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2005 Vol. 37, No. 3

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Unsteady flow mechanisms revisited in insect flapping flight
The unsteady flow mechanisms of insect flapping flight arerevisited with the theoretical modeling approach proposed. Accordingto analysis of the flapping motion in insect hovering flight, it is revealedthat, limitations of the aerodynamic lift at low Reynolds numbers may bereleased by the highly unsteady condition in insect wing flapping, in whichcase the controlling parameter is the Strouhal number (St \gg 1/Re).Furthermore,in the present theoretical modeling study, three factors have been found inlift generation and regulation: (1) the remarkable instantaneous addedinertial effect is excited by the high unsteadiness of wing flapping; (2)keeping the leading edge vortex on the upper wing surface can avoid liftdecreasing; (3) enhancing the strength of the trailing edge vortex andaccelerating its shedding can produce high lift.
2005, 37(3): 257-265. doi: 10.6052/0459-1879-2005-3-2004-137
Buoyant-thermocapillary convection of moderate prandtl number fluid
In order to understand the nature ofbuoyant-thermocapillary convection in an annular pool with the outer heatedcontainer of radius ro=40 mm and the inner cooled cylinder ofri=20 mm, and an adjustable depth d=3~17 mm, we conducted a series ofunsteady three-dimensional numerical simulations with the finite differencemethod. The pool was filled with the 0.65cSt silicone oil (Prandtl numberPr=6.7). Results show that a small temperature difference in the radialdirection generates steady roll-cell buoyant-thermocapillary flow. Withlarge temperature difference, the simulations can predict two types of flowinstability. In a shallow pool (d=3 mm), the hydrothermal wave characterizedby curved spokes traveling in the azimuthal direction is dominant while indeep pools (d≥6 mm), the three-dimensional stationary instabilityappears. The critical conditions for the onset of the instability flows andthe free surface temperature fluctuation are determined and compared withthe experimental results.
2005, 37(3): 266-271. doi: 10.6052/0459-1879-2005-3-2004-312
Numerical analysis of flow-induced residual stresses in injection molding for polymer
To simulate buildup and relaxation of flow-induced stresses and molecularorientation in injection molding process, a mathematical model is derivedthat describes the unsteady and non-isothermal flow of compressibleviscoelastic polymer melts in the thin wall mold cavity on the base of thinfilm lubrication approximation. The compressible Leonov viscoelasticconstitutive equation and Tait state equation are used in the model todescribe the effects of compressibility of polymer melt which occur in thepost-filling stage. The model is applied to the injection molding processwhich is treated in terms of a filling, post-filling and cooling stage andis solved using a finite difference method. Stresses calculated with themodel are coupled to birefringence by means of the stress-optical rule.Birefrigence is used to characterize the molecular orientation. The finalresults are given in terms of residual stresses and associated birefringencein the molded part, as influenced by the processing conditions. The resultindicates that, for a given polymer, the main factors affecting flow-inducedresidual stresses and associated birefringence are flow rate and melttemperature, and with the incompressible case flow-induced residual stressesand associated birefringence are increased when the compressibility of themelt is considered. The result are compared with the birfriengencemeasurement in the literature and reasonable agreement is obtained.
2005, 37(3): 272-279. doi: 10.6052/0459-1879-2005-3-2004-070
Researches on the enhancement of fracture toughness induced by friction between crack faces
Mechanical model is established for the mixed-mode crackin elastic-viscoplastic material with friction present between the crackfaces. Asymptotic and numeric solutions to the crack-tip fields are got andthe frictional effects are discussed with the crack loaded under compressionand shear. Calculations and analyses are made to determine the boundary ofthe crack-tip plastic region and to obtain the plastic deformation energy init. It is indicated that the crack-tip plastic region will be enlarged andthe plastic deformation energy in the crack-tip region will be enhanced whenthe crack faces are frictionally contacted. From the viewpoint of energy,the plastic deformation energy can be viewed as the fracture toughness ofthe material in the crack-tip region. Therefore, the fracture toughness ofthe material in the crack-tip region can be enhanced by the friction betweenthe crack faces. Further analysis indicates that the enhancement of thefracture toughness is mainly due to the increment of the plastic deformationenergy in the crack-tip region other than the frictional heat produced onthe crack faces. It is indicated by the calculation and analysis of thephase-angle of the crack-tip load that probable hysteresis of the crackgrowth can occur due to the friction between the crack faces. Inengineering, friction between the crack faces can be produced artificiallythrough design and manufacture to improve the carrying capacity and prolongthe service life of the cracked components loaded under compression andshear.
