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2007 Vol. 23, No. 6

Display Method:
Measurement and analysis of turbulent mean kinetic energy dissipation rate in the atmospheric surface layer
Xiaoqing Wu, Qun Nie, Qiang Fang
The triaxial sonic anemometer velocity and temperature flucturations were measured in the Hefei zone. Third order and second order structure functions and similarity theory were used to estimated the mean kinetic energy dissipation rate, which results were almost same. Correlation analysis with stability parameter show that maximum kinetic energy dissipation occurs at neutral condition and its value decreases with $| z/L| $. Because Kolmogorov microscale $\eta $ is inverse dependence on $\varepsilon ^{1 / 4}$, which changing tendency with stability parameter is just reversely. Minimum $C_n^2 $ occurs at neutral condition as well and increases wih $| z/L |$, however it increases more quick in unstable conditions. Thermal turbulence inner scale can not been calculated by kinetic energy dissipation rate $\varepsilon $, it may be decided by $\varepsilon _\theta $ which connected with temperature gradient.
2007, 23(6): 721-726. doi: 10.6052/0459-1879-2007-6-2006-605
Theory of the dynamics process of the conical bubble sonoluminescence
Shoujie He, Jing Ha, Xuechen Li, Qing Li, Long Wang
The dynamics process of the conical bubble sonoluminescence hasbeen discussed based on the adiabatic process. The equations of velocity ofbubble collapse, the pressure and temperature within the bubble have beenachieved. Result show the velocity of collapsing bubble approximatelylinearly increases with the decrease of the radius of collapsing bubblefirstly, then the maximal velocity of collapsing bubble can be achieved,subsequently the velocity of collapsing bubble quickly decreases. Based onthe supposition of initial pressure equal to 1\,000\,Pa, the maximal value ofthe velocity of bubble collapse reaches 5.8\,m/s, the minimum radius of thebubble is 1.37\,cm, then the huge pressure of $4.5\times 10^5$\,Pa, thecollapsing temperature above 37\,000\,K, and the maximal energy about 0.02\,Jproviding to the bubble can be achieved. The equations obtained in thispaper could explain the phenomena of experiment. Finally, results show thatthe initial pressure within the bubble has important effects on the finalextreme conditions.
2007, 23(6): 727-731. doi: 10.6052/0459-1879-2007-6-2007-131
Numerical simulation of nonlinear wave propagation on non-uniform current
Yaling Wang, Hongsheng Zhang
A numerical model is developed with a new type ofBoussinesq equations with explicit consideration of currents employed as thegoverning equations. In the present numerical model, the seven-pointfinite-difference scheme is used to discretize the spatial derivatives, thefifth-order Runge-Kutta-England scheme is employed to perform the timeintegrations, and the appropriate outflow boundary condition is adopted.Numerical modeling of wave propagation is performed with uniform currentsand depth, and submerged bars with weak or strong currents in a wave flume.The calculation results show that the numerical model can effectivelyreflect the effects of currents on waves.
2007, 23(6): 732-740. doi: 10.6052/0459-1879-2007-6-2006-410
Numerical study of the interface instability experimental
Jinsong Bai, Ping Li, Duowang Tan, Yang Jiang
A multi-fluid parabolic piecewise method (MFPPM) is developed to simulation of the interface instabilities in this paper. To verification and validation our code MFPPM, one experiment model from Lawrence Livermore National Laboratory (LLNL) is simulated by MFPPM, the numerical results of the gelatin-ring excellent agreement with that experiment and simulation by CALE. At the same time, the two experiment models from our Laboratory for Shock Wave and Detonation Physics are given, in which the outer and the inner surfaces of the gelatin-ring are set by mode numbers 10, amplitude 1mm in top-top and top-bottom initially. Shape, position and acceleration of the outer and the inner surfaces of the gelatin-ring simulation results are presented, and the basic physics phenomena and numerical images are excellent consistent each other.
