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2008 Vol. 40, No. 2

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Gust response prediction with CFD-based reduced order modeling
Guowei Yang, Jikang Wang
raditional gust responses are mainly analyzed based on linearaerodynamic load calculations in frequency-domain, which is unsuitable forand the viscous and transonic flows. Since gust response for aircraft designneeds to be calculated for the many gust cases with various frequencies andshapes, direct CFD-based gust response predictions are huge time-consuming.In the paper, a new gust response method is developed based on CFD methodcoupled with ARMA reduced order model. CFD is only used once for a specialgust to identify coefficients of ARMA model. The computational efficiency ofgust response analysis for any shaped gust can be improved significantlybased on the determined ARMA model compared with the direct CFD method. Tovalidate the new developed method, first, for NACA0012 airfoil at Machnumber of 0.11, the gust responses are analyzed through the comparisons ofthe results of CFD, ARMA model and an early incompressible analyticresolution. Then, the method is also testified to be valid for transonicflows.
2008, 40(2): 145-153. doi: 10.6052/0459-1879-2008-2-2007-230
Numerical investigation on the collision between detonations and shocks
Guilai Han, Zonglin Jiang, Deliang Zhang
Collisions between detonations and shock waves of differentstrength have been numerically simulated by using NND scheme implementedwith the improved two-step chemical reaction model. The collision effects onthe detonation transition zone were investigated. In the case of detonationinteracting with weaker shock waves, the detonation transition is dominated byflow expansion which lowers the post-shock thermo-states and reduces thechemical reaction rate. The detonation transition can be divided into threestages, named as the collision effect zone, the detonation growth zone andthe steady detonation development zone respectively, which indicates somecharacteristics of detonation-decoupling and reigniting. When detonationinteracts with a stronger shock waves, the thermal properties of the explosivemixture are so high that the induced chemical reactions become more activeand the flow expansion is compensated. The transition appears to be a directtransformation from a weak detonation to a quasi-steady CJ detonation.
2008, 40(2): 154-161. doi: 10.6052/0459-1879-2008-2-2006-633
A space-marching algorithm for solving the parabolized Navier-Stokes equations
Bing Chen, Xu Xu, Guobiao Cai
A new implicit finite-volume Single-Sweep ParabolizedNavier-Stokes (SSPNS) algorithm is developed. Theoretical analysis isfocused on the mathematic properties about the parabolized Navier-Stokes(PNS) Equations, especially on the treatment of streamwise pressuregradient. Then the original implicit time iterative Lower-Upper SymmetricGauss-Seidel (LU-SGS) method is successfully extended to integrate the PNSEquations in the streamwise direction. The hybrid upwind schemes, includingAdvection Upstream Splitting Method (AUSM) family schemes and Low-DiffusionFlux-Splitting (LDFSS) schemes, are used to compute the crossflow inviscidfluxes, while central schemes for the viscous fluxes. Four typical flows,i.e., supersonic flat plate flow, 15$^\circ$ ramp hypersonic flow,10$^\circ$ coneflows with different angles of attack, and side-compression hypersonic inletflows are calculated with the SSPNS codes. Numerical results agree well withthose obtained from NASA's UPS PNS codes and experimental results by Tracy,Holden, or Holland et al. All the numerical results indicate that SSPNS is ahighly efficient, highly accurate, and also highly robust algorithm forsteady supersonic/hypersonic flows without any large streamwise separation.Comparison to the traditional time-iterative Full Navier-Stokes (FNS) flowsolvers, the SSPNS codes show 1~2 order of magnitude of computationalspeed faster and at least 1 order of magnitude of memory storage saving.
