
In 1963, Dr. Qian Xuesen (Tsien Hsue-Shen) pointed out the significance of the study on interplanetary travel, and revealed the potential utilization of electric propulsion in his book ``Introduction to Interplanetary Travel''(in Chinese). Compared to traditional chemical propulsion, the high-specific-impulse electric propulsion is promising to carry more payloads and achieve enhanced flight performance for interplanetary travel. Meanwhile, the design and optimization of continuous-thrust transfer trajectories resulting from the use of electric propulsion have brought new research contents to the traditional spacecraft's orbital dynamics, and meanwhile guides the future development of electric propulsion. This article will present technological progress of electric propulsion, continuous-thrust trajectory design, and comprehensive optimization of interplanetary flight, attempting to describe the fundamental content and approach of the utilization of electric propulsion for interplanetary travel, as well as for manned deep-space flight.
2011, 43(6): 991-1019. doi: 10.6052/0459-1879-2011-6-lxxb2011-332
Unsteady dynamic aerodynamic hysteresis effects and linear modeling about the slide-skin swept-angle morphing wing
Peng Bai Qian Chen Liu Xinyu Feng Li
In this paper, three jobs were carried out about theunsteady dynamic aerodynamic effects during the sliding skin swept-anglewing morphing under the incompressible condition. (1) The wind tunnelexperimental measure technologies about the unsteady dynamic aerodynamiccharacteristic during aircraft morphing were studied; (2) The aerodynamichysteresis effects during the swept-angle morphing were investigated and themechanisms were analyzed initially; (3) The unsteady dynamic aerodynamiclinear models were made during morphing based on the experimental results.The primary research indicated that: (1) the method of the forced periodicmorphing could obtain the unsteady dynamic aerodynamic hysteresis effectseffectively; (2) there were two mechanisms which bring the effects: ``Themoving boundary effect'' and ``The flow structure hysteresis effect''. Andthe hysteresis effects in this paper might be caused by the latter mainly;(3) the dynamic derivatives of the lift and pitching moment coefficients tothe morphing rate of swept-angle were defined in this paper, which can makethe linear model about the unsteady dynamic aerodynamics during morphing.
2011, 43(6): 1020-1029. doi: 10.6052/0459-1879-2011-6-lxxb2011-125
Experimental study of the flow focusing under an electric field
Si Ting Ruijun Tian Guangbin Li Xiezhen Yin
The instability characteristics of the cone and theelectrified jet coupling the electric and pneumatic forces have beeninvestigated experimentally by applying an electric field in the region ofthe coaxial liquid-gas jet of flow focusing. The experiments were carriedout on a well-designed flow focusing device. The effects of the mainlycontrollable parameters including the external electric voltage, the gaspressure drop and the liquid flow rate on the flow focusing process wereanalyzed. The flow modes of the cone, including the cone-shaky mode, thecone-steady mode and the transition between them, were obtained. The shapesand transitions of the jet flow modes including the dripping mode, theaxisymmetric mode, the coexisting mode and the non-axisymmetric mode werealso observed, and the effects of the electric field on the jet dimensionswere further performed quantitatively. The results indicate that thiscombining method is capable of stabilizing the cone, enhancing theatomization and reducing the size of the production compared with the singleflow focusing. As a result, the method has remarkable applications in fieldsof science and technology, and would be valuable in engineering practice.
2011, 43(6): 1030-1036. doi: 10.6052/0459-1879-2011-6-lxxb2011-156
Experimental investigation on hairpin vortex packets in the later stage of bypass transition induced by cylinder wake
Zhanqi Tang Jiang Nan
The hairpin vortex packets structure and characteristicscale in the later stage of bypass transition induced by cylinder wake areinvestigated by TR PIV technique for both the side-view and top-view cases.The two-dimensional velocity components are correlated with \lambda_{ci} criterion, and linear stochastic estimation is used to estimate theconditional average of the velocity field. For the side-view case, theconditionally averaged structure consists of a series of swirling motionslocated along a line inclined at a larger angle (17^\circ) from the wall, anda low-speed region occupied by cylinder wake appearing right above it in thefree stream. In the (x, z)-plane at the top of the log layer (y/δ=0.2), the dominant motions are shown to be large-scale regions of lowmomentum elongated along the streamwise and within a spanwise width of0.55δ, whichare consistently bordered by small-scale counter-rotating vortex pairsorganized in the streamwise. The results suggest that in the later part ofthe transition zone, due to the upward induction of wake vortex, the hairpinvortex packets statistically perform a skeleton frame of larger scale androbust physique.