2005, 37(3): 280-286. doi: 10.6052/0459-1879-2005-3-2003-331
Dynamic responses of a multilayer spherically isotropic pyroelectric hollow sphere
The dynamic solution of a multilayer spherically isotropicpyroelectric hollow sphere for spherically symmetric problem is obtained. Bythe principle of superposition, the solution is divided into two parts: Oneis quasi-static and the other is dynamic. The quasi-static part is obtainedin an explicit form by the state space method, and the dynamic part isderived by the initial parameter method coupled with the separation ofvariables method as well as the orthogonal expansion technique. By using theobtained quasi-static and dynamic parts and utilizing the electric boundaryconditions as well as the electric continuity conditions, a Volterraintegral equation of the second kind with respect to a function of time isderived, which can be solved successfully by means of the interpolationmethod. The displacements, electric potentials and stresses can be finallydetermined. The present method is suitable for a multilayer sphericallyisotropic pyroelectric hollow sphere consisting of arbitrary layers andsubjected to arbitrary spherically symmetric thermal loads. Numericalresults are presented and discussed at the end.
2005, 37(3): 287-294. doi: 10.6052/0459-1879-2005-3-2004-188
Robust optimization for structures using non-probabilistic convex method of set theory
Based on the conventional structural optimal theory andconsidering the uncertainties of structural parameters, we present robustoptimal method for structures using non-probabilistic convex set theory. Wemodel the uncertain parameters which exist in the object function andconstraint conditions as convex set, and need not know their detailedstatistical information bur bounds of uncertainties. The proposed method canendure the variation of structural performance resulting from the variationof uncertain parameters. According to the variation range of them, we candetermine the range or interval of optimal solution. In this sense, theoptimal solution is one domain rather than a point. Numerical example often-bar truss is used to illustrate the method using non-probabilisticrobust optimization, which shows both the feasibility and superioritycompared with conventional methods.
2005, 37(3): 295-300. doi: 10.6052/0459-1879-2005-3-2003-347
Optimization method of hybrid element stress function for strain gradient theory based on Hellinger-Reissner principle
Recent experiments have shown that materials will displaystrong scale effect when the scale of non-uniform plastic deformation fieldassociated their intrinsic length scale is on the order of microns. In orderto explain such scale effect phenomena, Fleck and Hutchinson developed acouple stress theory of strain gradient plasticity based on the reducedcouple stress theory, which incorporates the rotation gradient ofdeformation into constitutive model, and introduces a materialcharacteristic length parameter related to the rotation gradient.Theoretical predictions agree well with the micro-torsion and micro-bendingexperiments.In the finite element implementation of Fleck-Hutchinson couple stressplasticity, the higher order nature of theory requires that both thedisplacement and its first-order derivatives to be continuous across theadjacent elements' boundaries. Noticed that the micro-rotation ω, an independent kinematic quantity with no direct dependence ondisplacement u, is introduced in the general couple stresstheory. This enables the C0-continuous element to be developed based onthe general couple stress theory. Fitting within the framework of generalcouple stress theory, the energy consistency condition of the discretefinite element system for couple stress strain gradient theory is derived byintroduction of incompatible displacement trial functions. Furthermore, theoptimization condition of stress trial functions for hybrid element ofstrain gradient theory is constructed based the energy consistencycondition. A 4-node C0 kind hybrid element is designed in terms of theoptimization condition. Numerical tests show that the scale effects can bereflected with the element designed in the paper and reliable results isdelivered both for compressible and incompressible materials.
2005, 37(3): 301-306. doi: 10.6052/0459-1879-2005-3-2004-139
A homotopy method for parameter inversion of solute transport through unsaturated soils
Parameter inversion of solute transport insideunsaturated soils was generally solved through a nonlinear operatorequation. In this paper, we propose a homotopy method to deal with thisproblem. The original problem is finally transformed into an unconstrainedoptimization problem of minimizing the homotopy function. Considering theregularization effect of homotopy parameter, we adopt a two-step updatescheme of homotopy parameter. In the early stage, a quasi-sigmoid method isused to assure the stability of computation, while in the later stage, thecalibration of the homotopy parameter is governed by the computationalresiduals in order to compensate the error of observed data. Problems ofparameter inversion of solute transport coupled with equilibrium andnon-equilibrium effects through one-dimensional unsaturated soils arecarried out as numerical examples and the computational results clearlydemonstrate the feature of global convergence of the homotopy method.Moreover, even though experimental quantities are contaminated heavily bynoise, a favorable solution is still obtained.
