力学学报

Numerical simulation of gaseous detonation reflection over wedges

In this paper, the chemically reacting flow-field ofdetonation reflection over wedges was simulated numerically. Thedispersion-controlled dissipative scheme (DCD) was adopted to solvetwo-dimensional Euler equations implemented with detailed chemical reactionkinetics of hydrogen-oxygen-argon mixture. The fractional step method wasapplied to treat the stiff problem arising from computation of chemicalreaction flow. The wedge angle, initial pressure and composition of themixture were taken into consideration respectively to evaluate their effecton the angle $\chi$ of triple-point trajectory of detonation reflectionover wedges. From the numerical results it is observed that the criticalwedge angle $\alpha_{\rm crit}$ for the transition from Mach reflection toregular reflection of detonation wave is close to the experimental data orCCW theoretical result. The numerical results also show that the angle$\chi$ of triple-point trajectory is mainly depend on wedge angle$\alpha$ and is not sensitive to variation of the initial pressure $P_{0}$.

2004, 36(4): 385-392. doi: 10.6052/0459-1879-2004-4-2003-313

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A universal numerical discretization method on different meshes

A universal discretization method is prestented in this paper, it can be used on arbitary meshes.Considering the common properties of all different kinds of meshes, we established this numericaldifference scheme by Taylor series expansion and the least square method.We can obtain the local difference matrix(LDM) and global difference matrix(GDM) on any mesh by this method,then the difference operator can be interpreted as its matrix form in discreted space directly. This skill can apply tomany numerical schemes developed on structured grid, then those schemes will work on arbitary meshes,the complexity of the computation domain will no longer be any problems.In order to verify the skill in this paper, we first compute the numerical difference of an analytical function,and compare the results with the exact solutions. It shows that the method has the 2nd order accuracy as the center difference scheme.Another two examples are numerical simulation of incompressible flow in a two dimension backward-facing step and three dimension driven cavity. The vorticity-stream function equation and Navier-Stokesequations in velocity-pressure form are used respectively. The results in this paper are agreement withthe classical ones on structured meshes. But the method here can be applied on any grid.

2004, 36(4): 393-400. doi: 10.6052/0459-1879-2004-4-2003-170

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Computation of lateral turbulent jets using M-SST des model

DES(detached eddy simulation) is a hybrid methodcombining RANS and LES to simulate flowfields with detached eddies. The mainidea is that, RANS is used near the wall and LES method is used in the otherregion of the field. In this paper, DES method based on M-SST was used tosimulate the complicate turbulence flows on hybrid unstructured grids andthe Osher scheme was used for the spatial discretisation. The computationsof the flow around a missile with a lateral jet was performed by using thenewly-developed codes. The obtained results demonstrate that DES method isefficient for some simulation of the separated turbulence flowfields.

2004, 36(4): 401-406. doi: 10.6052/0459-1879-2004-4-2003-236

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Simulation of well-log response of the acoustically-induced electromagnetic field in a porous formation

During acousto-electric logging, the acoustic waveexcited by a point acoustic source in a fluid-filled borehole propagatesinto the fluid-saturated porous medium and causes relative motion betweenthe charge-bearing pore fluid and the skeleton, inducing electromagneticfield. To simulate the logging response, a numerical full-waveformsimulation method is proposed. The acoustic field is taken as uninfluencedby the converted electromagnetic field, and is solved separately. Theelectric field is taken as quasi-steady. The full Biot-Rosenbaum model isadopted to obtain expressions for the acoustic field around the borehole.These expressions are then used to formulate the converted electric andmagnetic fields in and out of the borehole. Calculations show there areelectric and magnetic fields that accompany the compressional, the shear andthe Stoneley waves. And there is a critically refracted electromagneticwave, which travels along the borehole wall. The amplitude of this wave isvery weak in the full waveform. Both the axial and the radial components ofthe electric field increase when the receiver is placed farther off theborehole axis. On the borehole wall, the shape of the waveform of magneticfield is similar to that of the axial electric field.

