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2004 Vol. 36, No. 3

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Nonlinear Stochastic Finite Element Analysis Of Viscoelastic Structures
The large deformation problems of viscoelastic structureswith random parameters were investigated. The nonlinear viscoelasticstochastic principle of virtual work based on the Total Lagrangian approachwas established in which incremental method was applied to solve thehereditary integrals, local averaging method was adopted to discretize therandom field, and perturbation method was employed to consider therandomness of parameters. The uncorrelated transformed random variables wereintroduced into formulations by correlation matrix decomposition algorithm.Only a few independent random variables were required to represent the majorcharacteristics of stochastic structures. It simplified the formulation andsaved the computer cost. The geometrically nonlinear relations aswell as randomness between displacement and strain field were investigated.After deriving the stochastic constitutive relations between the secondPiola-Kirchhoff stress tensor and Green strain tensor, the nonlinearviscoelastic stochastic finite element formulae were put forward. TheNewton-Raphson iterative method was used for the solution of the nonlinearequilibrium equations. The combined influence of viscoelasticity,geometrically nonlinearity and randomness could be investigated using theinnovated method. Monte-Carlo simulation was used to verify the accuracy ofthe proposed methods. As a numerical illustration, the responses ofviscoelastic solid rocket motor grain under internal pressure werepresented. It is proved by the numerical results that the present method isespecially suitable for viscoelastic stochastic structures with largedeformation.
2004, 36(3) doi: 10.6052/0459-1879-2004-3-2003-198
Load-Induced Damage Of The Interface Between Structure And Coarse Grained Soil
The monotonic and cyclic behavior of the interfacebetween structure and coarse grained soil was investigated through teststudy in both macroscopic and microscopic way. The internal relationshipbetween micro-physical state change and macro-mechanical response isdiscovered through analyzing the observationresults of the interface. The concept of damage is therefore extended tocharacterize the evolution of the physical states as well as resultingevolution of the behavior of the interface between structure and coarsegrained soil, which develops continuously from the initial state to theultimate state. The evolution of the physical statesmainly consists of the crushing and compression of soil particles near thestructure. The volumetric strain due to dilatancy of the interface could bedivided into reversible and irreversible dilatancy component, in which theirreversible dilatancy component could essentially indicate the evolution ofthe physical states as well as the behavior of the interface. Theirreversible volumetric strain due to dilatancy is then demonstrated as ameasurement of the damage extent of the interface, which could be normalizedas damage variable. Finally, a new scheme is presented to constitute adamage model of the interface between structure and coarse grained soil.
2004, 36(3) doi: 10.6052/0459-1879-2004-3-2003-231
Analytical Solutions For Axisymmetric Bending Of Functionally Graded Circular/Annular Plates
Based on the first-order shear deformation plate theory, governing equationsfor the axisymmetric bending of functionally graded circular/annular platesare derived in terms of displacements. Then, analytical solutions for thedisplacements, force and moment resultants are obtained by directly solvingthe governing equations. It is assumed that the temperature field variesthrough the plate thickness only, and the mechanical and thermal propertiesof the plate vary continuously through the plate thickness and obey a simplepower law related to the volume fraction of the constituents. As examples,solutions for the clamped and simply supported circular plates are derived. Effects of the gradient constant of material, sheardeformation and boundary conditions on the deflection of the plate arediscussed in details. The following conclusions can be reached.(1) The effect of transverse shear deformation on the axisymmetric bendingof functionally graded circular plate can be effectively considered by useof the first-order shear deformation plate theory.(2) The method used in the present paper is simple and effective. If thethermal loading is neglected, the present solutions reduce to the solutionsobtained by Reddy et al. If the gradientconstant of material is equal to zero, then the present solutions reduce tothe solutions for isotropic plates. Moreover, if one neglects the gradientconstant of material and the transverse shear deformation, the presentsolutions reduce to the solutions based on the classical plate theory.(3) The material constant $n$ and boundary conditions have important effectsonthe bending behavior of functionally graded circular plates. Thermal loadinghas no effect on the deflection of the clamped plate, but has significanteffect on the deflection of the simply supported circular plate.
