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2009 Vol. 41, No. 4

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Analysis of long-range ultra-low flight trajectory
Jing Fan, Jianzheng Jiang, Quanhua Sun, Zuowu Li, Chenxi Wu
An ultra-low, long-range flight trajectory with themaximum altitude of about 100km is investigated. Such an ultra-lowtrajectory employs the satellite mode against the gravitation by thecentrifugal force. Different from a running satellite, the rarefied gaseffects on the ultra-low trajectory are essentially important. It is shownthat under the same payload and range, the power requirements of theultra-low trajectory and classic minimum energy trajectory are almostthe same. For anaxial symmetric configuration with the nose radius of 5cm, its stagnationheat flux along an ultra-low trajectory arrives at a maximum value of50MW/m2 around altitude 25km, which is about half of the maximumstagnation heat flux along a minimum energy trajectory. The aerodynamicheating along an ultra-low trajectory can be solved using conventionalmature techniques such as ablation, because it does not require lift. Ingeneral, the power and aerodynamic requirements of ultra-low flighttrajectories can be satisfied based on existing technologies, and thereforeit is realistic to promote the anti-defense ability of long-range missilesby taking the ultra-low flight trajectory.
2009, 41(4): 449-454. doi: 10.6052/0459-1879-2009-4-2009-154
On the ignition process in a model scramjet combustor
Yu Pan, Weidong Liu, Jianhan Liang, Zhenguo Wang
Three processes of ignition were investigated by usinghigh speed camera and schlieren system with the inflow condition ofMa=2.64, T_0=1483K, P_0=1.65MPa, T=724K, andP=76.3kPa, which are autoignition ofhydrogen injection, the spark igniting hydrogen and the pilot flame ignitingthe kerosene in a constant area model scramjet combustor. The flamepropagation and shocktrains evolution in the combusotr was gained, whichrevealed that the flame originated from the downstream of the combustor,then propagated to upstream untill the whole combustor was ignited. Theresults also showed that flow velocity of combustor and installation schemeof flame holders will extremely affect the ignition delay or occurringposition of ignition. Furthermore, the fuel residence time will be increasedby using more cavity flameholders, which was benificial to fuelautoignition.
2009, 41(4): 455-462. doi: 10.6052/0459-1879-2009-4-2009-142
Shock Tube Study of Phenolic Resin Pyrolysis
Weifeng Yan, Su Wang, Wei Ma, Shuaihui Li, Bingcheng Fan, Yuzhong He, Jiping Cui
The pyrolysis of phenolic resin was studied in a single-pulse shock tube at high temperatures between 1100 and 1800K. Considering the very high temperature and short duration time as the special condition met in a shock tube, the heat transfer process of sample particles in high temperature gas was analyzed and the conditions how can it reaches the temperature equilibrium between the phenolic resin powder and the ambient high temperature gas was discussed. The pyrolysis product distribution and the pyrolysis rate constants of phenolic resin were determined by using gas chromatograph and mass spectrometry. The major gas products were identified as water, carbon monoxide, hydrogen, acetylene and benzene. The pyrolysis process was divided into the lower and higher temperature regions at 1400K. The different dependency relationships of the pyrolysis rate constant with temperature for the lower and higher temperature regions were obtained.Key words: phenolic resin, pyrolysis, re-entry process, shock tube, mass spectrometry analysis, chromatography analysis
2009, 41(4): 463-468. doi: 10.6052/0459-1879-2009-4-2009-143
Static aeroelastic analysis of a flying-wing using different models
Dawei Chen, Guowei Yang
A loosely-coupled procedure for static aeroelasticanalysis of a flying wing is presented. Firstly, the flow solvers used arebased on an Euler model and a RANS model with structured grid, and an Eulermodel with unstructured grid. Secondly, the structure modal analysis andflexibility matrix method are all applied. Furthermore, a theoretical caseof the flying wing is carried out in cruise condition of Mach number of 0.6and the angle of attack of 2? at 20km altitude. The results show thatthe flexibility matrix method is more suitable for static aeroelasticanalysis than the structure modal analysis. Meanwhile, a surface deflectionmethod is validated to be more efficient than the grid deformation method inthe computation analysis due to the three-dimensional geometriesdeformation.
