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2007 Vol. 23, No. 5

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Implicit algorithm based on dynamic hybrid mesh for incompressible unsteady flows
Laiping Zhang, Xinghua Chang, Xupeng Duan, Zhenya Wang, Hanxin Zhang
An implicit solver for incompressible unsteady flows is presented,based on the dynamic hybrid mesh proposed by the authors previously. Thesolver is based on an artificial compressibility method with dual-timestepping for time advancing. To accelerate the convergence insub-iterations, we use a block LU-SGS coupling with the multi-gridtechnique based on hybrid grids. Several typical cases are simulated tovalidate the flow solver. The numerical results show the efficiency andaccuracy of the solver for incompressible unsteady flows.
2007, 23(5): 577-586. doi: 10.6052/0459-1879-2007-5-2006-397
The coupled numerical model of non-linear wave in harbour
Daguo Wang, Zhili Zou, Chunan Tang
An accurate and efficient 2-D time-domain coupled model fornonlinear wave forces on a ship in a harbor is developed in thepresent paper. The whole domain is divided into an inner domain and an outerdomain. The inner domain is the area around the ship, where the flow isexpressed by Laplace equations. The other area is the outer domain,where theflow is expressed by Boussinesq equations. Matching conditions on theinterface boundaries between the inner domain and the outer domain are thecontinuity of volume flux and the equality of wave elevations. Theprocedure of the coupled solution and the length of the common domain arediscussed in detail. In addition, the boundary element method in complexvariables isadopted to verify the coupled model and the relevant physical experiment isconducted to validate the two numerical models. It is shown that thenumerical results agree well with experimental results, but the computationalefficiency of the boundary element method is much lower than that of thecoupled model, so the coupled model can be used for the wave motions in aharbor with large area and is especially useful for the study on the effectsof harbor boundaries and bottoms on wave forces of a ship.
2007, 23(5): 587-594. doi: 10.6052/0459-1879-2007-5-2006-389
A combined refraction and diffraction water wave model using phase-averaged approach
Jingxin Zhang, Hua Liu
It is important in practical engineering to study the propagation of waterwaves in coastal waters using mathematical modeling methods. The research ofwater waves has progressed very much in the recent decades. Water wave models, suchas mild-slope equation, Boussinesq equation and so on, have been put intopractical engineering applications. But different water wave models havedifferent effectiveness. The respective theoretical basis of the water wave modelsdetermines the features of these models. As mathematical models,based on the conversation law of wave energy or wave action, spectral wavemodels are used to determine wave conditions in coastal regions, which canaccount for all relevant processes of generation, dissipation andpropagation. But the conventional spectral wave models can not simulate thewave diffraction. With diffraction being incorporated, the spectralwave models can be more widely used to simulate waves in the coastalregions. In this paper, a new phase averaged wave model is developed, inwhich the conservation of wave energy or wave action is used to formulatethe wave propagation and a combined refraction and diffraction contributionis coupled through introducing a diffraction factor based on analysis of themild slope equation. Computational results in extreme diffraction casesagree reasonably well with observations. It is shown that the new model canbe used to simulate refraction and diffraction of water waves in coastalregions.
2007, 23(5): 595-601. doi: 10.6052/0459-1879-2007-5-2006-114
Stability analysis of heated panels in supersonic air flow
An investigation on stability of heated panels insupersonic air flow is carried out in this paper. A nonlinear aeroelasticmodel for a two-dimensional heated panel is established using Galerkinmethod. The quasi-steady piston theory is employed to calculate theaerodynamic load on the panel and the even temperature field is considered.At first, the static and dynamic stabilities for flat panels are studied byusing Lyapunov's indirect method and the stability boundary curve isobtained. Then the static deformation of a post-buckled panel is calculatedby Newton iterative approach, and the local stability of the post-bucklingequilibrium is analyzed. The results show that a two-mode model is suitablefor panel static stability analysis and static deformation calculation; butmore than four modes are required for dynamic stability analysis. Theeffects of temperature elevation and non-dimensional parameters related topanel length/thickness ratio, material density and Mach number on thestability of heated panels are also investigated. It is found that panelflutter (secondary instability) may occur at relatively low aerodynamicpressure when there are several stable equilibrium points for theaeroelastic system of heated panels.