2011, 43(6): 1037-1042. doi: 10.6052/0459-1879-2011-6-lxxb2011-124
Theoretical and experimental studies of H∞ control for a flexible plate with time delay
Tong Zhao Longxiang Chen Guoping Cai
This paper presents theoretical and experimental studiesof H∞ control for a flexible plate with time delay. Firstly, thetime-delay dynamic equation of the plate is established. Secondly, a matrixinequality for system asymptotic stability is derived by using theLyapunov-Krasovskii functional and free-weighting matrix method. Based onthe matrix inequality, two control design problems are solved by using theparameter adjustment method and genetic algorithm: (1) H∞controller design with known maximum time delay of the system; (2)determination of maximum time delay with known controller. Finally,simulation and experiments are carried out to verify the theoreticalresults. Simulation and experimental results demonstrate that the designedH∞ controller is effective in reducing the plate vibration and thedetermined maximum time delay guaranteeing the system stability is close tothe real time delay of the system.
2011, 43(6): 1043-1053. doi: 10.6052/0459-1879-2011-6-lxxb2011-076
Experimental investigation of the transition of temperature oscillation in Bénard-Marangoni convection
Di Wu Yang Zhang Li Duan Liang Hu Yongqiang Li Qi Kang
In this paper, temperature oscillation is found in theexperiment. The experimental research focus on the critical Ma number ofonset of temperature oscillation, and discuss the transition of temperatureoscillation as the Ma increase. The experiment result shows that onset oftemperature oscillation in silicon oil with different physical propertiesmeet the same law. The super critical temperature oscillation showsdifferent transition routes in the different fluid, but the same route isperformed in the same fluid with different depths. Besides, convectionpattern and its transition are studied by particle trace method.
2011, 43(6): 1054-1060. doi: 10.6052/0459-1879-2011-6-lxxb2011-149
Measurement of flow parameters in a scramjet combustor based on near-infrared absorption
Fei Li Xilong Yu Hongbin Gu Zhi Li Lihong Chen Xinyu Zhang
A multi-channel tunable diode laser absorptionspectroscopy (TDLAS) system was constructed to measure flow parameters in adirect-connected scramjet test facility fueled with ethylene. Two fiberscoupled distributed feedback (DFB) lasers with narrow line width were usedto probe two H_{2}O absorption featuresby using direct absorptiontime-division-multiplexing (TDM) strategy at a 4kHz scan rate. Flowparameters were measured, which included the distribution of temperature,water vapor concentration and velocity at the exit cross section of thecombustor, the distribution of temperature and water vapor concentration inthe cross section near the cavity. Combustion efficiency was obtained byusing the water vapor partial pressure distribution and the wall staticpressure. Mach number distribution was deduced from the temperature andvelocity parameters distributions at the exit cross section of thecombustor, and the distributions of temperature and water vaporconcentration in the cross section near the cavity were used to analyzecombustion characteristics in the combustor.
2011, 43(6): 1061-1067. doi: 10.6052/0459-1879-2011-6-lxxb2010-729
Aerodynamic optimization design of new type tandem airship based on response surface methodology
Feng Li Zhengyin Ye Chao Gao
The new type tandem buoyancy-lifting airship, based onthe NACA aerofoil, not only possesses considerable volume efficiency, butalso the aerodynamic efficiency. In order to improve its aerodynamicefficiency farther, the optimum design for aerodynamic configuration oftandem airship is executed with the response surface methodology. Adoptingthe uniform experimental design method, taking the sweepback tandem airshipas the basic configuration, axis and normal coordinate of back wing as thedesign variable, lift, drag and lift-drag ratio as the objective function,the second-order response surface optimization model of aerodynamicparameter has been constructed via CFD and response surface approximationtheory. With the presented method, the optimization design is applied tolift-drag characteristic of tandem airship. The results indicate that theresponse surface methodology is effective, feasible and applicable foraerodynamic optimum design.