2004, 36(3): 6-6. doi: 10.6052/0459-1879-2004-3-2003-200
The Study Of Aerodynamic Characteristics Of Afterbody And Effect Of Cable-Mounting
The purpose of this paper is to study the effect ofcable-mounting on flow over an afterbody of a aircraft. The experimentalresults show that: (1) the flow patterns over afterbody can be divided intoupper-separated, non-separated and under-separated type; (2) thecable influences the aerodynamic characteristics of the model by affectingthe vortex structure over it; (3) the basic flow patterns overafterbody have not been changed evidently by any of these three types ofcable-mounting configuration.
2004, 36(3): 257-264. doi: 10.6052/0459-1879-2004-3-2002-426
Numerical Modelling Of Dusty Atmospheric Flows Over An Erodible Surface
In the framework of the two-fluid model of dilute dusty gases, the present paper gives the governing equations for dusty atmospheric flows, where the two-way coupling is taken into account in the source terms. The similarity criteria are derived for dynamical behaviors of the carrier- and dispersed-phase and they include seven parameters such as the Froude number, the dust mass loading and so on. As a model problem, the aerodynamic entrainment of the dust and sand particles in the fully developed turbulent atmospheric boundary layer over an erodible surface are studied and the aerodynamic drag as well as the Saffman lifting and gravity forces are considered. To overcome the difficulties associated with the non-uniqueness of the flow parameters due to the intersection of particle trajectories, the continuity equation of the dispersed phase is introduced in the Lagrangian coordinates. The motion characteristics and concentration distributions of the dispersed phase are simulated numerically at two different wind speeds and four different particle sizes and the effects of wind velocity and dust size are discussed in detail. These results are also relevant to the energy exchange process between the two phases in the atmospheric boundary layer. The equations, criteria and method may be useful in interpretation of some natural disaster phenomena such as wind erosion and sand-dust storm.
2004, 36(3): 265-271. doi: 10.6052/0459-1879-2004-3-2002-413
Finite Element Of Elasticity With Couple-Stress Using The Analogy Between Plane Couple-Stress And Reissner/Mindlin Plate Bending
In order to include the effect of microstructure, thetheory of elasticity with couple stress considers couple stress which doesnot appear in the classical elasticity theory. However, there exists acrucial C$^{1}$ continuity difficulty in the finite element formulation ofelasticity with couple stress.The analogy between plane elasticity with couple stress and Reissner/Mindlinplate bending provides an important way to avoid the C$^{1}$ continuitydifficulty. According to the analogy, the C$^{1}$ continuity difficulty canbe avoided naturally by the formulation in the space of stress functions,and the formulation can be analogous to the one of certain Reissner/Mindlinplate bending element in the space of transversal deflection and rotation.The unsettled problem is how to transform the finite element with stressfunctions as degree of freedom (DOF) into the one with usual planardisplacement and rotation as DOF. Using the analogy, the present workprovides an effective and rigorous method to deal with this problem. Thefinal finite element has two important characteristics. Firstly, theformulation in space of stress functions avoids C$^{1}$ continuitydifficulty. Secondly, the discrete unknown DOF are usual displacement androtation.As an application of the present method, a finite element of plane couplestress with 12 DOF is transformed from the eight nodes serendipityReissner/Mindlin plate bending element. Numerical results of typicalproblems show that the present element has satisfactory precision andconvergence.
2004, 36(3): 272-280. doi: 10.6052/0459-1879-2004-3-2003-203
A Study Of Calculating Methods For Residual Strength Of Corrosion Pipelines
In this paper, common criterions about residual strengthevaluation at home and abroad are generalized and seven methods areacquired, namely ASME-B31G, DM, Wes-2805-97,CVDA-84 and J integral methods.BP neural network are combined with genetic algorithm (GA) named by modifiedBP-GA methods to successfully predict residual strength and criticalpressure of injecting corrosion pipelines. Examples are shown thatcalculation results of every kind of method have great difference andcalculating values of Wes-2805-97 criterion, ASME-B31G criterion and CVDA-84criterion fracture mechanics model are conservative and higher than those ofJ integral methods, while calculating values of DM fracture mechanics modelare dangerous and less than those of J integral methods and calculatingvalues of modified BP-GA methods are close and moderate to those of J integral methods. Therefore modified BP-GA methods and J integral methodsare considered better methods to calculate residual strength and criticalpressure of injecting corrosion pipelines.