2008, 40(2): 162-170. doi: 10.6052/0459-1879-2008-2-2007-440
The experimental study on unsteady horseshoe vortex structure in juncture flow with PIV
Hua Zhang, Zhiyong Lu, Shengdong Sun
The PIV technique was utilized to study thecharacteristics of laminar unsteady horseshoe vortex in juncture flow. Thevisulization and the PIV show that there are three unsteady modes:amalgamating, shedding off-amalgamating and shedding off-dissipating. At acertain Reynolds number the shedding off vortex can be presented as sheddingoff-amalgamating or shedding off- dissipating, witch depend on the leadingedge shape of modals, for it changes the stretch of the vortices so that itinfluence the dissipation and diffusion of the corner vortex. The PIV showthat secondary vortex forms a growing negative vorticity tongue, which mayeventually penetrate into the boundary layer and effectively isolates theprimary vortex from the impinging B.L., allowing the primary vortex to shedoff. In unsteady oscillation mode, the vortex singular points show rathercomplex structure combination, which indicate the alternating stretch andcompression of the vortices.
2008, 40(2): 171-178. doi: 10.6052/0459-1879-2008-2-2007-246
Exact solution of the anti-symmetric plane bimaterial transverse crack
Tianhu Hao
Because of the mathematical difficulty, exact solutions of the transverseinterface crack are rare. In this paper, on the basis of the exact solutionsfor the antiplane and plane symmetric cases, the exact solution of the planeanti-symmetric case has been obtained. On the two topics of the crack, theexact solutions of the SIF have also been obtained. These results areinteresting to the scientists and engineers who are working in the area ofinterface cracks. Further study must focus on the obtaining more exactsolutions of the complex elasticity and the influence of the largedeformation.
2008, 40(2): 179-184. doi: 10.6052/0459-1879-2008-2-2007-118
Exact solution of thermoelastic bending for functionally graded truncated conical shells
Jinghua Zhang, Shirong Li, Liansheng Ma
The deformation of functionally graded truncated conicalshell subjected to transverse mechanical load as well as non-uniformlythermal load is studied. Based on classical linear theory of shell, themixed-form equations governing the axi-symmetrical deformation of FGMconical shells are derived, taking transverse shear force and mid-surfaceangle of rotation as basic unknown functions. In the analysis, it is assumedthat the material properties of the shell vary continuously as a powerfunction of the thickness coordinate. And then obtain exact solution of theproblem by using analytic method. For FGM shells with simply supported andfixed boundary conditions, characteristic curves of the deformation versusthe loads and gradient of the material parameters are plotted. Especially,the effects of temperature rise and the parameter of gradient of thematerials variation on the deflection of the FGM conical shell are examinedand discussed.
2008, 40(2): 185-193. doi: 10.6052/0459-1879-2008-2-2007-160
Dynamic response of cellular metallic sandwich plates under impact loading
Guiping Zhao, Tianjian Lu
The steel plate -- cellular metallic core sandwichconstruction is a new type of composite sandwich plate for protectiveapplications. We study in this paper the shock resistance of this sandwichstructure under impact loading by using two different finite element codes:ABAQUS and LS{\_}DYNA. The dynamic response of the all-metallic sandwichhaving three different types of core topology: aluminum foam core, squarehoneycomb core and corrugated core is simulated and analyzed. The effect ofvarying core thickness is also investigated. The four kinds of sandwichplates have the same density per unit area. The focus is placed upon on theenergy absorption capabilities of different sandwich plates having the samedensity per unit area. Results of the study indicate that sandwich platewith 22\,mm aluminum foam core is an excellent sandwich structure withstrongest energy absorption capability and smallest deflection inall-metallic sandwich plates by loading the plates with metal foamprojectiles. Further, it is found that the sandwich plates with latticecores have a higher shock resistance than sandwich plates with metallic foamcores of equal mass under penetration impact of rigid bullet.