2007, 23(6): 741-748. doi: 10.6052/0459-1879-2007-6-2006-073
Pressure stabilized fractional step algorithm for incompressible N-S Equations and coupled finite element and meshfree discretization
Qinglin Duan, Xikui Li
In virtue of an additional variable in the framework ofthe Finite Increment Calculus(FIC) theory, a pressure stabilized fractionalstep algorithm is developed in this paper with enhanced pressure stabilityin comparison with the classic one. In addition, the calculation of the highorder spatial derivatives which exists in the standard FIC procedure is alsoavoided. To ensure superior overall performance of the proposed numericalscheme in accuracy, efficiency and robustness, a coupled finite element andmeshfree method is developed for the spatial discretization andinterpolation approximation, in which the meshfree approximation is adoptedin the region where the mesh is distorted to preserve the accuracy androbustness of numerical solutions from the deterioration of the meshquality, while the finite element approximation is employed in the regionwhere the quality of the mesh is acceptable and on the boundaries whereessential boundary conditions of flow problems are imposed to ensure highcomputational efficiency and proper imposition of the essential boundaryconditions. Numerical results for the lid-driven cavity flow problemdemonstrate the better pressure stability of the proposed pressurestabilized fractional step algorithm than that of the classic one, and itscapability in removing the spurious oscillations in the resulting pressurefield induced by the incompatible interpolation approximations for thevelocity and pressure fields violating the LBB condition. The two exampleproblems, i.e. the plane Poisseuille flow and the injection molding problemsare illustrated to prominently demonstrate the superiority of the proposedcoupled finite element and meshfree method over the independent finiteelement and meshfree methods in the overall performance.
2007, 23(6): 749-759. doi: 10.6052/0459-1879-2007-6-2006-351
Mode III crack in two bonded functionally graded magneto-electro-elastic materials
Xing Li, Lifang Guo
In this paper, the mode III crack intwo bonded half infinite functionally gradedmagneto-electro-elastic materials is investigated. It is assumed thatthe elastic stiffness, piezoelectric constant, and dielectricpermittivity of the magneto-electro-elastic material vary continuously alongthe thickness of the strip. The crack is assumed to be eithermagneto-electrically impermeable or permeable. Integral transformsand dislocation density functions are employed to reduce theproblem to Cauchy singular integral equations which can be solvednumerically by Gauss-Chebyshev method. Numerical results are obtainedto illustrate the variations of the stress intensity factors (SIFs)with the parameters such as material nonhomogeneityfactor, crack sizes, loading conditions, which are shown graphically.
2007, 23(6): 760-766. doi: 10.6052/0459-1879-2007-6-2006-649
Experimental and constitutive model study of Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-0.32PbTiO$_{3}$ relaxor ferroelectric single crystal poled along <001>crystallographic direction
Qiang Wan, Changqing Chen, Yapeng Shen
The stress and strain properties of $\langle 001 \rangle$ oriented PMN-0.32PTrelaxor ferroelectric single crystals have been investigated. Obtainedresults show that the stress and strain behavior along $\langle 001 \rangle$crystallographic direction is different from that of the ferroelectricpolycrystal. Polarization rotation models are developed to explain theobserved behaviors of PMN-0.32PT. Based on the experimental phasetransformation mechanism of ferroelectric single crystal, a constitutivemodel of ferroelectric single crystal is proposed based micromechanicalmethod. In the model, the phase transformation systems on 8 possible slidingplanes are characterized by a viscoplastic law. The behavior offerroelectric single crystal is then derived from phenomenalcrystallographic theory through the transformation strain on sliding planes.The developed model has been applied to simulate the experimentalstress-strain curve of $\langle 001 \rangle$ oriented PMN-0.32PT. It is shown that thedeveloped model can faithfully capture the key characteristic of theobserved constitutive behavior of $\langle 001 \rangle$ oriented PMN-0.32PT.
2007, 23(6): 767-773. doi: 10.6052/0459-1879-2007-6-2006-538
A regularized solution for the inverse two-order transient heat conduction problems with multi-variables
Qiwen Xue, Haitian Yang
In the present work, Tikhonov's regularization approachhas been used to solve inverse two-order transient heat conduction problemswith multi-variables, using Bregman distances and weighted Bregman distancesin the construction of regularization terms for the Tikhonov's function. Theinverse problem is formulated implicitly as an optimization problem with thecost functional of squared residues between calculated and measuredquantities.The eight-point finite element is used for the discretization inthe space system and a time stepping scheme is used for transient analysis.A finite element model is given, facilitating to sensitivity analysis fordirect and inverse problems, and taking account of inhomogeneity andparameters distribution. Combined identifications can be carried out forthermal parameters and boundary conditions etc. Satisfactory numericalvalidation is given including a preliminary investigation of effect of noisedata on the results and the computational efficiency for differentregularization terms. Results show that the proposed method can identifysingle and combined thermal parameters and boundary conditions for two-ordertransient heat conduction problems with precision.
