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