2009, 41(4): 469-479. doi: 10.6052/0459-1879-2009-4-2008-042
Complex variable numerical manifold method for elasticity
Hongfen Gao, Yumin Cheng
The numerical manifold method (NMM) is a more generalnumerical method than finite element method with mathematical and physicalmeshes. The mathematical mesh provides the nodes to form a finite coveringof the solution domain and the partition of unity functions, while thephysical mesh provides the domain of integration. The numerical manifoldmethod has some advantages, for example, the solution domain is discretizedas an arbitrary mesh which is independent on the complex geometry of theboundary of the solution domain or the interface of bi-materials. However,the generalized degrees of freedom in the NMM will be enhanced to inducemore computing cost when the higher polynomial interpolating function isused as the displacement function. In this paper, based on the complexvariables theory, the approximation function of a two-dimensional problem isdeveloped with one-dimensional basis function, and the approximationfunction is applied to the NMM for two-dimensional elasticity. Then thecomplex variable numerical manifold method (CVNMM) for 2D elasticity ispresented, and the formulae of the CVNMM are obtained. The influences ofboundary conditions and initial stress on the final linear algebra equationssystem are discussed. In addition, two numerical cases were carried out.When the composite material structure is simulated using the CVNMM, thecomputing meshes can be easily generated along the interfaces of materials,then the CVNMM is more flexible than the finite element method. Furthermore,bi-material interface crack problem is analyzed using the CVNMM, and thestress intensity factor of the interface crack is obtained with thenumerical extrapolation method. The CVNMM has greater computationalefficiency and precision validated with the numerical cases.
2009, 41(4): 480-488. doi: 10.6052/0459-1879-2009-4-2007-485
Buckling analysis of the electrode delamination on the piezoelectric substrate
Changjin Yang, Yaochen Li
The paper investigated the electrode delaminationbuckling of the layered system containing a through-the-width delaminationbetween the metallic electrode and the half-space piezoelectric substratebased on the finite deformation theory of elasticity and the biasing fieldtheory of the electroelastic body. The layered system in the plane strainproblem is subjected to the compressive strain-load parallel to the freesurface. Meanwhile, the theoretical model is reduced to the second kindCauchy-type singular integral equations by means of the Fourier integraltransform, the boundary conditions and the interfacial continuousconditions. The singular integral equations are solved numerically byutilizing Gauss-Chebyshev integral formulae. As an example, the layeredsystem of the metallic electrode Pt and piezoelectric substrate PZT-4 isconsidered. Numerical results for the critical strains of buckling and thecorresponding delamination buckling shapes are presented for, respectively,various ratios of the delamination length to thickness and the effect ofelectromechanical coupling in the piezoelectric substrate. The curves of thesingular oscillating factors in the delamination tip with respect to theratios of delamination length to thickness are also given.
2009, 41(4): 489-502. doi: 10.6052/0459-1879-2009-4-2007-556
Shape design sensitivity analysis of elastoplastic frictional contact problems with finite deformation
Wan Jun, Guo-jin Tang, Dao-kui Li
A new shape design sensitivity analysis algorithm oftwo-dimensional multi-body elastoplastic frictional contact problems withfinite deformation was presented in this paper. In the direct analysis ofcontact problems, the variational inequality of contact constraints wereanalyzed with the active set strategies, and the contact interface wasdiscretized by the mortar method. The same nominal penalty parameters wereadopted in the normal and tangential directions of mortar surface'ssegments, and the normal and tangential contact conditions were regularizedby the moving friction cone algorithm based on the nominal penaltyformulation. A new two-dimensional multi-body finite deformation frictionalcontact algorithm was proposed, and the algorithm could inherit the advantagesof the moving friction algorithm and mortar method. In the shape designsensitivity analysis of contact problems, the incremental (path-dependent)sensitivity problem was derived by the direct differentiation of thediscretized equations governing the direct problem. The shape designsensitivity equation was linear and could be solved at each increment stepwithout iterations. In contrast to the classical shape design sensitivityalgorithm, normal and tangential directions was not to be divided in thepresent algorithm and its formulation was more concise to program. Numericalexamples were presented to illustrate the accuracy and efficiency of thisapproach.