2004, 36(3): 281-287. doi: 10.6052/0459-1879-2004-3-2003-089
Adjoint Shape Sensitivity Analysis Based On Generalized Variational
Variational principle for adjoint design sensitivity analysis wasfirst developed by Arora. The original form of the principle is stated interms of an augmented functional that is defined by adding to the responsefunctional whose sensitivity is required, the weak form equilibrium equationof the primary problem. In the present paper, a new adjoint shapesensitivity analysis method for shape optimization of continuum structuresis proposed. Based on the generalized variational principle, the shapevariation of the displacement prescribed boundary and the associatedderivatives of the prescribed boundary conditions is considered in aconsistent way. The proposed method eliminates the limitation of Arora'smethod for dealing with the variations of Dirichlet boundaries and providesa new framework for shape sensitivity analysis. An analytical exampleillustrates the effectiveness and validity of the proposed approach.
2004, 36(3): 288-295. doi: 10.6052/0459-1879-2004-3-2003-220
Piezoelectric Cantilever Actuator Subjected To A Linearly Distributed Loading
The inverse method is traditionally used to solve elasticproblems. In the present paper this method is applied for a piezoelectriccantilever actuator subjected to a linear distributed loading on the uppersurface. Nonlinear body force $F_z $ is also considered. The stress functionand induction function in the form of polynomials are obtained. The generalsolutions as well as the influence of the distribution profile of body forceon this solution are discovered. From this conclusion the solutions of thecantilever actuator with constant body force and without body force can beeasily found. This work provides a feasible method to study other kinds offunctionally gradient piezoelectric microstructures.
2004, 36(3): 305-310. doi: 10.6052/0459-1879-2004-3-2002-039
A Kind Of New Nonsingular Boundary Integral Equations For Elastic Plane Problem
A new approach is presented, in which thenonsingular IBIE is established. A numerically systematic scheme isestablished by adopting quadratic Lagrange's elements.A new geometry boundary approximatetechnique is presented. Some numerical examples will be applied to validate the current scheme. It is shown that a betterprecision and high computational efficiency can be derived by thepresentation, especially the numerical results of boundary quantities match theexact solutions very well. Besides, it can be easily extended to the threedimensional problems.Compared with the direct unknown's situation, the present approach has manyadvantages:1) it is not necessary to deal with the HFP so that it is simpler,and with better precision and high computational efficiency. 2) The presentation only requires algebraic manipulations so that it can easilybe extended to the other problems, such as potential problems and Stokesproblems. 3) This paper establishes a technique applicable for thecalculation of CPV integrals.
2004, 36(3): 311-321. doi: 10.6052/0459-1879-2004-3-2003-153
Dynamic Characteristic Analysis Of Liquid-Filled Tanks As A 3-D Fluid-Structure Coupling System
In this paper, the 3-D liquid-filled tank is considered as aFluid-Structures Interaction (FSI) system that consists of the ideal,compressible fluid with free surface and the linear, elastic solid withthin thickness. This system is simulated with Finite Element (FE)method. In the FE model, the liquid is discrezied by pressure bodyelement and the tank is characterized by displacement shell elements.Since the coupling equation of this FSI system is unsymmetric, Arnoldi'smethod is adopted to get the dynamic characteristics of theliquid-filled tank. In addition, the shift-frequency technique isintroduced to solve the problem of zero frequency and an iterationmethod is adopted to make the computation both accurate and economical.A numerical simulation of a liquid-filled tank is carried out to confirmthe effectiveness of these methods.