2004, 36(4): 407-413. doi: 10.6052/0459-1879-2004-4-2002-316

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Semi-analytical element method for double-K fracture parameters computations in concrete

The double-$K$ fracture criterion describes initiation,stable propagation and unstable propagation of cracks in concretestructures. The corresponding double-$K$ fracture parameters (initialcracking roughness $K_{\rm IC}^{\rm ini} $and unstable fracture toughness$K_{\rm IC}^{\rm un})$ introduced in the criterion are determined using asimple experiment method combing with an analytical evaluation based on thecohesive force on the fictitious crack zone. Based on the Hamiltoniangoverning equations of plane elasticity for sectorial domain, the variableseparation and eigenfunction expansion techniques are employed to develop anovel analytical finite element for the fictitious crack propagation linearforce model in fracture mechanics of concrete in this paper. The newanalytical element can be implemented into FEM program systems to solvecomputational problems of double-$K$ fracture parameters for concrete crackedplane structures with arbitrary shapes. Numerical results indicate that themethod is efficient and accurate.

2004, 36(4): 414-418. doi: 10.6052/0459-1879-2004-4-2003-365

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Application of stress functions and its dual theory to finite element

Cosserat's continuum is a generalized model of the classical elasticity. Many important elastic problems can be taken as itsspecial case subjected to some geometric/mechanical constrains. In some ofthese problems, there exist the C$^{1 }$ continuity difficulty in finiteelement formulation when the elements are constructed in the displacementspace. Using Cosserat's continuum, the present work discusses the reason ofthe appearance of the C$^{1 }$ continuity difficulty. It is noted that whengeometric or/and mechanical constraint(s) is(are) enforced upon Cosserat'smodel there must exist C$^{1 }$ continuity requirement for eitherdisplacement field or stress function field. And the key point is that onlyone of these two fields has the C$^{1 }$ continuity requirement and the otheris free from this difficulty. So for some problems with C$^{1 }$ continuitydifficulty in displacement formulation, it is a natural approach to avoidthis difficulty by using formulation in stress function space. Nevertheless,the finite element constructed in stress function space is not convenient toapply because stress functions have no explicit physical meaning and then itis difficult to appoint boundary condition for them. For this practicalreason, the dual theory of stress functions is presented to provide anapproach to transform an element with stress functions as degree of freedom(DOF) to the element with ordinary displacement as DOF. Based on this dualtheory, a general way to construct finite element using stress functions isdiscussed.

2004, 36(4): 419-426. doi: 10.6052/0459-1879-2004-4-2003-277

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Heat source function method for coupling analyses of thermal consolidation in saturated soil

Based on the governing equations of thermal couplingconsolidation for saturated homogeneous isotropic porous materials, thesolutions in transform space are given by repeated Fourier transformationsand Laplace transformation. Considering initial temperature field as afictitious heat source or equalizing heat source as specified initialtemperature field, an analytical method for calculating the unsteadytemperature field, stress field and displacement field of saturated soilsdue to instantaneous line heat source is deduced by using the so-called heatsource function method. The influence of full coupling effects between thefield quantities are considered. By integration in temporal and spatialdomain, a calculation method of two-dimensional thermal consolidationproblem with initial temperature field and variable strength of heat sourcewith time is established. For convenience of analyses, the concepts ofthermal consolidation time factor and coefficient of thermal consolidationare defined. The evolutions of temperature, pore water pressure anddisplacement with time factor around rectangular heat source are analyzed bythe proposed method. The thermal consolidation characteristics and itsmechanism are studied. It is showed that this method can be used to solvesome complicated thermal consolidation problems effectively, and has animportant theoretical and practical meaning.

2004, 36(4): 427-434. doi: 10.6052/0459-1879-2004-4-2003-487

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Vertical vibration of an end bearing pile embedded in saturated soil

Dynamic interaction of pile and soil plays an importantrole in structure design. Although many researches have been carried out onthe field in past two decades, the emphasis is mainly focused on pilevibration in single phase medium. Such a fact has been neglected that soilis multi-phase medium. The effects of ground water on the interaction areseldom discussed.In this paper, vertical vibration of an end bearing pile embedded in asaturated soil layer is theoretically investigated. The pile is assumed tobe vertical and can be dealt with one dimensional elastic theory. The soilis considered as a linear saturated isotropic poroelastic medium andsatisfies rigorous three dimensional poroelasticity. Potential functions areapplied to decouple governing differential equations of the soil layeroriginally presented by Biot. By virtue of differential operator splittingand variable separation method, soil vibration displacement solutions withan undetermined constant are obtained at first. Under the assumption ofperfect contact between the pile and the soil, the pile response to anarbitrary vertical load is analytically derived in a closed form. Thenharmonic complex stiffness and admittance at the pile head are defined infrequency domain. And velocity response in time domain is gained by means ofFourier inverse transform. Based on the solutions, a parametric study isconducted to determine the main features of the soil-pile interaction invertical vibration. As a result, the pile slenderness and the pile-soilmodulus ratio are major on the pile dynamic response, while the seepageforce has minor influence on the response. Finally, it is shown that thetheoretical curves are in good agreement with those obtained from fieldtest.

