有限元分析中英文对照资料.docx

有限元分析中英文对照资料.docx

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有限元分析中英文对照资料

Thefiniteelementanalysis

Finiteelementmethod,thesolvingareaisregardedasmadeupofmanysmallinthenodeconnectedunit（adomain）,themodelgivesthefundamentalequationofsharding（sub-domain）approximationsolution,duetotheunit（adomain）canbedividedintovariousshapesandsizesofdifferentsize,soitcanwelladapttothecomplexgeometry,complexmaterialpropertiesandcomplicatedboundaryconditions

Finiteelementmodel:

isitrealsystemidealizedmathematicalabstractions.Iscomposedofsomesimpleshapesofunit,unitconnectionthroughthenode,andunderacertainload.

Finiteelementanalysis:

istheuseofmathematicalapproximationmethodforrealphysicalsystems（geometryandloadingconditionsweresimulated.Andbyusingsimpleandinteractingelements,namelyunit,canusealimitednumberofunknownvariablestoapproachinginfiniteunknownquantityoftherealsystem.

Linearelasticfiniteelementmethodisaidealelasticbodyastheresearchobject,consideringthedeformationbasedonsmalldeformationassumptionof.Inthiskindofproblem,thestressandstrainofthematerialislinearrelationship,meetthegeneralizedhooke'slaw;Stressandstrainislinear,linearelasticproblemboilsdowntosolvinglinearequations,soonlyneedlesscomputationtime.Iftheefficientmethodofsolvingalgebraicequationscanalsohelpreducethedurationoffiniteelementanalysis.

Linearelasticfiniteelementgenerallyincludeslinearelasticstaticsanalysisandlinearelasticdynamicsanalysisfromtwoaspects.Thedifferencebetweenthenonlinearproblemandlinearelasticproblems:

1）nonlinearequationisnonlinear,anditerativelysolvingofgeneral;

2）thenonlinearproblemcan'tusesuperpositionprinciple;

3）nonlinearproblemisnotthereisalwayssolution,sometimesevennosolution.Finiteelementtosolvethenonlinearproblemcanbedividedintothefollowingthreecategories:

1）materialnonlinearproblemsofstressandstrainisnonlinear,butthestressandstrainisverysmall,alinearrelationshipbetweenstrainanddisplacementatthistime,thiskindofproblembelongstothematerialnonlinearproblems.Duetotheoreticallyalsocannotprovidetheconstitutiverelationcanbeaccepted,so,generalnonlinearrelationsbetweenstressandstrainofthematerialbasedonthetestdata,sometimes,tosimulatethenonlinearmaterialpropertiesavailablemathematicalmodelthoughthesemodelsalwayshavetheirlimitations.Moreimportantmaterialnonlinearproblemsinengineeringpracticeare:

nonlinearelastic（includingpiecewiselinearelastic,elastic-plasticandviscoplastic,creep,etc.

2）geometricnonlineargeometricnonlinearproblemsarecausedduetothenonlinearrelationshipbetweendisplacement.Whentheobjectthedisplacementislarger,thestrainanddisplacementrelationshipisnonlinearrelationship.Researchonthiskindofproblem

Isassumesthatthematerialofstressandstrainislinearrelationship.Itconsistsofalargedisplacementproblemoflargestrainandlargedisplacementlittlestrain.Suchasthestructureoftheelasticbucklingproblembelongstothelargedisplacementlittlestrain,rubberpartsformingprocessforlargestrain.

3）nonlinearboundaryproblemintheprocessing,problemssuchassealing,theimpactoftheroleofcontactandfrictioncannotbeignored,belongstothehighlynonlinearcontactboundary.Atordinarytimessomecontactproblems,suchasgear,stampingforming,rolling,rubbershockabsorber,interferencefitassembly,etc.,whenastructureandanotherstructureorexternalboundarycontactusuallywanttoconsidernonlinearboundaryconditions.Theactualnonlinearmayappearatthesametimethesetwoorthreekindsofnonlinearproblems.

Finiteelementtheoreticalbasis

Finiteelementmethodisbasedonvariationalprincipleandtheweightedresidualmethod,andthebasicsolvingthoughtisthecomputationaldomainisdividedintoafinitenumberofnon-overlappingunit,withineachcell,selectsomeappropriatenodesassolvingtheinterpolationfunction,thedifferentialequationofthevariablesintherewrittenbythevariableoritsderivativeselectedinterpolationnodevalueandthefunctionoflinearexpression,withtheaidofvariationalprincipleorweightedresidualmethod,thediscretesolutionofdifferentialequation.Usingdifferentformsofweightfunctionandinterpolationfunction,constitutedifferentfiniteelementmethods.1.Theweightedresidualmethodandtheweightedresidualmethodofweightedresidualmethodofweightedresidualmethod:

referstotheweightedfunctioniszerousingmakeallowanceforapproximatesolutionofthedifferentialequationmethodiscalledtheweightedresidualmethod.Isakindofdirectlyfromthesolutionofdifferentialequationandboundaryconditions,toseektheapproximatesolutionofboundaryvalueproblemsofmathematicalmethods.Weightedresidualmethodistosolvethedifferentialequationoftheapproximatesolutionofakindofeffectivemethod.