2007, 23(5): 602-609. doi: 10.6052/0459-1879-2007-5-2006-539
Analysis of fracture behavior of honeycomb sandwich specimens
Shidong Pan, Linzhi Wu, Yuguo Sun
The flatwise tension test (FWT) and the double cantilever beam (DCB)experiment were used to investigate the fracture behavior of honeycomb sandwichspecimens. In the FWT test, not the interfacial debonding, but the interlaminardelamination was observed. So the test results show that the interfacial peelstrength is higher than the interlaminar peel strength. From the resultsof DCB experiment,a different fracture mode, namely IKP (initiation of interlaminar delamination,kinking into facesheet and propagation of interlaminar delamination), was found. Inorder to simulate the IKP of DCB honeycomb sandwich, a computational modelbased on the Tsai-Hill failure criterion and the cohesive zone model was proposed. Bycomparing with experimental results, it is shown that the computational model caneffectively simulate the IKP of a honeycomb sandwich structures with a reasonableaccuracy.
2007, 23(5): 610-617. doi: 10.6052/0459-1879-2007-5-2006-440
Shape control and design optimization of the piezoelectric curved shell structures
Jian Wang, Guozhong Zhao, Hongwu Zhang
Some flexible structures, like airfoil and satelliteantenna, usually consist of shells and plates. Their working performancesare sensitive to their shape and deformation. However, there are lots ofunpredictable factors, such as temperature, impact, creep and moisture etc.,which could influence the performance of structure. It is impossible anduneconomical to consider all detrimental factors in the design stage. Thus, it isnecessary to control the structure shape by some technologies. This paperpresents a finite element formulation for the numerical simulation of thespatial curved shell structures with piezoelectric actuators, in which thehost shells and piezoelectric patches are related with constraint equationsdirectly. The use of the constraint equations reduces the number of the DOFand improves the computation efficiency. Based on the proposed model, theoptimum structure shape and a perfect voltage distribution can be obtainedby using the linear least squares method (LLSM). Furthermore, thicknessdistribution of the piezoelectric patches is obtained by nonlinearconstraint optimization method (NCOM). Numerical examples are given todemonstrate the validity of the model proposed.
2007, 23(5): 618-625. doi: 10.6052/0459-1879-2007-5-2006-508
Analysis of critical axially copmressive loads for viscoelastic laminated circular cylindrical shells
Fan Peng, Yifan Liu, Yiming Fu
The critical buckling loads of viscoelastic laminatedcircular cylindrical shells under axial compression are investigated withinthe theory of classic buckling. Boltzmann hereditary linear constitutiverelationship is used to model the viscoelastic behavior of lamina. Bothgoverning equations of Donnell type and boundary conditions in phase domainare obtained by Laplace transformation. The deflections and in-plane forcefunctions are expressed in series form of separate variables with circumferentialpart in trigonometric functions. The generalized eigenvalue problemin phase domain of determining the critical axial load is studied by means ofthe differential scheme with respect to the axial coordinate. Applying thetheorems of asymptotic value and initial value for Laplace inversetransformation, we obtain, respectively, the formulation of transientelastic critical loads and durable critical loads. The focus of thispaper is on the investigation of these criticed loads. Boron fibre/epoxy andgraphite fibre/epoxy materials are used in the analysis. Numericalresults indicate that, in the cases of both symmetrical and antisymmetricalply-up configuration, transient elastic critical loads and durablecriticalloads see similar trends of variation with ply angle and reach theirmaximum values at a respective ply angle of little difference regardless ofboundary conditions at two ends. It may be observed, however, that the plyangles corresponding to the peak values of these two types of critical loaddiffer by $5^{\circ} \sim 10^{\circ}$ in the arbitrary ply-up mode and thisdifference is dependent on the stacking sequence, the geometric parametersand the type of material as well. The conclusions drawn in the paper canexpect to be applicable to the optimal design of laminated circularcylindrical shells concerning the capability in delayedbuckling.