2004, 36(4): 435-442. doi: 10.6052/0459-1879-2004-4-2003-265

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Periodic and chaotic oscillation of a parametrically excited viscoelastic moving belt with 1:3 internal resonance

In this paper, the bifurcations of periodic solutions andchaotic dynamics for a parametrically excited viscoelastic moving belt with1:3 internal resonance are investigated for the first time. The externaldamping and the internal damping of the material for viscoelastic movingbelt are considered simultaneously. First, the nonlinear equation of planarmotion for viscoelastic moving belt with the external damping isestablished. The Kelvin viscoelastic model is adopted to describe therelation between the stress and strain for viscoelastic material. Then, thetransverse nonlinear oscillations of viscoelastic moving belt areconsidered. The method of multiple scales and the Galerkin approach areapplied directly to the partial differential governing equation ofviscoelastic moving belt to obtain the averaged equations under the case of1:3 internal resonance and primary parametric resonance of the $n$th mode.Finally, numerical simulation method is used to investigated thebifurcations of periodic solutions and chaotic dynamics for viscoelasticmoving belt. The chaotic motions are found under the cases of differentparameters. The results of numerical simulation demonstrate that there existperiodic, 2-periodic, 3-periodic, 5-periodic and quasiperiodic responses andchaotic motions in viscoelastic moving belt.

2004, 36(4): 443-454. doi: 10.6052/0459-1879-2004-4-2003-369

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Composite equations of water waves over uneven and porous seabed

Huang Hu & strXing &

The composite equations for water waves propagating over aporous uneven bottoms are derived from Green's second identity, whichincorporates the effects of porous medium in the nearshore region andconsiders the advances in models of water waves propagation over rigidbottoms. Assuming that both water depth and thickness of the porous layerconsist of two kind of components: The slowly varying component whosehorizontal length scale is longer than the surface wave length, and the fastvarying component with the horizontal length scale as the surface wavelength. The amplitude of the fast varying component is, however, smallerthan the surface wave length. In addition, the fast varying component of thelower boundary surface of the porous layer is one order of magnitude smallerthan that of the water depth. By Green's second identity and satisfying thecontinuous conditions at the interface for the pressure and the verticaldischarge velocity the composite equations are given for both water layerand porous layer, which can fully consider the general continuity of thevariation of wave number and include some well-known extended mild-slopeequations.

2004, 36(4): 455-459. doi: 10.6052/0459-1879-2004-4-2003-416

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Oscillation and elevation difference of thermally driven two-phase on its thermal performances

A high speed data acquisition system was used to detectthe pressure and temperature oscillations of the thermally driven two-phaseloop for different operation parameters using methanol as working fluid. Theoscillation time period and the amplitudes are smaller at high heat fluxthan those at low heat flux. It was found that bubbly flow or slug flowexists in the vapor line at low heat flux, while the annular flow exists athigh heat flux. In addition to these, the effect of the relative elevationdifference between the evaporator and the condenser on the operation of thethermally driven two-phase loop was studied. The maximum heat flux ofevaporator was obtained with the pure natural or the forced air convectionof the fin heat sink condenser under the condition of the upper limittemperature of 90${^\circ}$C of the heating block. The present study is toprovide guidelines for the design and operation of the miniature electriccooling.