Hybridmethodforthetrialfunctionselectedisthemostconvenient,butundertheconditionofthesameprecision,theworkloadisthelargest.Forinternalmethodandtheboundarymethodbasisfunctionmustbemadeinadvancetomeetcertainconditions,theanalysisofcomplexstructurestendtohavecertaindifficulty,butthetrialfunctionisestablished,theworkloadissmall.Nomatterwhatmethodisused,whensetuptrialfunctionshouldbepaidattentiontoarethefollowing:

（1）trialfunctionshouldbecomposedofasubsetofthecompletefunctionset.Havebeenusingthetrialfunctionhasthepowerseriesandtrigonometricseries,splinefunctions,beisaier,chebyshev,Legendrepolynomial,andsoon.

（2）thetrialfunctionshouldhaveuntilthantoeliminatesurplusweightedintegralexpressionofthehighestderivativelowfirstorderderivativecontinuity.

（3）thetrialfunctionshouldbespecialsolutionwithanalyticalsolutionoftheproblemorproblemsassociatedwithit.Ifcomputingproblemswithsymmetry,shouldmakefulluseofit.Obviously,anyindependentcompletesetoffunctionscanbeusedasweightfunction.Accordingtotheweightfunctionofthedifferentoptionsfordifferentweightedallowancecalculationmethod,mainlyinclude:

collocationmethod,subdomainmethod,leastsquaremethod,momentmethodandgalerkinmethod.Thegalerkinmethodhasthehighestaccuracy.

Principleofvirtualwork:

balanceequationsandgeometricequationsoftheequivalentintegralformof"weak"virtualworkprinciplesincludeprincipleofvirtualdisplacementandvirtualstressprinciple,isthefloorboardoftheprincipleofvirtualdisplacementandvirtualstresstheory.Theycanbeconsideredwithsomecontrolequationofequivalentintegral"weak"form.Principleofvirtualwork:

getformanybalancedforcesysteminanystateofdeformationcoordinateconditiononthevirtualworkisequaltozero,namelythesystemofvirtualworkforceandinternalforceofthesumofvirtualworkisequaltozero.Thevirtualdisplacementprincipleistheequilibriumequationandforceboundaryconditionsoftheequivalentintegralformof"weak";Virtualstressprincipleisgeometricequationanddisplacementboundaryconditionoftheequivalentintegralformof"weak".Mechanicalmeaningofthevirtualdisplacementprinciple:

iftheforcesystemisbalanced,theyonthevirtualdisplacementandvirtualstrainbythesumoftheworkiszero.Ontheotherhand,iftheforcesysteminthevirtualdisplacement（strain）andvirtualandisequaltozeroforthework,theymustbalanceequation.Virtualdisplacementprincipleformulatedthesystemofforcebalance,therefore,necessaryandsufficientconditions.Ingeneral,thevirtualdisplacementprinciplecannotonlysuitableforlinearelasticproblems,andcanbeusedinthenonlinearelasticandelastic-plasticnonlinearproblem.

Virtualmechanicalmeaningofstressprinciple:

ifthedisplacementiscoordinated,thevirtualstressandvirtualboundaryconstraintcounterforceinwhichtheyarethesumoftheworkiszero.Ontheotherhand,ifthevirtualforcesysteminwhichtheyareandiszeroforthework,theymustbemeetthecoordination.Virtualstressinprinciple,therefore,necessaryandsufficientconditionfortheexpressionofdisplacementcoordination.Virtualstressprinciplecanbeappliedtodifferentlinearelasticandnonlinearelasticmechanicsproblem.Butitmustbepointedoutthatbothprincipleofvirtualdisplacementandvirtualstressprinciple,relyontheirgeometricequationandequilibriumequationisbasedonthetheoryofsmalldeformation,theycannotbedirectlyappliedtomechanicalproblemsbasedonlargedeformationtheory.3,,,,,theminimumtotalpotentialenergymethodofminimumtotalpotentialenergymethod,theminimumstrainenergymethodofminimumtotalpotentialenergymethod,thepotentialenergyfunctionintheobjectontheexternalloadwillcausedeformation,thedeformationforceduringtheworkdoneintheformofelasticenergystoredintheobject,isthestrainenergy.

Theconvergenceofthefiniteelementmethod,theconvergenceofthefiniteelementmethodreferstowhenthegridgraduallyencryption,thefiniteelementsolutionsequenceconvergestotheexactsolution;Orwhenthecellsizeisfixed,themorefreedomdegreeeachunit,thefiniteelementsolutionstendtobemoreprecisesolution.Convergenceconditionoftheconvergenceconditionofthefiniteelementfiniteelementconvergenceconditionoftheconvergenceconditionofthefiniteelementfiniteelementincludesthefollowingfouraspects:

1）withintheunit,thedisplacementfunctionmustbecontinuous.Polynomialissingle-val