2011, 43(6): 1068-1076. doi: 10.6052/0459-1879-2011-6-lxxb2011-053
Osculating curved cone(occ) waverider: design methods and performance analysis
Xuzhao He Hongli Ni
The osculating curved cone (OCC) waverider design methodsare put forward in the present paper. The flow field structure andaerodynamic characteristics of OCC waverider are also analysed. The OCCwaverider uses curved cone as basic osculating flow field in which hasstraight shock wave and isentropic compression wave structures. Theosculating axisymmetric and streamline tracing techniques are used togenerate the OCC waverider when defining the inlet capture curve (ICC) andfront capture tube (FCT). Computational Fluid Dynamic (CFD) methods are usedto simulate the designed OCC waverider. Theoretical design results agreewell with numerical simulating results. The comparisons are also madebetween osculating cone (OC) waverider and OCC waverider. It is show thatOCC waverider overcomes the disadvantages of low compression abilities andsmall volumetric capabilities which OC waverider has.
2011, 43(6): 1077-1082. doi: 10.6052/0459-1879-2011-6-lxxb2010-502
Subgrid scale stabilized finite element for solution of incompressible viscous flows
Shuangbing Liu Haihu Liu
Started with the concept and fundamental of Subgrid Scalestabilized (SGS) method, an improved SSS finite element formulation isproposed to obtain time independent solutions by solving the unsteadyincompressible Navier-Stokes equations. Based on some rational approximationand simplification, a new stabilization parameter which has relation withthe selective time step size is deduced. As a result, the numericalinstability resulting from high Reynolds and/or small time step size iseliminated. Combined with standard k-\varepsilon turbulence model andwall function method to estimate turbulent viscosity, the improved SGS method is applied to solve incompressible turbulent flows. Thefinite element implementation of wall function along with solution ofturbulence transport equations is discussed in detail and the positivitypreserving limiter for turbulence variables is introduced. A segregatedalgorithm for time stepping to solve incompressible turbulent flows isdeveloped. The numerical examples of laminar and turbulent flows over abackward facing step are presented in order to show the possibility,stability and high accuracy of the proposed approach for simulating steadyincompressible viscous flows.
2011, 43(6): 1083-1090. doi: 10.6052/0459-1879-2011-6-lxxb2010-268
Theoretical analysis on dispersion coefficient in wave field
Liangduo Shen Zhili Zou
Transportation and diffusion caused by coastal waves hadthe different characteristics due to the flow conditions. Through solvingthe vertical diffusion equations by analytic methods, this paper inferred atheoretical formula for the dispersion coefficient under the combined actionof the wave and the tidal current. It divided the general dispersioncoefficient into six sections, which included coefficients caused by tidalcurrent, Stokes drift, wave oscillation and interaction among them.Meanwhile, it drew a conclusion that the contribution of dispersion effectcaused by coastal waves was mainly produced by Stokes drift, while thecontributions on time-averaged dispersion coefficient by the motion of waterpoints and the wave-current interaction were much smaller. Furthermore, theresults without the tidal current were in agreement with those of numericalsimulation and experiments, which proved the correctness of theoreticalderivation. This paper introduced the variation characteristics that thetime-averaged dispersion coefficient and the amplitude of dispersioncoefficient changed with the variation of wave period and wave height.Meanwhile, we applied the results to vertical circulation and obtained thecharacteristics of dispersion coefficient compared to stokes drift.
2011, 43(6): 1091-1102. doi: 10.6052/0459-1879-2011-6-lxxb2010-444
Thermodynamic analysis of the tropical cyclone
Jianfeng Li Junfu Lv Guofu Yao
Thermal dynamic model of the tropical cyclone wassuggested in the paper. With the model, the thermal dynamic characteristicsof the tropical cyclone were analyzed. It is found that the energy totropical cyclone was provided by the steams condense. The steam condensingcauses the forming of circle, which outputs the power of the tropicalcyclone. This circle efficiency reaches the maximum peak with itstemperature increase within a certain height range. If the bottomtemperature is constant, the circle efficiency increases to be the maximumand then falls down with the increase of the height when the saturationtemperature is lower. However, when the saturation temperature is higher,the circle efficiency increases constantly with the increase of the height.When the ambient temperature at the sea surface in the range of 33~34oC, the efficiency achieves the maximum of about 7.4%. While theoutput power of the typhoon increases at all times with the temperatureincreasing. This indicates that the frequency and strength of the typhoonwill accelerate with the ambient temperature.