2007, 23(5): 626-632. doi: 10.6052/0459-1879-2007-5-2006-536
Lower bound limit analysis by using the element-free galerkin method with orthogonal basis
Shenshen Chen, Yinghua Liu, Zhangzhi Cen
The limit analysis of structures is a very usefulin plasticity, which can determine the load-carrying capacityof structures and provide a theoretical foundation necessary forengineering design. The elasto-plastic incremental analysis is moregeneral and yields more information often at higher computational effort.But, in many practical engineering problems, only limit loads and collapsemodes are important, and the stress and strain field histories are notrequired. In order to avoid the complicated computations ofelasto-plastic incremental analysis, the limit analysis is an appealing directmethod for determining the load-carrying capacity.Based on the lower bound theorem of limit analysis, a solution procedure forlimit analysis of structures made of elasto-perfectly plastic material ispresented firstly making use of element free Galerkin (EFG) method withorthogonal basis. The numerical implementation is very simple and convenientbecause it is only necessary to construct an array of nodes in the domainunder consideration. In addition, the orthogonal basis functions areconstructed in the moving least squares (MLS) approximation so that the matrixinversion at each quadrature point is avoided. The elastic stress field forlower bound limit analysis can be computed directly by using the EFG methodwith orthogonal basis. The self-equilibrium stress field is expressed bylinear combination of several self-equilibrium stress basis vectors withparameters to be determined. These self-equilibrium stress basis vectors aredetermined by an equilibrium iteration procedure during the elasto-plasticincremental analysis. Through modifying the self-equilibrium stress subspacecontinuously, the whole solution process of the problem is reduced toseveral sub-problems of nonlinear programming. The complex method is used tosolve these nonlinear programming sub-problems and determine the maximalload amplifier. Numerical examples show that the present method overcomesthe dimension obstacle and improves the computational efficiency of the limitanalysis.
2007, 23(5): 633-640. doi: 10.6052/0459-1879-2007-5-2006-567
Non-probabilistic set-based model for structural reliability
Xiaojun Wang, Zhiping Qiu, Zhe Wu
Due to the limitations of the originaldata for a probabilistic reliability model and the fuzzy reliability model, a new non-probabilistic set-based model for structural reliabilityanalysis is proposed, with the uncertain information in structural reliability being described as interval set. Based on the non-probabilistic set-basedstress-strength interference model established in this paper, the ratio ofthe volume of safe region to the total volume of the region constructed bythe basic interval variables is taken as the measure of structuralnon-probabilistic reliability. This kind of measure has a clearermeaning than the allowable maximum amount of uncertainty before structurefailure proposed by Ben-Haim and the minimum distance from theorigin to the failure plane proposed by Guo. Furthermore, thecompatibility of measures between the presented non-probability set-basedreliability model and the probabilistic reliability model is proved.
2007, 23(5): 641-646. doi: 10.6052/0459-1879-2007-5-2006-629
Chaos control of form iterative algorithm in structural reliability analysis
The HL-RF algorithm of First Order ReliabilityMethod (FORM) in structural reliability analysis is an iterativealgorithm for reliability index with a wide application. However, itsometimes suffers from convergent failure such as periodic oscillation,bifurcation and chaosfor some nonlinear limit state functions. The convergent failure of FORM iscontrolled by using chaos control principle in the present paper. Theinherent relationship of various kinds of methods for global and local chaosfeedback control is clarified. It is shown that the stability transformationmethod and adaptive adjustment method are global chaos feedbackcontrol method, and the adaptive adjustment method can be viewed as aspecial case of the stability transformation method. The parameter adjustmenthybrid method is only a different form of the relaxed Newton method, bothof which are local chaos feedback control methods. Thecorresponding relationship between the formulations of chaos feedbackcontrol and iterative schemes for convergence control in engineeringmechanics is explored. Furthermore, the effectiveness and limitations ofthese measures for convergence control of iterative algorithms arediscussed.An effective, simple and general chaos feedback control methodcombining the stability transformation and relaxed Newton method isproposed, which is applied to control the periodic oscillation, bifurcationand chaos of FORM iterative algorithm for reliability analysis.
2007, 23(5): 647-654. doi: 10.6052/0459-1879-2007-5-2006-501
Conical vortex induced wind loading on the roof of a building
Xuerui Chen, Zhifu Gu, Yan Li
By means of wind tunnel simulation the wind loading on theroof of building induced by conical vortex is investigated. The pressuredistributions on the roof of the model are obtained and the mechanism of the flowis analyzed. The structure of separated flow from the roof of buildingis shown to vary with wind directions and its developing process is also analyzed.It is indicated that appearance of conical vortex is the main reason ofoccurrence of the peak suction on the roof. Results show that under certainwind directions the local time mean pressure coefficients are greater than$-1.0$. Moreover, the intensity of conical vortex reaches the maximum valueat the wind direction $\beta =30^\circ$ and the time-mean peak suction andfluctuating coefficients may reach $-2.4$ and $-5.7$, respectively. It isusually the main cause of damage for the roof of buildings duringstrong winds.