2008, 40(2): 194-206. doi: 10.6052/0459-1879-2008-2-2007-129
The evaluation of nearly singular integrals in the boundary integral equations with variable transformation
Yaoming Zhang, Cuilian Sun, Yan Gu
The numerical solution of boundary value problemsusing boundary integral equations demands the accurate computationof the integral of the kernels, which occur as the nearly singularintegrals when the collocation point is close to the element ofintegration but not on the element in boundary element method(BEM). Such integrals are difficult to compute by standardquadrature procedures, since the integrand varies very rapidlywithin the integration interval, more rapidly the closer thecollocation point is to the integration element. Practice showsthat we can even obtain the results of superconvergence for thecomputed point far enough from the boundary; however, usingstandard quadrature procedures, which neglect the pathologicalbehavior of the integrand as the computed point approaches theintegration element, will lead to a degeneracy of accuracy of thesolution, even no accuracy, which is the so-called ``boundarylayer effect''. To avoid the ``boundary layer effect'', the accuratecomputation of the nearly singular boundary integrals would bemore crucial to some of the engineering problems, such as thecrack-like and thin or shell-like structure problems.The importance of the accurate evaluation of nearlysingular integrals is considered to be next to the singularboundary integrals in BEM, and great attentions have beenattracted and many numerical techniques have been proposed for itin recent years. These developed methods can be divided on thewhole into two categories: ``indirct algorithms'' and ``directalgorithms'', which have obtained varying degree of success, butthe problem of the nearly singular integrals has not beencompletely resolved so far. In this paper, a new efficienttransformation is proposed based on a new idea of transformationwith variables. The proposed transformation can remove the nearlysingularity efficiently by smoothing out the rapid variations ofthe integrand of nearly singular integrals, and improve theaccuracy of numerical results of nearly singular integrals greatlywithout increasing the computational effort. Numerical examples ofpotential problem with their satisfactory results in both curvedand straight elements are presented, showing encouragingly thehigh efficiency and stability of the suggested approach, even whenthe internal point is very close to the boundary. The suggestedalgorithm is general and can be applied to other problems in BEM.
2008, 40(2): 207-214. doi: 10.6052/0459-1879-2008-2-2007-123
Numerical inversion of Laplace transfors in viscoelastic problems by Fourier series expansion
Fan Peng, Yaojun Chen, Yifan Liu, Yiming Fu
In this paper, the effective application of numericalinversion of Laplace transforms, based on Fourier series expansionsdeveloped by Dubner, Abate and Durbin, is studied for problems ofviscoelastic mechanics. A crucial free parameter is involved in this sort ofmethod and required to be reasonably valued for particular application inadvance since its improper choice leads to obvious errors. An optimal modelto determine the free parameter is constructed in the paper and itsapplicability is validated by the numerical inversion of two types of simplefunctions. As examples to illustrate the practical implementation ofproposed method, the quasi-static and dynamic analysis, within the scope ofaxisymmetric problem, are performed for viscoelastic laminated circularcylindrical shells under uniformly axial pressure and viscoelastic cylindersubjected to inner pressure with abrupt loading respectively. Numericalexperiments show that the optimal model yields valid free parameter, and theproduction of free parameter and calculation time $t$ lies in a definite range.Also it is concluded that the free parameter can be set to be inverselyproportional to $t$ with the proportional coefficient chosen among an effectiverange or determined directly by the result from optimal model for specificcalculation time, and the range of this proportional coefficient isconsidered to be irrelevant to parameter T.
2008, 40(2): 215-221. doi: 10.6052/0459-1879-2008-2-2007-142
A bending moment beam eigenelement with piecewise shape functions
Yufeng Xing, Yang Yang
The classic eigenelement method is proposed by XING Yufeng and TIAN Jinmei recently. This method can be used to deal with the macroscopic properties such as frequencies and elastic parameters of composites. Compared to conventional homogenization method, the classic eigenelement method calculates the global stiffness of unit cell directly, instead the homogeneous modules. The eigenelement method is more precise than the conventional homogenization method with the same number of elements, and the amount of computational work reduces greatly compared with the ordinary finite element method with a good agreement between them. In order to calculate microscopic properties more precisely, a bending moment beam eigenelement is proposed based on the variational principle, in which the eigen-shape functions are defined in segments, so the discontinuous of materials and geometries is allowed within the beam eigenelement.The bending moment beam eigenelement is derived in details according to the static analysis of the beam cell subjected to a unit bending moment at one end. In order to evaluate the new proposed bending moment beam eigenelement (BBEE), the displacements, stresses and inherent frequencies are computed by using the new beam eigenelement method, ordinary finite element method, the classic eigenelement method and conventional homogenization method respectively. The comparison among the results by different methods, show that the bending moment eigenelement method is more precise than the classic eigenelement method and conventional homogenization method with the same number of elements. The larger the difference of parameters for each subelement in eigenelement is, the larger the advantages of the eigenelement. And the amount of computational work reduces greatly compared to the ordinary finite element method with the same precision.