2005, 37(3): 307-312. doi: 10.6052/0459-1879-2005-3-2003-308
Theoretical analysis of the critical impact velocity of aeolian saltating grains to rupture microbiotic crusts
The rupture of a microbiotic crust under the impactof a single saltating grain was theoretically studied using the classical theoriesof elastic thin plate and plastic mechanics. A quantitative relation between thecritical impact velocity of saltating grain and the characteristics of microbioticcrust was obtained. The effects of microorganisms were taken into account throughthe values of Young's modulus, Possion ratio and the yield stress of microbiotic crust,which are mainly determined by component species, numbers, and development stagesetc. The current study indicates that a rigid and weak microbiotic crust ismore easily broken down by saltating grains than a soft and strong one. The formulawe obtained will be helpful to evaluate the relationship between the microbiotic crustand the motions of wind-driven grains.
2005, 37(3): 313-316. doi: 10.6052/0459-1879-2005-3-2004-016
Cell cleavage model based on active microfilaments contraction
The current experiments suggest that the asters of themitotic apparatus determine the position of the contractile ring duringcytokinesis. Ultrastructural observation indicates that microfilaments arebound to the cortex with cross bridges. Microfilaments initially randomlyorientate and homogeneously distribute on the membrane. At late anaphase,the microfilaments distribution at the equator plane is changed from randomand uniform to aligned parallel. In the present study, on the basis ofZinemanas and Nir's hydrodynamics model, a new model was constructed tostimulate the relationship between the active microfilaments redistributionby biochemical stimulus from the MA asters and cytokinesis. The effectivecoefficient $m$ due to biochemical stimulus was incorporatedinto the model, and the distribution function $c$ is modifiedto move with the plasma membrane motion. In the model, it is assumed thatthe biochemical stimulus from the asters inhibit the formation of activefilaments through a very simple kinetic scheme; the reorientation of activemicrofilaments follows the cytoplasm flow; the motion of active filamentsfollows the plasma membrane's motion due to passive deformation. Thecell-division is driven by the anisotropic tension of surface. The surfacetension consists of two parts: one is the contractile force of the activefilaments paralleling to their symmetry axis, the other is the passivedeformation tension of the membrane by cytoplasm flowing. The numericalresults showed that the active filaments by redistribution due tobiochemical stimulus and actively contraction may play a crucial role incell division. Compared with Zinemanas and Nir's model, the results of ourmodel are more correspondent with the Hiramoto's experimental results.
2005, 37(3): 317-321. doi: 10.6052/0459-1879-2005-3-2004-030
Cable-pulley element to analysize pulley sliding on cable
In order to analysis the cable structures with pulleysliding on the cable, or cable sliding under pulley, a new element wasdeveloped. The three node element, which is called cable-pulley, models onesegment of cable supporting pulley, and takes the center of pulley as themiddle node, the two ends of the cable segment as the other two nodes. Thederivation was based on the foundational principles of finite elementanalysis, and the relation of the forces in the element at equilibrium statewas used. This new element simplifies computations by automaticallyadjusting the cable on each side of pulley in order to maintainequilibrium. Examples proved the correctness of the derivation and theprogram developed by the author, and presented its practical usage. Theexplicit formulas of matrixes composing the stiffness are given. The elementcan be incorporated into conventional finite element analysis schemes, toanalysis the cable structures in service or during construction.
2005, 37(3): 322-328. doi: 10.6052/0459-1879-2005-3-2003-175
Direct treatment and discretizations of non-linear dynamics of suspended cable
The applications of direct treatment anddiscretizations of non-linear dynamics are investigated in thispaper. These two approaches are applied to attack the primaryresonance of the $n$th mode of suspended cables. These lead toobtain the second order approximate solutions and the associatedfrequency-response curves. The results obtained with these twoapproaches are compared. And the differences of these results arediscussed. Finally, the results are obtained that thediscretization of nonlinear dynamic of non-symmetric structure maylead to erroneous results.
2005, 37(3): 329-338. doi: 10.6052/0459-1879-2005-3-2003-478
Nonlinear dynamics modeling and analysis of liquid sloshing in rectangle tank
Based on the assumption of the ideal fluid, the coupled dynamics equationsof movement of rigid tank and nonlinear sloshing of liquid are establishedthrough H-O principle, with the modified potential function introduced todescribe the moving boundary of rigid tank and fluid. Galerkin's method isused to discrete the equations. Benchmarked with some FEM and BEM results,feasibility of the present method is proved. The responses of the coupledsystem to the excitement by some forces are simulated. The equivalent theoryis used to explain the increase of the natural frequencies.