2009, 41(4): 503-517. doi: 10.6052/0459-1879-2009-4-2007-619
Structural topological optimization based on displacement and stress sensitivity analyses
Jianhua Rong, Sen Ge, Guo Deng, Xiaojuan Xing, Zhijun Zhao
Stress constrained topology optimization problem has notbeen paid the same attention as the minimum compliance problem in theliteratures. The traditional minimum compliance formulations offer someobvious advantages to avoid dealing with a large number of highly non-linearconstraints. This could be considered crucial, if one takes into account thelarge number of design variables, i.e. inherent to topology optimization.However, one can also argue that this gives rise to several importantdrawbacks since no constraints are imposed on stresses and displacements,for example, multiple load cases cannot be considered; different solutionsare obtained for different restrictions; the final design could beunfeasible in practice. This paper deals with topology optimization ofcontinuum structures with stress and displacement constraints or with onlystress constraints, based on the ICM method and the evolutionary structuraloptimization method. New displacement and stress constraint limits areformed and introduced into the optimization model at the beginning of eachoptimization iteration sub-loop, so that moving limits of design variablescan be easily constructed. Instead of all stress constraints, only the mostpotential effective stress constraints are considered. In this way, stresssensitivity analysis is much less costly. Moreover, the element deletion anda set of structural optimization strategies are given. In order to make thestructure optimized be non-singular and the proposed method be of elementrestorable functions, some elements with artificial material property areinserted around the cavities and boundaries of the structure optimized.Meanwhile, an equivalent topological optimization model is developed.Incorporating displacement and stress sensitivity analyses, a new continuumstructural topological optimization method is also proposed. Two simulationexamples demonstrate that the proposed method is of validity andeffectiveness.
2009, 41(4): 518-529. doi: 10.6052/0459-1879-2009-4-2007-540
Structural topology optimization under inertial loads
Tong Gao, Weihong Zhang, Jihong Zhu
Structural topology design optimization under inertialloads is studied in the paper. Based on the sensitivity scheme of structuralcompliance, the non-monotonous feature of the objective function isdescribed. Due to the design-depedent effects of loads and elementstiffness, various material penalization models are investigated to showtheir influences on the optimization results and iteration processes.Subsequently, an improved RAMP model with variable parameter is proposed andvalidated. For the problem with inequality volume constraint underself-weight loading, the optimal solution is obtained in stable convergenceway for the first time, also to approach the theoretic solution associatedwith a void structure without material. Theoretical and numerical resultsshowed that the compliance sensitivity remains no longer to be negative dueto the the design-dependent effect of inertial loads. This means that theobjective function is non-monotonous. As a result, the inequality volumeconstraint is not always active at the optimum solution. In other words,less material may lead to a stiffer structure for an optimum materiallayout. Besides, it is shown that the integration of a proper RAMP modelwith the BESO method can improve greatly the result so that both BESO and MPmethods become consistent for self-weight design problem whereas previouslyexisting optimization results obtained by BESO and MP methods are quitedifferent.