2008, 40(2): 222-228. doi: 10.6052/0459-1879-2008-2-2007-263
Multi-Objective Game Design of Bionics Based on Mixed-Behavior
Nenggang Xie, Yuwan Cen, Linsong Sun, Lu Wang
Taking the design objectives as different game playersand calculating the factors of design variable to objective function andfuzzy clustering the design variable set is divided into the strategicspace owned by each game player. According to the characteristics of threekinds of lizard's behavior style they are defined as egoism collectivismand opportunism and endowed with each game player. For the bionic researchon lizard's survival of multiply mechanism this paper takes three kinds oflizard's behavior as game player and establishes the mapping relationshipbetween game players' payoff and objective functions. In their own strategicspace each game player takes their payoff as mono-objective foroptimization. It gives the best strategy upon other players. All the beststrategies are combined to be a game strategic set. With convergence andmulti-gaming the final game solution is obtained. Taking tri-objectiveoptimization of Baihetan arch dam shape design as example the results showthat the dam volume decreased by 16.412\times 10^4m3 which is2.38%; and the maximum tensile principal stress decreased by 0.036MPawhich is 0.31%; the strain energy of dam decreased by 0.167GJ which is4.47%; these prove that the method is effective.
2008, 40(2): 229-237. doi: 10.6052/0459-1879-2008-2-2007-183
Energy function of population of neural oscillators in cerebral cortex under coupling condition
Rubin Wang, Zhikang Zhang
This paper explores the intrinsic relationship betweenenergy consumption of a large scale neural population and neural signalprocessing under coupling condition in neural networks in activity of localbrain, and energy functions of variety of the neuronal membrane potentialare obtained for interactive neural population at the sub-threshold and thesupra-threshold states. These energy functions can accurately reproduceexcitatory postsynaptic potentials (EPSP), inhibitory postsynapticpotentials (IPSP), action potential, and action potential given by theneuro-electrophysiological experimental data. Recently, it has been provedthat signal transmission and neuronal energetic demands are tightly coupledto information coding in the cerebral cortex in functional magneticresonance imaging (fMRI) experiments. Therefore, the analytic resultsobtained in this paper show that the principle of energy coding is quitefundamental and is beneficial to the study of the important scientificproblem as how the brain performs coding at the level of local neuralnetworks.
2008, 40(2): 238-249. doi: 10.6052/0459-1879-2008-2-2007-115
Turbulent characteristics of ctab surfactant solution flows in turbulent boundary layers
Shuping Cai, Lin Yang, Chuanlin Tang
In order to clarify the drag-reducing mechanismwith a surfactant solution, the turbulent chara-cteristics of CTABsurfactant solution flow for a zero-pressure gradient boundary layer on flatplates is investigated by using a two dimensional LDV system. The resultsobtained are found as follows compared with the corresponding statistics forwater flow. The viscous sublayer for the surfactant solution is thicker thanthat for water flow. The mean streamwise velocity profile falls betweenthose of laminar and turbulent velocity profiles in Newtonian fluid flow.The peak of the streamwise turbulence intensity is smaller than that forwater, the location where it appears is further away from the wall and thesecond peak appears near the center of the boundary layer. The wall-normalturbulence intensity is greatly suppressed and the Reynolds shear stress isalmost zero throughout the boundary layer, which shows that the surfactantsolution can weaken the correlation between the two components of velocityfluctuation, thus, it can reduce the production of turbulent kinetic energyso that the driven power for transporting fluids can be saved.