2007, 23(5): 655-660. doi: 10.6052/0459-1879-2007-5-2006-396
Study on reaction zone structure of gaseous detonation wave by planar laser induced fluorescence technique
Changjian Wang, Shengli Xu, Lisen Fei
The reaction zone structure of gaseous detonationwave in stoichiometric hydrogen-oxygen mixture diluted with 76.92{\%} argonwas directly observed by planar laser induced fluorescence technique. Suchhigh argon dilution was employed to degenerate natural fluorescence mainlycaused by detonation chemical reaction. The synchronization of the PLIFsystem, the detonation wave and ICCD were carefully adjusted. The images ofOH fluorescence distribution in the wake of the detonation front were obtained.These images show that the reaction zone is spatially and temporallychangeable and the reaction front is not planar and is very unstable. Thedistinct keystone-like structure, with the incident shock,the shear layers and the reaction front as its boundaries, can be clearly observed. Whetherthe OH concentration is behind the Mach stem or the incident shock, itabruptly increases to the maximum value at the end of the induction zone andthen decreases with increase of the distance from the reaction front. Due tothe effects of the detonation mode and laser sheet direction, the transversewave spacing measured from the PLIF images exhibits a relatively largescatter, and assumes a value smaller than the cell width.
2007, 23(5): 661-667. doi: 10.6052/0459-1879-2007-5-2005-639
Phase errors and their correction in symplectic implicit single-step algorithm
Yufeng Xing, Rong Yang
For dynamic systems, an algorithm without theaccumulation of phase errors and magnitude errors isideal, but not easy to be found. Although there is no accumulation ofmagnitudes errors in Symplecticdifference algorithms, but the phase errors do accumulate. In this paper, thephase errors of single-step implicit symplectic algorithms, such assymplectic RK algorithms, are analyzed for linear systems withdamping and without damping, and the correction technique is proposed, which issimple and practical. The Euler implicit midpoint integration algorithm isadopted to solve several linear problems, and the results show that thecorrection technique of phase errors is valid. It is concludedthat the phase error is directly related to the quantity $h\omega $,which is the product of time step and frequency. The higher the frequency,the higher the phase error; and it is hard to control the phaseerrors for MDOF systems.
2007, 23(5): 668-671. doi: 10.6052/0459-1879-2007-5-2006-561
A Generalized Precise Time Step Integration Method
Minghui Fu, Zuoqiu Liu, Jinghua Lin
A precise time step integration method (PTSIM) applied for linear time-invariant dynamic system with non-homogeneous vectors is presented, which is of the same accuracy of the precise time step integration method of general solution. Firstly, the domain of integration is separated into sections. And then a particular solution in the form of integration is chosen and is solved by precise numerical algorithm. Secondly, when the non-homogeneous vector is kind of polynomial, exponential function or trigonometric function, the integration can be converted to a recursion. So the particular solution in the form of integration is precisely obtained by only matrix multiplications. The merit of the new PTSIM is that the process of calculating the general solution and the one of calculating the particular solution are organically combined together. And it is of high precision, efficiency and widely applicability. Numerical examples are given to demonstrate the validity and efficiency of the new PTSIM.
2007, 23(5): 672-677. doi: 10.6052/0459-1879-2007-5-2007-048
Love waves in a graded half-space with a graded layer
Ligang Zhang, Bingzheng Gai, Hong Zhu, Lin Yuan
The dispersion of Love waves is studied in afunctionally graded elastic half-space covered with a functionally gradedmaterials layer and the general form of Love wave dispersion equation isobtained. In the functionally graded elastic half-space and thefunctionally graded covered layer, the motion control equations for the antiplaneshear wave are solved, the analytical solutions for displacement and stressare obtained, and with these analytical solutions, the dispersion equation of Lovewave is obtained. As an example, with the properties of the coveredlayer, theshear elastic modulus and mass density, varing gradually in exponentialforms, and those of the half-space varing gradually in parabolicforms, the dispersion equations are solved by using the iteration method and thecurves of dispersion are obtained. The results show that cut-off frequencyappears in the dispersion curve of the lowest mode.
2007, 23(5): 678-684. doi: 10.6052/0459-1879-2007-5-2006-436
Fracture analysis of a functionally graded coating under plane deformation
Zhanqi Chen, Zheng Zhong
In this paper, the plane elasticity problem for afunctionally graded coating containing a crack bonded to homogeneousmaterial substrate is studied. It is assumed that in the coating,the reciprocal of the shear modulus is a linear function of the coordinate,while Poisson's ratio keeps constant. By utilizing the Fouriertransformation technique and the transfer matrix method, the mixed boundaryproblem is reduced to a system of singular integral equations, which aresolved numerically. The influences of the geometric parameters and thegraded parameter on the stress intensity factors are investigated. Thenumerical results show that the graded parameters, the thickness of coating,and the crack size have significant effects on the stress intensity factors.