2009, 41(4): 530-541. doi: 10.6052/0459-1879-2009-4-2008-326
Nonlinear finite element analysis and experiments of distributed fiber optic sensor system for crack detection
Jiang Chen, Haowu Liu
The micro-mechanical behaviors of fiber-concrete complexin the technology of distributed fiber optic sensor system for crackdetection were investigated. 3-D nonlinear numerical simulation wasperformed with ANSYS, considering the nonlinear interfaces of coating-sheathand sheath-concrete. The bilinear isotropic hardening model was applied forconcrete to relax local stress concentration and avoid excessive penetrationbetween the sheath and the concrete. The mechanical parameters of contactpairs were determined by tests. The microscopic stress distribution infiber-concrete complex and curvature distribution of fiber were obtained.The relationship between crack width and bending loss was analyzedquantitatively. The computational results have shown a good accordance withexperimental results. The influences of fiber layout and sheath thickness onsensing sensitivity and dynamic range have been proved theoretically.Meanwhile, an improved micromechanical analysis was developed for thetechnology of distributed fiber optic sensor system for crack detection.
2009, 41(4): 542-548. doi: 10.6052/0459-1879-2009-4-2008-345
Experimental research and numerical analysis of frozen soil based on endochronic theory
Zhiwu Zhu, Jianguo Ning, Shuncheng Song
Based on the endochronic theory, the basic principle ofthe irreversible thermodynamics of continuum media was used to derive a newendochronic rheological constitutive equation of frozen soil by redefiningthe intrinsic times. The corresponding parameters in the endochronicequations can be determined by the method of the Matlab fitting. Thesolution, analysis and experimental validation of the new equations underuniaxial and triaxial stress were performed. The stress-strain curves oftheoretical calculation are very consistent with the experimental results.Therefore endochronic theory, compared with plastic theory, can be used toavoid the determination of yield surface. Finally, by utilizing theconstitutive relation, we discuss and analyze the numerical solutions offrozen roadbed. The results indicate that the endochronic theory has itsextensive applicability.
2009, 41(4): 549-554. doi: 10.6052/0459-1879-2009-4-2008-017
Convergence of integral functional and variational solutions of displacement and stress of soil due to pile-driving
Zikun Gao, Jianyong Shi
Driving-in piles are widely used in the constructionengineering. There are many theoretical and practical problems with thecompaction effects of pile driving on the soil. Generally, the process ofpile penetration occurs in the semi-infinite and stratified soil. Singlepile has spatial axial symmetry, and the shape and length of piles aredifferent. Therefore, squeezing model due to pile-driving is developed inthis paper to study the effect of the final shape and displacement boundaryof pile wall, stress-free ground surface, the finite length of pile andnon-linearity of soil material. Displacement, strain and stress solutionsare then obtained based on variation principal and their convergence ofimproper integral is also verified. The theoretical scheme is validatedusing passive soil pressure theory, classical CEM results and the numericalsimulation results with Ansys code. The theoretical results illustrate theconvergent three-dimensional improper integral of energy functional and thevalidity of variational solutions.
2009, 41(4): 555-562. doi: 10.6052/0459-1879-2009-4-2007-597
Effect of girder's vibration on performance of cable dampers for cable-stayed bridges
Dong Liang, Limin Sun, Wei Cheng, Hongwei Huang
With the span of cable-stayed bridge increasing, the staycable becomes longer to obtain the close fundamental frequencies of bridgeand cable, and to increase the probability of coupled vibration betweencable and girder. Generally, the dynamic characteristics of long cable aredetermined by the interactions among pylon, cable and girder. One of themost effective vibration mitigation measures is to use mechanical damper forlong stay cables of large span cable-stayed bridges. In the conventionaldesign theory for cable damper, it is assumed that the cable's ends arefixed and one end of the damper is connected with cable and the other end isfixed to girder. However, when the span of cable-stayed bridge becomes largeand the structure becomes more flexible, the effect of girder vibration onthe cable damper performance should be considered. Furthermore, the dampingratio in theoretical analysis is always smaller than in the full-scale cablevibration mitigation tests on actual cable-stayed bridges. Therefore, therelation between girder vibration and the efficiency of cable damper isinvestigated in this paper. A simplified theoretical model with cable,Kelvin damper and girder is analyzed by complex mode method. Model tests arealso carried out to study the influence of girder vibration on the modaldamping ratio of cable. Both theoretical and experimental results show thatthe girder vibration should be taken into account in cable damper design forlong span cable, especially for the coupling vibration with cable andgirder.