2008, 40(2): 250-254. doi: 10.6052/0459-1879-2008-2-2007-321
Efficient method for transient analysis in laminated plates based on reduced-basis method
Yonghui Huang, Xu Han, Chengxin Ran
n this paper, the combination of hybrid numerical method(HNM) and reduced-basis method (RBM) is suggested to more effectivelyanalyze the transient displacement response in composite laminated plates.The large eigenvalue problem in wavenumber domain is projected onto areduced basis space constructed by the truncated eigenvectors from thesample set. The numerical examples demonstrate the efficiency and accuracyof the presented method, which also can be extended to effectively solveother structural dynamic problems.
2008, 40(2): 255-260. doi: 10.6052/0459-1879-2008-2-2007-076
Analyzing liquid nonlinear sloshing in circular cylindrical tank by multidimensional modal theory
Yansheng Yu, Xingrui Ma, Benli Wang
The multidimensional modal theory is applied to solveliquid nonlinear sloshing in right circular cylindrical tank intranslatory motion. The general infinite dimensional modal system describingliquid nonlinear sloshing is derived first by pressure integral variationalprinciple. After selecting two dominating modes and three secondarymodes based on the Narimanov-Moiseev third order asymptotichypothesis, the infinite dimensional modal system is reduced to afive dimensional asymptotic modal system. The numericalintegrations of this modal system reveal some typical nonlinearcharacteristics, such as the amplitude difference between wave peak and wavetrough and the dispersion effect.
2008, 40(2): 261-266. doi: 10.6052/0459-1879-2008-2-2007-190
Mesh update algorithm in ale finite method within free surface flow
Hong Zhou, Junfeng Li, Tianshu Wang
The arbitrary Lagrange-Euler method affords tracking themotion of free interface in liquid slosh problems through defining the nodalvelocities of reference frame. Based on reviewing the three elementaryalgorithms applied in mesh updating, the method that computational nodes canmove more than one direction is used in special numerical example. Thisachievement demonstrates that the ALE method is available for more complexgeometrical boundaries. The nodal velocities and mesh configurations duringthe sloshing in horizontal cylinder are illustrated at the section ofnuemerical example.
2008, 40(2): 267-272. doi: 10.6052/0459-1879-2008-2-2007-064
Parametric vibration of a rotating er sandwich beam with periodically varying velocity
Kexiang Wei, Guang Meng
The dynamic stability of a rotating electrorheological(ER) sandwich beam with periodically varying velocity is studied by usingthe method of multiple scales. Assuming the angular velocity of the beam isgiven as a harmonic function of time, the rotating sandwich beam is regardedas a parametrically excited system. The effects of structure parameters andworking condition on the instability boundaries in parametric resonance ofthe rotating beam are investigated. Numerical results show that thevibration characteristic and dynamic stability of the rotating ER sandwichbeam can be adjusted when it subjected to an electric field, and the ERmaterial layer can be used to improve the dynamic stability of the rotatingflexible beams.
2008, 40(2): 273-280. doi: 10.6052/0459-1879-2008-2-2007-252
Recursive solution on layer after layer for sensitivity analysis of modes on defective linear vibration system
Tai Xu, Lan Yu, Wei Ju, Yongli Wang, Fei Cheng, Wenfeng Chen
Generalized modes method of defective systems foreigenvector sensitivity analysis is presented. It is proposed to establish afeature space about generalized modes by using the theory of generalizedmodes for sensitivity analysis in linear vibration defective systems whichdoes not possess a complete set of eigenvectors in N-space. Simultaneously abrief and rapid algorithm is introduced to calculate the coefficients of thepower series expression of generalized modes by gradual and recursivesolution. A numerical example is provided to illustrate the accuracy andefficiency of the algorithms.
2008, 40(2): 281-289. doi: 10.6052/0459-1879-2008-2-2006-234