2007, 23(5): 685-691. doi: 10.6052/0459-1879-2007-5-2006-503
Determination of the direction of plastic strain increment for geomaterials
Yangping Yao, Kai Sun, Dechun Lu
As shown in a great amount of test results and theoreticalanalyses, the direction of plastic strain increment for geomaterials isdifferent from that of stress. The direction of plastic strain increment formetals is determined by the stress on its characteristic plane--octahedralplane and it is the same as the direction of stress. Based on the analogybetween geomaterials and metals as well as the concept of the characteristicplane, the direction of plastic strain increment for geomaterials can bedetermined by the direction of the stress on their characteristic plane (SMPplane). The equations for the determination of the direction of plastic strainincrement are proposed. They can be applied to the cohesivematerials by adding a material parameter. Finally these equations arevalidated by the test data. The proposed equations are also used in ModifiedCam Clay revised by transformed stress, which can simulate the test data well.
2007, 23(5): 692-698. doi: 10.6052/0459-1879-2007-5-2006-582
Stress analysis for an elliptical hole with two straight cracks
Junhong Guo, Guanting Liu
Using the complex variable function method and the technique of conformalmapping which transforms the complicated region in physical planeonto the interior of the unit circle in $\zeta$ plane, then based on Cauchy integral theory, the plane elasticity problem of anelliptical hole with two straight cracks is solved, and the analyticsolutions of the stress intensity factors for mode Iand mode II problems are obtained. Under the limiting conditions, the present results are reduced tothe results of the well-known Griffith cracks. Moreover, they include the cross crack and the circular hole withtwo straight cracks. Analytic solutions obtained in thispaper are useful in materials science and engineering.
2007, 23(5): 699-703. doi: 10.6052/0459-1879-2007-5-2007-017
Conjugate second-order deflection differential equation of global shell axial symmetrical bending problem
Cunxu Fan
In this paper, the conjugate second-order deflectiondifferential equation is derived for the global shell axial symmetricalbending problem, and the solution in elementary functions is obtained.Shell of revolution is one of the three basic shells in thin shell theoryand the global shell differential equation is a typical equation for shell ofrevolution. The conjugate second-order deflection differential equation is notonly the simplest global shell differential equation but also the deflectiondifferential equation most commonly used. Differential equationof deflections can satisfy the boundary conditions simply, whichsimplifies the calculation.
2007, 23(5): 704-707. doi: 10.6052/0459-1879-2007-5-2006-442
Multi-objective design of the multi-phase microstructure for thermal conductivity optimization
Fengwen Wang, Weihong Zhang, Shiping Sun, Xiaolu Gong
In this paper, a new method based on the heat dissipation ofmicrostructure is proposed to predict the thermal conductivity of thematerial microstructure. This method is shown to be equivalent to the homogenizationmethod both theoretically and numerically. Based on the finite elementdiscretization of the microstructure, the sensitivity analysis for theeffective thermal conductivity is carried out and the topologyoptimization model of the heat-conducting microstructure is built tomaximize the different combinations of effective thermal conductivitycoefficients related to 2D and 3D multiphase materials. The dualoptimization scheme and the quadratic perimeter constraint are used tosolve the problem and to control the checkerboard pattern duringoptimization procedure. Numerical examples show that the design of themicrostructure using the heat dissipation is effective and can providesatisfactory design results with respect to material microstructures.
2007, 23(5): 708-715. doi: 10.6052/0459-1879-2007-5-2006-278
Analytical approximations for nonlinear dynamic system with multiple limit cycles
Jun Cheng, Shijun Liao
A modified Rayleigh oscillator with multiplelimit cycles is investigated by means of a new analytical method fornonlinear problems, namely, the homotopy analysis method (HAM). TheHAM is independent upon small parameters. More importantly, unlike other traditional techniques, the HAM provides us with asimple way to ensure the convergence of solution series. Thus, theHAM can be used for strongly nonlinear problems. Comparisons of thesolutions given by the HAM, the method of averaging, and Runge-Kuttamethod show that the method of averaging is not valid for stronglynonlinear cases, and the Runge-Kutta numerical technique does notwork for the instable limit cycles,however, the HAM not only works for strongly nonlinear cases, butalso can give good approximations for the instable limit cycles.
2007, 23(5): 715-720. doi: 10.6052/0459-1879-2007-5-2006-408