2007, 23(6): 774-780. doi: 10.6052/0459-1879-2007-6-2007-062
Equivalent static wind loads on long-span roof structures with modal response correlations
Jiyang Fu, Zhuangning Xie, Qiusheng Li, Jiurong Wu, An Xu
This paper presents a new description of the equivalentstatic wind loads (ESWLs) on long-span roof structures based on theload-response-correlation approach. The ESWL for a given peak displacementresponse is expressed in terms of the mean and dynamic components. It isnoteworthy that in the proposed approach, the total dynamic response isdirectly calculated by the complete quadratic combination approach, which isnot separated into the background and resonant responses any longer; and thecontributions of multimode response and modal response correlations aretaken into consideration. Finally, an extra-long-span roof structure whichis the world's longest spatial lattice structure is considered to illustratethe determination of the ESWLs and to demonstrate its effectiveness in thedesign and analysis of long-span roof structures.
2007, 23(6): 781-787. doi: 10.6052/0459-1879-2007-6-2007-180
Integrated topology optimization and scale effect analysis of cyclic symmetry sandwich structures
Shiping Sun, Weihong Zhang, Kepeng Qiu, Zhongze Guo, Bassir Hicham
A scale-related optimization method is proposed for thetopology design of cyclic symmetry structures. Within the scope ofmaximizing the structural rigidity, influences of the scale and topology ofrepresentative volume element (RVE) as well as different loading cases uponthe optimal configurations are studied. A dimensionless structure topologyfactor is proposed in this paper to quantify the optimized structureefficiency. By means of solid isotropic material with penalization (SIMP)model and perimeter control method, macro material layout and RVE areoptimized. A contrast topology configuration is obtained withoutcheckerboard. The results demonstrate that the scale-related topologyoptimization method is valid for optimal design of cyclic symmetry structureand that the scale effect of RVE can be well revealed in the optimalconfiguration of the structure.
2007, 23(6): 788-795. doi: 10.6052/0459-1879-2007-6-2006-518
A level set method for structural topology optimization based on topology random mutations
Jianhua Rong, Qingquan Liang, Duansheng Yang
The level set method was firstly introduced into the structuraltopology optimization by Sethian et al. Wang et al. studied structuraltopology optimization by incorporating the shape derivative or sensitivityanalysis with the level set model. In essence, the method employs theimplicit moving material interface models or the level set vector torepresent complex interfaces, and the movement of the material interfaces isgoverned by a Hamilton--Jacobi type partial differential equation, whoserobust numerical algorithm can handle topology merging or breaking naturallyduring the topology optimization process. In order to consider limitedmaximum design domain etc. practical requirements, Rong proposed an improvedlevel set method for topology optimization of continuum structures. However,the level set based topology optimization method is unable to nucleate holeswithin the structural material, which is far from the structural boundaries.In order to overcome the difficulty generating new material holes, thematerial topological derivative analysis was incorporated into the level setmethod.The level set method based on topological derivatives employs topologicalderivative information and the structural volume reduction quantity toidentify hole nucleation sites. And the initial structure must be set to themaximum design domain structure for this method. Moreover, it is not fit tosolving the topology optimization problem with an equality volumeconstraint. In order to solve this problem and overcome the difficulty ofthat the level set based topology optimization method is unable to nucleateholes within the structural material, this paper proposes a new level setmethod for structural topology optimization based on random topologymutations. At first, this paper introduces a new optimization scheme withtopology mutations in the optimization iteration process in a smallpossibility random way. Second, a mutation operator is given and theproposed algorithm convergence is discussed. Finally, a new topologyoptimization method, which incorporates topology mutations into the levelset method for structural topology optimization with maximum design domainlimits, is proposed. The algorithm of the objective function of the problembeing the strain energy with a material volume constraint is implemented.The benefit and advantages of the proposed method are illustrated withexamples.
2007, 23(6): 796-803. doi: 10.6052/0459-1879-2007-6-2007-191
Analytic study on 1:1:1 internal resonance nonlinear dynamics of a liquid-filled spacecraft with elastic appendages
Jing Lu, Junfeng Li, Tianshu Wang, Baozeng Yue
The coupling dynamics of the pitching of spacecraft, thesloshing of liquid fuel and the vibration of elastic appendages areinvestigated. The coupling dynamics equations deduced by using H-O principleare adopted. The attitude of spacecraft is controlled. The multiple scalemethod is proposed to analyze the 1:1:1 internal resonance of therigid-liquid-elastic coupling system. The effect mechanism of the couplingdynamics are obtained by the analytic study. The amplitude-frequencyresponse switches between soft and hard spring type with liquid depth. Theresonances of the spacecraft and elastic appendages occur at both of thenatural frequencies of spacecraft and elastic appendages.