2011, 43(6): 1103-1109. doi: 10.6052/0459-1879-2011-6-lxxb2010-225
Effects of growth on the deformation and the stability of hyper-elastic spherical shells
Jiusheng Ren Xuegang Yuan Changjun Cheng
A mechanical model for the large deformation analysisof an incompressible hyper-elastic spherical shell subjected to theinner pressure is established within the framework of the finite elasticitytheory of continuum mechanics. The effect of growth on the deformation andthe stability of the shell are examined with the elastic model forvolumetric growth based on multiplicative decomposition of the deformationgradient. The deformation curves and the distribution of stresses, theresidual strain and the distribution of residual stresses due to growth aregiven by numerical computation of the relation between the deformation andthe inner pressure. It is shown that the effect of growth on the deformationof the shell is obvious. The critical thickness and the critical pressurefor the shell to take an unstable deformation are affected by growth, andthe stability of the shell may be changed by growth in some cases. Residualdeformation and residual stresses can be developed in the shell by growth,and the distribution of stresses also affected by growth. Furthermore,unstable deformation may be rendered only by the residual stress induced bya sufficiently large growth even in the absence of the external loading.
2011, 43(6): 1110-1116. doi: 10.6052/0459-1879-2011-6-lxxb2011-066
Constitutive model of niti single crystal with laminated microstructure
Yiguo Zhu Dan Zhao
A stress-induced constitutive model of laminated NiTisingle crystal was constructed. Based on the laminated microstructure ofmartensite twins and the difference of the elastic anisotropic propertiesbetween austenite and martensite phases, we constructed the model usingthermodynamics with perfect interface condition. We also numericallysimulated the evolution of micro-stress and strain during phasetransformation and the response of stress-strain to the different loadingdirections. The numerical results show that NiTi single crystal hashardening or softening mechanical properties during transformation accordingto the different loading directions.
2011, 43(6): 1117-1124. doi: 10.6052/0459-1879-2011-6-lxxb2010-412
Spallation characteristics of K9 glass with prefabricated defects
Changming Hu Xiang Wang Cangli Liu Lingcang Cai
The kernel issue of spallation is the nucleation anddynamic evolution process of meso-micro damages inside materials. Usinglaser etching method, some initial inter-connected damages wereprefabricated inside K9 glass. Combining with power gun loaded plate testsand multi-point Doppler pin system (DPS) measurements, the free surfacevelocity profiles of the sample were obtained, and the dynamic real-timeevolution of internal damages inside materials was studied. From obtainedfree surface velocity profiles, some experimental phenomena were analyzed,including spallation oscillation time, unspalled signal, spallationstrength, and so on. These results can provide some novel information fordynamic damage evolution process of materials.
2011, 43(6): 1125-1132. doi: 10.6052/0459-1879-2011-6-lxxb2010-629
An efficient adaptive importance samping method for structural reliability analysis
Hongzhe Dai Wei Zhao Wei Wang
This study develops an efficient adaptive importancesampling method based on adaptive Markov chain Monte Carlo and fast Gausstransform technique for reliability analysis. In the proposed method, thesamples on the failure domain are generated by the adaptive Metropolisalgorithm, then the importance sampling density is constructed by means ofadaptive kernel density estimation method, and the fast Gauss transform arefinally adopted to accelerate the computation of the kernel function in theimportance sampling procedure. The adaptive Metropolis algorithm can obtainmore different samples on failure domain with the same computational effortwhen compared with the original Metropolis method. In another word, it caneffectively decrease the number of structural analyses and thereby canimprove the efficiency of the proposed method. The fast Gauss transform canconsiderably decrease the computational complexity of the kernel densityestimation method and avoid mounts of CPU time needed in the importancesampling procedure. Numerical examples illustrate that the proposed methodcan provide accurate and computationally efficient solutions of the problem.