2004, 36(3): 328-335. doi: 10.6052/0459-1879-2004-3-2002-289
Buoyancy Effects On Mixed Convection Flow And Heat Transfer
A combination of a hot/cold wire technique was used for thesimultaneous measurements of instantaneous velocity and temperature in avertical pipe. The detailed study of the effects of buoyancy on flowcharacteristics and heat transfer of opposing mixed convection had beencarried out experimentally. The performance of cold wire for temperaturecompensating the velocity reading of a hot-wire probe due to varying fluidtemperature was assessed. Heat transfer results for opposing mixedconvection have been presented in non-dimensional equations using thebuoyancy parameterΩ(Ω= Grd / Red2), inwhich Red ranges from 900 to 18,000 andΩfrom 0.004899 to0.5047. It is found that theheat transfer is enhanced due to buoyancy effect. With the increasing ofGrd (Grashof number), the temperature fluctuation, streamwise Reynoldsnormal stress and streamwise heat flux are increased, especially in the nearwall region. The combination of hot/cold wire enables the study ofnon-isothermal flow characteristics, thus it is helpful to look inside ofbuoyancy effects on heat transfer in the mixed convection flows.
2004, 36(3): 336-341. doi: 10.6052/0459-1879-2004-3-2002-411
Transient Disturbance In A Half-Space Due To Moving Line Heat Source Using Thermoelasticity Without Energy Dissipation
In this paper transient problem created by a line heat sourcethat suddenly starts moving with auniform velocity inside isotropic homogeneous thermoelastic half-spaceare studied using the GN theory of generalized thermoelasicity.The problem is reduced to the solution of three differential equationsby introducing the elastic and the thermoelastic potentials. Using theLaplace and Fourier transforms, the solutions are first obtained in thetransform domain. Applying the inverse transforms, the approximatesolutions, valid in short time range, are then derived. Thedisplacements are calculated at the boundary for short time. Also theapproximate region valid for the solutions is given and two specialcases, (i) the source is motionless and (ii) the uncoupled theory, arestudied. Numerical evaluations are presented for the medium of copper.
2004, 36(3): 342-347. doi: 10.6052/0459-1879-2004-3-2003-147
Analyses Of Crack-Tip Fields Of Plane Piezoelectric Materials By The Hybrid Stress Finite Element Method
A hybrid stress finite element based on the complexpotential theory and hybrid variational principle is proposed formechanical-electrical coupling analyses. The formulations are given indetail in this paper. The complex series solutions satisfying theequilibrium equations and compatibility equations are chosen as thedisplacement and stress fields in the element domain. Assume that the seriessolutions satisfy exactly the traction free and the zero normal electricaldisplacement boundary conditions along the crack surface in advance. Whilethe displacements along the element outer boundaries vary parabolically. Theelement stiffness matrix is then obtained by using the Gauss quadraturemethod. Numerical examples verify the accuracy of the program and theefficiency of the proposed element. Meanwhile, the theoretical results areverified by the finite element results.
2004, 36(3): 354-358. doi: 10.6052/0459-1879-2004-3-2003-110
Multiscale Methods For Nonlinear Analysis Of Composite Materials
A composite material is called spatially periodic if itis possible to be decomposed into elementary components or cells ofperiodicity. The characteristic size of the single cell of periodicity isassumed much smaller than the geometrical dimensions of the structure whichis therefore composed of a large number of cells. The great achievementshave been obtained from the research of homogenization algorithm based onthe elastic assumption. Because the failure process of material is generallyrelated to the nonlinear analysis of the materials, the research work on themulti-scale analysis of the nonlinear behaviors of the materials is moresignificant for engineering applications. However, due to the difficultiesof the solving of nonlinear problems, the research work will be more complexand more difficult than those performed for the elastic homogenizationanalysis. The numerical approach in the paper differs somewhat from thoseproposed in previous studies. For micro-macro analysis of periodic materialcomposed of elastic granules with contact characteristics, this paper adoptsthe method which was developed by the first author. The basic principle ofthe method is based on the numerical constitutive model. The importantfeatures of developed algorithm are that during the process of establishingmacroscopic constitutive law the stick-disengage-slip behaviors in thegranular contact interfaces are taken into account. Different from the purecontact problem, the stick relationship considers initial stick cohesionbetween the granules when the sticking state is destroyed (the material willthus proceed a damaged state). For the micro-macroscopic analysis ofmulti-phase elastic-plastic materials, according to transformation fieldtheory, a consistent algorithm for elastic-plastic material analysis onmicro-macroscopic is proposed. The basic theories for the establishing ofthe numerical method are introduced first in the paper, and then thenumerical technique is described in detail. Finally, the numerical exampleis presented to demonstrate the validity and efficiency of the twoalgorithms.