2005, 37(3): 339-345. doi: 10.6052/0459-1879-2005-3-2004-015
Bifurcation and fractal of the coupled logistic maps
The bifurcation of the coupled Logistic map is analyzedtheoretically. By using phase graphics, bifurcation graphics, power spectra,the computation of the fractal dimension and the Lyapunov exponent, thepaper reveals the general features of the coupled Logistic map transitionfrom regularity to chaos, the following conclusions are shown: (1) Chaoticpatterns of the map may emerge out of double-periodic bifurcation and Hopfbifurcation, respectively; (2) During the process of double-periodbifurcation, the system exhibits the self-similar structure and invariancewhich is under scale variety in both parameter space and phase space. Fromthe research on attractor basin of the coupled Logistic map andMandelbrot-Julia set, the following conclusions are indicated: (1) Theboundary between periodic and non-periodic regions is fractal, and thatindicates the impossibility to predict the moving end-result of the pointsin phase plane; (2) The structures of the Mandelbrot-Julia sets are determinedby the control parameters, and their boundaries have the fractal characteristic.
2005, 37(3): 346-355. doi: 10.6052/0459-1879-2005-3-2003-403
A local mixing particle-in-cell method for fluid-particle multiphase flows
In this paper, a local mixing particle-in-cell method isproposed for multiphase flows. The method can be used for dense particleflows. Under the grid of particle parcel scale, which is called as Eulercell in this paper, the total particle volume in the cell is calculateddirectly based on the Lagrangian method. Therefore the particle volumefraction (concentration) on the Euler cell and the fluid control volume canbe obtained accurately. Meanwhile, at new time step, particles on the Eulercell are assumed to be mixing sufficiently and come into being a new parcel.Comparing with the previous methods, the proposed method is more efficientand accurate. For the sedimentation in vertical and inclined vessels, andthe bimodal suspension in a vertical vessel, the numerical results agreewith the experimental results.
2005, 37(3): 356-362. doi: 10.6052/0459-1879-2005-3-2003-207
Numerical simulation of multi-physics characteristic of hydrogels in salt solutions
Numerical simulations are conducted in this paper to predict themulti-physics behavior of ionic-strength-sensitive hydrogels in aqueous saltsolutions. The main governing equations in the presently developed modelconsist of the convection-diffusion equations calculating the distributionof ionic concentrations, the Poisson equation describing the electricpotential and the thermodynamic equations computing the swellingdeformation. To solve the multi-field coupled nonlinear partial differentialgoverning equations, a Newton iteration procedure is carried out and thesteady-state responses of the hydrogels in aqueous salt solutions arenumerically simulated by meshless finite cloud method. The ionicconcentrations, electric potentials interior and exterior the hydrogels aswell as swelling deformation of the hydrogels are investigated. The majorfactors that influence the swelling behaviors of the hydrogels are alsodiscussed. The numerical results in good agreement with the experimentaldata validate the developed multi-physics model.
2005, 37(3): 363-367. doi: 10.6052/0459-1879-2005-3-2003-226
The representation of failure criterions in generalized mohr space and its applications
The paper deals with the strength and the yield (failure) ofmaterials in generalized Mohr space and finds out the transformations offailure criterions represented in the principal stress space and in thegeneralized Mohr space. A universal compatibility relations for the failurestress and the failure plane, which is independent of the failurecriterions, is also discovered. For double shearing strength theory, owingto its representation in the generalized Mohr space, the theory isconsidered the equivalent of the maximal deviator stress.
2005, 37(3): 368-373. doi: 10.6052/0459-1879-2005-3-2004-251
Identification of damage in rectangular plates based on neural network technique with sub-regions
This paper presents an identification approach based onneural network method with sub-regions to identify damages in a rectangularplate using the LM optimized algorithm. The numerical results of simulationsfor the cantilever plate with some damages show that this approach is betterthan that from the conventional method with single network. Since thismethod realizes the synchronous output of position and intensity of damagesin the structure, this approach does not need many sub-networks appeared ina conventional hierarchical identification method.
2005, 37(3): 374-377. doi: 10.6052/0459-1879-2005-3-2003-261
Dynamic response analysis of fuzzy truss under fuzzy excitation
Not only considering the fuzziness of structuralphysical parameters and geometric dimensions, but also considering fuzzinessof applied load simultaneously, fuzziness of structural dynamic response isstudied in this paper. Firstly, a new method (fuzzy factor method) to dealwith fuzzy variable is proposed. By means of this new method, a fuzzyvariable can be described as its fuzzy main value multiplied by its fuzzyfactor. Secondly, from Duhamel integral, the expressions of structural fuzzydynamic response are deduced by combining mode superposition method withcalculus, fuzzy factor method and interval arithmetic, and membershipfunctions of dynamic response can be derived in the end. To testify thecorrectness and rationality of the model and solution to it given in thispaper, Monte Carlo method is used to simulate the fuzzy structure in theexample. At last, through engineering example, the influences of the fuzzystructural parameters and fuzzy applied load on structural fuzzy dynamicresponse are inspected and some significant conclusions are obtained.
2005, 37(3): 378-384. doi: 10.6052/0459-1879-2005-3-2004-169