2011, 43(6): 1133-1140. doi: 10.6052/0459-1879-2011-6-lxxb2010-805
Research on static and dynamic mechanical properties of spruce wood by three loading directions
Weizhou Zhong Shuncheng Song Xicheng Huang Zhiming Hao Ruoze Xie Gang Chen
Quasi-static and dynamic compression experiments ofspruce wood along axial, radial and tangential loading directions areimplemented by INSTRON and Hopkinson pressure bar equipments. Averagemoisture content and density of the spruce specimens are 12.72{\%} and413kg/m^{3}. Compression modulus and curves of quasi-static compressionstress versus strain are gained by static compression experiment. And therelation of dynamic stress versus strain is obtained by dynamic compressionexperiments with three strain rates. The experiment results show that thefailure modes of spruce specimens are fiber buckling and wrinkle whenloading direction is along the grain. When loading direction is along radialor tangential across to the grain, the failure modes is wood fiber slippageand delamination. Axial compression modulus is about twenty-one times asthat of radial across to the grain, and about thirty-two times as that oftangential across to the grain. Axial quasi-static compression yieldstrength is about nine times as that of radial and tangential across to thegrain. The radial and tangential quasi-static compression yield strengthsare almost equal. Dynamic compression yield strength of spruce wood issensitive to strain rate. The axial, radial and tangential dynamiccompression yield strengths increase greatly when strain rate is from500 to 1000s^{ - 1}. In addition, theory analytic solution tosingle wood cell failure under different direction compression is carriedout. The obtained expression shows that the mean limit loading is relativeto yield stress, cell structure dimension and wrinkle length for completewrinkle cases.
2011, 43(6): 1141-1150. doi: 10.6052/0459-1879-2011-6-lxxb2010-450
Dynamical analysis of stretching process of helical rod to straight rod under constraint of cylinder
Yanzhu Liu Yun Xue
The deformation of an elastic helical rod under the unilateral constraint of a cylinder is discussed as a simplified model of the stretching process of an extendable space mast in astronautic technique. The deformation of the rod in stretching process is sufficiently large, and the hypothesis of small deformation can not be applied in analysis. The Kirchhoff's dynamical analogy theory is an effective approach in research of super-large deformation of thin elastic rod. Considering the existence of constraint force of the cylinder the Kirchhoff's equations of a rod without distributed force can not be applied directly, and the distributed constraint force should be added. In present paper the nonlinear differential equations of dynamics of an elastic rod constrained by a cylinder are established with the Euler angles as attitude variables of the cross section. Assume that the rod maintains the helical shape with unchanged radius in the stretching process as the result of cylindrical constraint, and only the variation of pitching angle of helix and the twisting of the rod are considered. Analytical solutions of the simplified differential equations can be obtained to describe the dynamical process of stretching motion, and simple formulas of stretching velocity and stretching time are given in analytical form.
2011, 43(6): 1151-1156. doi: 10.6052/0459-1879-2011-6-lxxb2010-820
Additional contact constraint method in impact stage of planar flexible multi-body dynamics
Dongting Wang J.-Z. Hong Tanhui Wu
Based on additional contact constraint method, the formof dynamic equation with and without impact is unified. According to impactdetection, automatic change of topological model is realized. Following theprinciple of no penetration between objects, contact force is calculated.Through the simulation with impact occurred many times, from the view ofaccuracy and efficiency, the additional contact constraint method andLS-DYNA penalty function method are contrasted.
2011, 43(6): 1157-1161. doi: 10.6052/0459-1879-2011-6-lxxb2011-016
Dynamic properties of corrugated-pipe type salim vibration isolator
Xue Gao Qian Chen H
Corrugated-pipe type solid and liquid mixture vibrationisolator (SALiM) is a new type of isolator for vibration isolation of heavyequipment with low frequency. Firstly, this paper establishes the mechanicsmodel of elastic solid elements by introducing plate-shell model. Based ongeometry nonlinearity of corrugated-pipe, the stiffness of the element underouter liquid pressure and inner air pressure can be obtained by theperturbation method. Then the stiffness of isolator is derived and analyzed,and as a result, the stiffness is piecewise nonlinear and determined byparameters of the solid elements and corrugated-pipe container. In addition,the equation of motion of a single degree of freedom system is given, whichconsists of a SALiM vibration isolator and mechanical equipment. Theproperties of the frequency response function of the system are analyzedusing average method which is a classical analytic method for solvingnonlinear differential equations. And it is found that this system withSALiM isolator shows softening stiffness behaviour. The jumping phenomenonclearly occurs under certain condition, and saddle-node bifurcation of theprimary resonance response can adequately illustrate the jumping phenomenon.