2009, 41(4): 563-574. doi: 10.6052/0459-1879-2009-4-2008-225
Study on the characteristics of interaction flowfields induced by supersonic multi-jets
Junqi Wang, Suxun Li
Transverse jet technology has been applied to many aircrafts as an effective way of attitudecontrol. It can provide thrust more rapidly and is affected by less flight conditions thanconventional aerodynamic surface control. Therefore, the maneuverability of the aircraft isenhanced. And less aerodynamic surfaces are needed, thereby the weight is reduced and the stealthperformance is improved. Recently, the method of jet attitude control is paid more and moreattentions.When a sonic or supersonic jet is injected laterally into supersonic or hypersonic free stream,the complex jet interactive flowfields is generated which involves complex flow structures such asshock/boundary layer interaction, multi-shocks interaction, flow separation vortices, and flowreattachment, etc. Although considerable investigations have been carried out for nearly half acentury, but there are many issues unresolved until now in understanding the flowfieldscharacteristics and flowing mechanism.The characteristics of the interaction flowfields induced by lateral supersonic single/multijets mounted longitudinally on the revolution body had been studied by numerical simulation inthis paper. The three dimensional compressible laminar N-S equations were solved by finitevolume method with Roe's two-order spatial scheme and multi-block structure grid. The methodwas validated qualitatively and quantitatively by experimental schlieren photo about theshockwaves showed in three jets interaction flowfields. The spatial structures of single/multi jetsinteraction flowfields and separation regions induced by shockwave/boundary layer interactionwere described in this paper. Four cases including single jet, twin jets, triple jets and five jetsinteraction flowfields had been simulated numerically and analyzed. It is shown that the influencesof the first jet on the structure and separation region of interaction flowfields upstream of the jetswas dominant.
2009, 41(4): 575-583. doi: 10.6052/0459-1879-2009-4-2008-286
Unsteady 1d exact solutions of non-darcy flow in post-failure rock
Ruixian Cai, Yuanyuan Li, Runhua Jiang
Coal will be still the main energy in China. Hence it isstill necessary to research various problems about coalmines In general,seepage flow in post-failure wall rock in coalmines is not controlled byDarcy' Law and described as a nonlinear penetrating system of theAhmed-Sunada's non-Darcy flow. In the present paper, some simple exactanalytical solutions of the partial differential equation set of unsteady1-D Ahmed-Sunada type flow are derived with the method of separatingvariables with addition (MSVA). The MSVA was developed recently by Cai andsuccessfully applied to derive many new analytical solutions. The unknownfunction F(x,y) is assumed to be F(x,y)=f(x)\cdot g(y) in the commonmethod of separating variable, while be F(x,y)=f(x)+g(y) in MSVA. As asequence, three simple exact analytical solutions of Ahmed-Sunada'snon-Darcy flow have been successfully derived.
2009, 41(4): 584-587. doi: 10.6052/0459-1879-2009-4-2008-289
The symplectic method for plane elasticity problem of functionally graded materials
Weiqiu Chen, Li Zhao
There are several typical methods that have been widelyemployed to analyze static and dynamic behavior of functionally gradedmaterial (FGM) structures, such as the simplified analytical methods (basedon one or two-dimensional structural theories), three-dimensional exactelasticity methods, approximate elasticity methods based on laminatedmodels, semi-analytical methods, and the numerical methods. In this paper,the symplectic approach, originally developed for homogeneous orpiece-wisely homogeneous materials, is extended to consider the planeelasticity problem with a rectangular domain of FGM. In the present FGM,Young's modulus varies exponentially with the axial coordinate, whilePoisson ratio remains unaltered. After introducing new stress components,the problem is formulated within the frame of state space, and solved usingthe method of separation of variables along with the eigenfunction expansiontechnique. The operator matrix, called shift-Hamiltonian matrix, is not inan exact Hamiltonian form, since the eigenvalues are symmetric with respectto $ - \alpha / 2$, rather than zero in the standard Hamilton matrix. Inthis case, the symplectic adjoint eigenvalue of zero is induced as $ - \alpha$.The Saint-Venant solutions derived in the paper exhibit some uniquecharacteristics, but they can be degenerated to the ones for homogeneousmaterials after imposing certain rigid motions.The symplectic method enriches the analysis methodology for heterogeneousmaterial. Furthermore, it can indicate the certain physical essence of theproblem that can not be revealed by other methods.