2007, 23(6): 804-812. doi: 10.6052/0459-1879-2007-6-2006-497
Stability of stationary motion for a rigid body with a flexible beam
Xiaoyan Ma, Yao Cheng
Stability of stationary motion for a rigid Body with a flexible beam wasinvestigated, and both of translation and attitude motion were underconsideration. Quasi-coordinates play an important role in electing statevariables. The Lyapunov functional was constructed by the first integrals ofthe dynamical equations. The state variables introduced in this papersimplify the Lyapunov functional, and make stability analyse easy. As aresult, the sufficient conditions for the normal stability of two classes ofstationary motion were given.
2007, 23(6): 813-821. doi: 10.6052/0459-1879-2007-6-2006-322
Analysis of interlaminar stress in composite laminated beam-plate with interfacial damage
Yiming Fu, Sheng Li
Based on the general six-degrees-of-freedom plate theoryand the accurate stress analysis, using the variational principle and theequivalent strain theory in damage mechanics, the three-dimensionalnon-linear equilibrium differential equations for the interlaminarstresses of laminated plates with the damage effect of the intra-layers andthe interlaminar interface are derived in the framework of the theory ofelasticity. With a simply supported laminated beam-plate withdamage as an example, an analytical solution is presented by using finite differencemethod to obtain the interlaminar stresses.
2007, 23(6): 822-828. doi: 10.6052/0459-1879-2007-6-2006-592
Simulation of compressive failure of hybrid plain woven fabric laminate with a hole
Xiaoquan Cheng, Jian Zou, Yanmin Xu, Jikui Zhang, Songnian Li
An damage developing finite element model of hybrid plainwoven composite laminates was established by secondary development on ANSYSsoftware with ANSYS parameter design language. The simulation of compressivebehavior of hybrid plain woven composites laminates with a hole was carriedon. It can be found from the results that this model can be used to simulatethe whole damage and failure course of hybrid plain woven compositeslaminates with a hole and to predict laminate damage styles, damagedevelopment and compressive strength accurately. Meanwhile, damage criteriaand stiffness attenuation rules fit for this type of laminates were putforward and proved. The results by this model are visual and intuitionistic,so this model is fit for engineering application.
2007, 23(6): 829-834. doi: 10.6052/0459-1879-2007-6-2007-043
Geometrical nonlinear analysis of truss structures with random parameters utilizing recursive stochastic finite element method
Bin Huang, Jianchen Suo, Wenjun Huang
Geometrical nonlinear analysis of truss structures withrandom parameters is carried out using a new stochastic finite elementmethod that is called as recursive stochastic finite element method in thispaper. Combining nonorthogonal polynomial expansion and perturbationtechnique, RSFEM has been successfully used to solve static linear elasticproblems, eigenvalue problems and elastic buckling problems. Although suchmethod is similar in form to traditional the second order perturbationstochastic finite element method, it can deal with mechanical problemsinvolving random variables of relatively large fluctuation levels. Differentfrom spectral stochastic finite element method utilized widely thattransforms the random different equation into a large deterministic equationthrough projecting the unkown random variables into a set of orthogonalpolynomial bases, the new method is more suitable for solving largedimensional random mechanical problem because of recursive solution method.The structural response can be explicitly expressed by using somemathematical operators defined to transform the random different equationinto a series of same dimensional deterministic equations. And moreimportant point is that the above advantages of this presented method makeit more helpful for solving static nonlinear problem than SSFEM. In thepresent paper, the stochastic equilibrium equation of geometrical nonlinearanalysis of random truss structures under static load is firstly set up.Apart from that the random loads and the random area parameters are expandedusing the first order Taylor series, both of the modulus and structuralresponses are expressed using nonorthogonal polynomial expansions. Then aset of deterministic recursive equations is obtained utilizing perturbationmethod. Transposition technique is given for solving the equationscontaining unknown coefficients according to operation rule of matrix andcharacteristics of truss structures. After the unknown coefficients aregotten, the second statistic moment can be easily obtained according torelationship matrix between orthogonal and nonorthogonal polynomialexpansions. In examples, the geometrical nonlinear analysis of a two barstructure and a plane truss arch are investigated. The numerical resultsshow that compared with traditional perturbation stochastic FEM based on thesecond Taylor series, the results obtained using the new method are moreclose to that of Monte-Carlo simulation when fluctuation of random variablesbecomes large. The interesting thing is that in the static geometricalnonlinear problem, when the second order perturbation stochastic finiteelement method is utilized, the divergence trend of the structural responsealso appears along with the increase of standard deviation of random crosssectional areas. However, this phenomenon disappears when the fourth orderRSFEM is used to solve this problem. In the end, some significantconclusions are obtained.