2011, 43(6): 1162-1169. doi: 10.6052/0459-1879-2011-6-lxxb2010-724
A new method for calculating seismic response of non-proportionally damped structures
Wei Guo Zhiwu Yu
For seismic response analysis of structures withnon-proportional damping characteristic, the derived and presentedtraditional calculation methods based on proportional damping will no longerbe accurate in theory, and in some cases even produce incorrect results. Inview of such problems, engineering and academia often adopt the directintegration method for exact solution, which would need relatively largecomputation cost, and the forced decoupling method with high efficiency forapproximate solution which would introduce unknown error. Taking intoaccount the equilibrium of accuracy and efficiency, a new method forcalculating non-proportionally damped structure's seismic response ispresented, which is named as multiple-degree-of-freedom modal equationmethod. The derivation also points out that the direct integration methodand forced decoupling method are two special extreme forms which can beobtained from the proposed method, and thereby the integrated theory systemfor non-proportionally damped structure's seismic response calculation isestablished. Finally, numerical study is carried out to verify theavailability of the proposed method in the calculation of seismic responseof non-proportionally damped structures, and it shows that along with thechanging of dimension number of equation and partitioned mode of structurethe efficiency and accuracy of the proposed method also gradually change andcan be adjusted.
2011, 43(6): 1170-1180. doi: 10.6052/0459-1879-2011-6-lxxb2010-756
An efficient algorithm for dynamic response of periodic structures
Qiang Gao Wei-An Yao Feng Wu Hongwu Zhang Jiaohao Lin Wanxie Zhong
In this paper, an efficient algorithm was proposed for computing the dynamic response of periodic structures. Based on precise integration method, by using the symmetry of periodic structures and the physical feature of dynamic structures, the special structure of matrix exponential for periodic structures was given, and then an efficient algorithm for computing matrix exponential and the dynamic response of periodic structures was proposed. The algorithm is confirmed to be efficient and memory-saving.
2011, 43(6): 1181-1185. doi: 10.6052/0459-1879-2011-6-lxxb2010-783
Symmetrization and applications of tangent stiffness matrix for UH model
Ting Luo Zhenhua Qin Yang-Ping Yao Xing Feng
Several common three-dimensional generalized methods for constitutive models and the superiority of the transformed stress (TS) method are analyzed in this paper. The non-associated flow of constitutive model based on the TS method is analyzed in detail. The symmetrization method of tangential stiffness matrix for the constitutive models is proposed. The essence of the constitutive models with non-associated flow of tangential stiffness matrix is the same as original one using the symmetrization method. The finite element analysis to some triaxial extension tests is carried out. Based on the analysis and the comparison, it is found that the symmetrization method of tangential stiffness matrix can improve the convergence of finite element analysis and reduce simulation time obviously.
2011, 43(6): 1186-1190. doi: 10.6052/0459-1879-2011-6-lxxb2010-538
Bifurcation research for piecewise linear system involved in discontinuous damping force
Chuanbo Ren Jilei Zhou
Based on some truck suspension model consisting of primary and subsidiary spring, a two-degree-of-freedom system with piecewise-Based on truck suspension model consisting of primary andsubsidiary springs, a two-degree-of-freedom system with piecewise-linearityinvolved in discontinuous damping force is established The stroboscopicPoincaré map is established, and the saltation matrix is deduced byzero-time discontinuity mapping method at the interface. The resultindicates that the saltation matrix is independent on spring rate, but isnot independent on damping force. The Neimark-Sacker bifurcation point isinvestigated by the numerical calculation. The research on bifurcation andchaos can contribute to optimizing design in impacting systems.
2011, 43(6): 1191-1195. doi: 10.6052/0459-1879-2011-6-lxxb2011-091
2011, 43(6): 1196-1204. doi: 10.6052/0459-1879-2011-6-lxxb2011-363