2009, 41(4): 588-594. doi: 10.6052/0459-1879-2009-4-2008-394
A computational inverse technique for reconstruction of multisource loads in time domain
Xu Han, Jie Liu, Weijie Li
The knowledge of the dynamic load acting on the structure is always requiredand important in many practical engineering problems, such as structuralstrength analysis, health monitoring and fault diagnosis, and vibrationisolation. However, it is difficult to directly measure the dynamic load ona structure in some situations, such as the wind load on the tall building,the exciting force from road on the vehicle, etc. Meanwhile, the dynamicresponse measurement is correspondingly easy and accurate on a structure.Therefore, it is necessary to develop some inverse analysis techniques forload identification based on the measured dynamic responses.With the linearity and time-invariant suppositions, the loads are firstlyexpressed as a series of kernels of impulse functions or step functions intime domain and the total response of the system can be obtained using theproduct of the convolution integral of the kernel response and the loads.Through the discretization of convolution integral, the forward model forload identification is established. In fact, the inverse analysis for theload identification is to solve a deconvolution problem, but thedeconvolution is an ill-conditioned problem in which the noisy responses andhigh condition numbers of the kernel matrix will induce the amplified errorsin the identified load. Therefore, it is difficult to obtain a stable andaccurate solution for such inverse problems. To deal with ill-condition ofload reconstruction from the noisy responses, zero-phase digital filter,several regularization methods and optimized strategy for stable loadidentification are discussed. Through general filter, the noisy responsesignal will be smooth. But, it has a phase delaying compared with theoriginal signal, and the errors will also be amplified in the identifiedload. The zero-phase digital filter, whose phase error is zero in the curveof phase-frequency characteristic, is realized through reversing the timeserials of the signal. Moreover, a new extension algorithm is applied toimprove the performance of the filter. Comparing with the common differencefilter, this zero phase digital filter can not only avoid phase delaying,but also improve the wave aberration of the start and end section. After theinvestigation the ill-posedness arising from the inverse problem of loadreconstruction, Tikhonov regularization, truncated singular valuedecomposition and total least squares method are adopted to provideefficient and numerically stable solution of the desired unknown load, andthe $L$-curve method is proposed to determine the optimal regularizationparameter. In order to avoid the inverse operation of the matrix, manyoptimized methods can be available and here the conjugate gradient method isadopted. In the numerical example, the reconstruction of dynamic loads fromtwo sources with the noisy responses in the hood structure is investigated.The result indicates that the presented computational inverse technique iseffective and stable for the load identification with the noisy response intime domain.
2009, 41(4): 595-602. doi: 10.6052/0459-1879-2009-4-2008-038
The vibration suppression system for vertical tail based on smart piezoelectric structures
Qiang Liu, Renwen Chen, Zhiwei Xu, Xinwei Wang
This paper investigated the vibration suppression systemfor vertical tail. Firstly, the actuators and sensors were divided into twogroups according to the results of modal tests, and attached to the oppositeside of vertical tail with a mirror image. To overcome the unstable problemcaused by the coupling of output signal and reference signal, a feed forwarddecoupling algorithm was proposed. Finally a smart vertical tail wasdesigned to reduce the fatigue damage through suppressing its vibration. Theexperimental results showed that the vibration response of vertical tail wassuppressed significantly.
2009, 41(4): 603-608. doi: 10.6052/0459-1879-2009-4-2008-476