2004, 36(3): 359-363. doi: 10.6052/0459-1879-2004-3-2002-364
Global Optimization Method For Computing Frequencies Of Structures With Interval Uncertain Parameters
Based on the inclusion monotone property of intervalfunctions, a global optimization method is proposed to compute the upper andlower bounds of the natural frequencies of uncertain structures. Twocomputational models are presented, in which the interaction among uncertainparameters in the stiffness matrix and the mass matrix was neglected ortaken into consideration respectively. A real code genetic algorithm is usedto solve these optimization models. A monotone analysis method, which canobtain the exact frequencies' intervals of shear-frame structures andmulti-mass-spring systems, is introduced to illustrate the effectiveness ofthe proposed method. Numerical examples showed that the interaction amongthe uncertain parameters in the stiffness matrix and the mass matrix shouldbe taken into consideration and the results of interval perturbation methodcould be improved distinctly. The method to form the interval stiffnessmatrix and the interval mass matrix firstly and then consider theeigenvalues' intervals of the general interval matrix eigenvalue problemabout the obtained interval matrices as the solution of the uncertainstructures may enlarge the solution domain of the original problem.
2004, 36(3): 364-372. doi: 10.6052/0459-1879-2004-3-2003-291
Approximate Analytical Solution Of The Piecewise-Smooth Nonlinear Systems Of Multi-Degrees-Of-Freedom ------The Self-Excited Vibration Of The Chinese Cultural Relic Dragon Washbasin
Piecewise-smooth nonlinear dynamics system caused by dryfriction is becoming hot problems in mechanics with the development ofscience and technology. The study of nonlinear dynamics including dryfriction systems has made many progresses. Because of the complexity ofequations, many researches were based on phase-plane orbit analysis andnumerical analysis and experimental research. In this paper, a mathematicalmodel of self-excited vibration caused by dry friction between two elasticstructures was established using the Chinese cultural relic dragon washbasinas an example. An approximate analytical solution of the piecewise-smoothnonlinear dynamics systems of multi-degrees-of-freedom induced by dryfriction was derived by means of averaging method. According to theapproximate analytical solution, the curves of relation between swing andrubbing velocity of hands, the relation between swing and natural frequencyof hands and the relation between phase angle and rubbing velocity of handswere obtained. The vibration mechanism of the water droplets spurtingphenomenon of the Chinese cultural relic dragon washbasin is furtherexplained. The results not only enhanced the precision but also explainedqualitatively the whole kinematic process. If the parameters of the systemin the design were changed, the design could be optimized according to therelated curves, which supplied the theoretical basis foridentifying parameter and analysis and research of steady region of thiskind of nonlinear vibration systems. Furthermore, the results are inexcellentagreement with that of the numerical solution, so that an efficient andcredible analytical method to investigate piecewise-smooth nonlinear systemsof multi-degrees-of-freedom was given in this paper.
2004, 36(3): 373-378. doi: 10.6052/0459-1879-2004-3-2003-103
Discussion On The Effect Of Gravity On Mass Transfer Of Hemodialysis Of Artificial Kidney
By means of numerically simulating mass transfer of ureaat four different placements (placed horizontally with dialysate entranceup, placed horizontally with dialysate entrance down, placed vertically withblood flow direction up, placed vertically with blood flow direction down)of artificial kidney, we qualitatively investigate the effect of gravity onmass transfer performance of hemodialysis, and acquire 3-D concentrationfields and clearances of urea at all placements. The results indicate thatthe effect of gravity on mass transfer of artificial kidney is notable.Under the gravity effect, the clearance with blood flow direction up (moduleis placed vertically) is the greatest, and the clearance with dialysateentrance up (module is placed horizontally) is the second. The results areof significance in improving the clinical efficiency and optimizing design ofartificial kidney.
2004, 36(3): 379-384. doi: 10.6052/0459-1879-2004-3-2002-367