2004, 36(4): 460-465. doi: 10.6052/0459-1879-2004-4-2003-376

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研究了雷诺数Re=200, 1000, 线速度比$\alpha =0.5$,

The unsteady flow past a circular cylinder which startstranslating and rotary oscillating impulsively from rest in a viscous fluidis investigated at Reynolds numbers $Re=200$ and 1000, rectilinear speedratios $\alpha =0.5$, 2.0 and 4.0, and for forced oscillating frequencies$f_{s}$ between 0.1 and 2.0. Numerical solutions of the Navier-Stokesequations are obtained by a finite volume method based on unstructuredcolocated meshes. The discretized schemes of the convective fluxes,diffusive fluxes and unsteadyterm are all of second-order accuracy. The SIMPLE algorithm is adopted todeal with the pressure-velocity coupling. The varieties of forcecoefficients with the control parameter are obtained after the discussion.The amplitudes of lift coefficients at natural shedding frequency and forcedoscillating frequency respectively are determined by the amplitude spectraanalysis, which show clearly the competitive relationship between the twofrequencies. Based on this relationship, the region of the classification offlow structure modes is given at last.

2004, 36(4): 466-471. doi: 10.6052/0459-1879-2004-4-2003-021

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Flow control effects of electromagnetic force in the boundary layer

The controlling effects of flow caused by electromagneticbody forces have been conducted. The key parameters of control experimentshave been confirmed by the theoretical analysis and the numerical simulation. Theelectrodes and the magnetic poles are flush mounted on the cylinder surfaceside by side in the order of magnet N-pole, positive(negative) electrode,magnet S-pole, negative(positive) electrode, and so on. The cylindercovered with electro-magnetic actuator is immerged in the flowingelectrolyte solution. The electromagnetic body forces, which localized onthe circular cylinder surface, have been used to modify the boundary layerof flow and control the flow flied structure. By means of theelectro-magnetic shielding and the time-region control methods, theseparation points of the circular-cylinder flow are moving between the frontstay point and the back stay point as the varieties of the space-timedistribution parameters of the electromagnetic forces, and it bringsdifferent control effects. The electromagnetic force modified on theboundary layer is convenient to controlling the flow flied structure of thecircular-cylinder flow and the cylinder wake, and it is achieved the obviouseffects of the vortex suppression and the vortex acceleration. There areprovided with the preferable effects of the oscillation absorption and thedrag reduce while the positive electromagnetic forces processed. There areexisted very strong effects of damping control while the negativeelectromagnetic forces processed, at that time the characteristics ofsymmetry and stability of the vorticity distribution on the cylinder surfaceare destroyed.

2004, 36(4): 472-478. doi: 10.6052/0459-1879-2004-4-2003-392

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Binghaw flows of retarded adhesive mortar in a single-screw extruder

The paper explores the flow for retardedadhesive mortar with Bingham liquid in a single-screw ectruder on the basisof test. By using the theories of rheology, the model of retarded adhesivemortar screw conveying is built. Discussed the principle for retardedadhesive mortar by screw conveying, the condition of successive conveyingretarded adhesive mortar is obtained, i.e. the screw revolutions must exceedthe critical revolutions. The test results suggest that it can be relizedsuccessive conveying and coating for retarded adhesive mortar with Binghamliquid in the mechanism of retarded adhesive mortar screw conveying andcoating, when the screw revolutions are within 78$\sim $240\,r/min. Thefindings of these investigations resolve the reliability problem of retardedadhesive mortar screw conveying and lay the foundation for developing thecoating device of retarted adhesive prestressed strand.

2004, 36(4): 479-483. doi: 10.6052/0459-1879-2004-4-2003-411

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Wave propagation in the piezoelectric hollow cylinder

Wei Jianping

In this article, the wave propagation in thepiezoelectric hollow cylinder is investigated by applying 3-D piezoelectricelastic axial symmetric model. While the cylinder has piezoelectricproperty, its guided wave very differs with the non-piezoelectric cylinder.When the wavelength tends to zero, the velocity of simulation-P wave (sim-Pwave) in the piezoelectric cylinder asymptotically tends to the quasi-P wavevelocity of transverse isotropic elastic body, but the velocity of sim-Pwave in the non-piezoelectric cylinder asymptotically tends to the P wavevelocity of 1-D bar model. The sim-SV wave in the piezoelectric cylinder hasthe standing wave phenomenon. The SH wave is independent of electric field,so the piezoelectric and non-piezoelectric cylinders have the same frequencydispersion curves about SH wave. In this paper, using Integral TransformMethod to combine the boundary condition and the governing equationstogether, a group of dynamics equations, which are about the displacementsand electric potential, is derived. To the assured boundary condition, theguided-wave condition and the frequency dispersion equations are obtained.Above such solution, the transient responses under a stress pulse at the endare simulated. At last the effect to the wave propagation about the radius'ratios of the hollow cylinders is discussed.