2007, 23(6): 835-842. doi: 10.6052/0459-1879-2007-6-2007-165
The meshless method for a two-dimensional inverse heat conduction problem with a source parameter
Rongjun Cheng, Yumin Cheng
Inverse problems are difficult to be solved in scientific research. And theyare widely applied in the aerospace, nuclear physics, metallurgyand other fields. The finite difference method and the finite element methodare main numerical methods to obtain numerical solutions of inverseproblems. The finite point method is one of meshless methods. Comparing withthe numerical methods based on mesh, such as finite element method andboundary element method, the finite point method only needs the scatterednodes instead of meshing the domain of the problem when the shape functionare formed. For problems with complicated domain which need to be re-meshed,the finite point method has the advantage of that no mesh is needed. In thispaper, the finite point method is used to obtain numerical solutions oftwo-dimensional inverse heat conduction problems with a source parameter,and the corresponding discretized equations are obtained. The collocationmethod is used to discretize the governing partial differential equations,and boundary conditions can be directly enforced without numericalintegration in the problem domain. This reduces the computation costgreatly. A numerical example is presented to show the method in this paperis effective. The finite point method, which is for two-dimensional inverseheat conduction problems with a source parameter, presented in this paperhas some advantages of arbitrary nodes distribution, simple numericalprocedures and low computation cost. The researches in this paper provide anew numerical method for inverse heat conduct problems, and can be appliedto other inverse problems.
2007, 23(6): 843-847. doi: 10.6052/0459-1879-2007-6-2007-074
The theoretical exploration of frost heave for saturated granular soil--numerical simulation of 1-D ice segregating model based on equilibrium of force and phase
Hongzhang Cao, Shi Liu, Fan Jiang, Jing Liu
Based on the theory in the rigid ice model, a new 1-D numerical icesegregating model is developed for freezing process in saturated, granularsoil. In this model according as O'Nell {\&} Miller' proposition, liquidwater is attracted toward the soil grain's surface and the attractive forceis greater for liquid than for air or ice. The strength of this attractiondecays with distance from the surface. A grain immersed in water issurrounded by a ``hydrostatic pressure field'' caused by this attraction.The water in the effective range of the ``hydrostatic pressure field''called adsorbed film. The water pressure in adsorbed film is equal to thepressure caused by surface adsorption plus the porous water pressure outsidethe film. In unfrozen soil, grains contact to each other through theadsorbed film. The pressure at the middle line of the adsorbed water film isequal to the contact stress between grains. In the saturated soil freezingprocess, the porous water outside the adsorbed film first freeze, then theice-water interface gradually enter into the film with the temperature drop.The adsorbed film between grains will be frozen while the temperature isless than the phase changing temperature corresponding to the grains contactstress. According to the states of porous water and the water film betweengrains, the freezing soil could be divided into frozen section, phasechanging section that called frozen fringe and unfrozen section. The watertransferring is ignored in frozen section and the phase-exchange not occursin unfrozen section. The ice segregating process could be considered as aquasi-steady process because that the temperature change slowly, then theassumption that phase and force are local equilibrium could be introduced.The governing equations are deduced from conservation of mass and energy andthe relation of porosity and effective stress is considered as approximatelinear. The relation of $( \partial I /\partialu_w )_T $ and $ ( \partial I / \partial T )_{u_w } $ is deduced based onClapeyron equation then $ ( \partial I / \partial T )_{u_w } $ could takeplace of $ ( \partial I / \partial T )_{u_w} $ in numerical simulation. Therelation of temperature $T$ and the porouswater pressure $u_w $ in the express $I(T,u_w )$ is deducedby similar method. When the water film between soil granules begins tofreeze to separate soil skeleton, ice segregating process initiated. Thatmeans the criterion of new segregated ice initiation is that the maximumwater pressure at ice-water interface in the frozen fringe become equal orgreater than the total load. In the ice segregating process, the porouswater pressure at the warm side of the warmest segregated ice drop with thetemperature lower. Thus cause that the moisture in the frozen fringe andunfrozen section transfer to the warm side of the segregated ice.1-D freezing process was simulated with similar condition to theexperiment (Xu et al., 1995). The calculated result showed the ice layers. Thetrend of heave change and the distribution of ice layers are similar to theexperiment phenomena.
2007, 23(6): 848-857. doi: 10.6052/0459-1879-2007-6-2006-430