2004, 36(4): 484-490. doi: 10.6052/0459-1879-2004-4-2003-468

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On load identification for piezoelectric smart structures

Based on BP neural network and finite element inverse analysis, a method isproposed to identify the location and magnitute of loads by measuring thepiezoelectric responsive charge on the piezoelectric smart structure. Firstly, the unitloads are acted on several different locations on the structure and the learingstylebook of net is calculated by the finite element method, by which the location ofloads may be finded. Then, the magnitute of loads is determined by finite elementinverse analysis and the least square method. The calculation example shows that themethod has high precise and rapid calculation velocity, which is suit for thepiezoelectric smart structures with complex shape and boundary conditions and mayfind its uses in the loads identification of the applied smart structures.

2004, 36(4): 491-495. doi: 10.6052/0459-1879-2004-4-2002-235

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Meshless numerical manifold method based on unit partition

In this paper the meshless numerical manifold method ispresented based on the numerical manifold method and the partition of unitymethod. In meshless numerical manifold method, two cover systems areemployed. The mathematical cover system provides the nodes for formingfinite covers of the solution domain and the partition of unityfunctions, and the physical cover system describes geometry of the domain of theproblem and the discontinuous surfaces in the domain. The shape function inthis method is formed by the partition of unity and the finite covertechnology, so the shape functions cannot be affected by discontinuousdomain, and crack problems can be treated better. To local problems, theshape functions are more effective than other method. So the method canavoid the disadvantages in other meshless methods in which the tip of thediscontinuous crack is not considered. Comparing with the conventionalnumerical manifold method, the shape of the finite cover can be selectedeasily. And the finite covers and the partition of unity functions areformed with the influence domains of a series of nodes. So the meshlessmanifold method has some advantages of the meshless and gets rid of thedisadvantage of the mesh in the numerical manifold method. Comparing withthe conventional meshless method, finite cover technology is used in themethod, and then the test functions cannot be influenced by thediscontinuity in the solving domain. And this method can conquer somedifficulties in the conventional meshless methods for the problems with adiscontinuous domain. The test function and the equations of the meshlessnumerical manifold method are obtained in detail. And a numerical example isgiven and it shows the method in this paper is correct.

2004, 36(4): 496-500. doi: 10.6052/0459-1879-2004-4-2003-442

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Antiplane problem of periodic crack in a strip of functionally graded materials

In this paper, a single crack problem and a periodic crackantiplane problem of functionally graded materials (FGMs) arestudied. An elementary solution is obtained, which represents the influencecaused by a point dislocation placed at a point $t$ on the real axis. TheFourier transform method is used to derive the elementary solution. Afterusing the obtained elementary solution, the singular integral equation isformulated for the periodic crack problem. In the solution of the singularintegral equation, the influence at the center crack caused by the manyremote cracks is considered approximately. Finally, numerical results arepresented, and the influence caused by the materials property $\alpha $is addressed.

2004, 36(4): 501-506. doi: 10.6052/0459-1879-2004-4-2003-384

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Stress-strain curves and yield loci of auto steel sheet

On the basis of biaxial tensile experimental system, twotypes of steel sheet were studied under different loading paths usingoptimized cruciform specimens with slots in the arms. According to theexperimental true stress-logarithmic strain curves, the stress-strain curvesof steel sheet vary with the stress state, and the strain-hardening exponentbecome larger when the load ratio is near the ratio 1:1.The contours of experimental yield loci for two steel sheets from 0.2{\%} to2{\%} plastic strain were determined based on the equivalent plastic workprinciple. It is found that the shape of yield loci does not show symmetryalong equibiaxial stretching path because of anisotropic mechanicalproperties.The geometry of the experimental yield loci were compared with the yieldloci calculated from several existing yield criteria and the analyticalresult shows that the Hosford yield criterion describes the general trendsof experimental yield loci of steel sheets very well, whereas the Hill48yield criterion overestimated the yield stress in all the contours. Inaddition, the Mises yield criterion that is generally used in isotropicmaterials also gives good fitness to the experimental yield loci.

2004, 36(4): 507-512. doi: 10.6052/0459-1879-2004-4-2003-130

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