Konečný element

Úvod do výpočtu

Čeština:FiniteElement

Thefiniteelementmethodisamoderncalculationmethodthathasdevelopedrapidlywiththedevelopmentofelectroniccomputers.Itisaneffectivenumericalanalysismethodfirstappliedinthefieldofcontinuummechanics-thestaticanddynamiccharacteristicsanalysisofaircraftstructuresinthe1950s,andthenitwasquicklyandwidelyusedtosolvecontinuityproblemssuchasheatconduction,electromagneticfields,andfluidmechanics.

Metody

Thethinkingandmethodsoffiniteelementmethodanalysisandcalculationcanbesummarizedasfollows:

Diskretizace objektů

Discreteintoacalculationmodelcomposedofvariouselements,thisstepiscalledelementdivision.Afterdiscretization,theelementandtheelementareconnectedwitheachotherbyusingelementnodes;thesetting,natureandnumberofelementnodesshouldbedeterminedbythenatureoftheproblem,theneedtodescribethedeformationformandthecalculationaccuracy(generally,themoredetailedthedivisionoftheelementistodescribethedeformation.Themoreaccurate,theclosertotheactualdeformation,butthegreatertheamountofcalculation).Therefore,thestructureanalyzedinthefiniteelementisnolongertheoriginalobjectorstructure,butadiscreteobjectconnectedinacertainwaywithmanyelementsofthenewmaterial.Inthisway,theresultsobtainedbyfiniteelementanalysisandcalculationareonlyapproximate.Ifthenumberofdivisionunitsisverylargeandreasonable,theresultobtainedisconsistentwiththeactualsituation.

Vyberterežim posunutí

Inthefiniteelementmethod,whenthenodaldisplacementisselectedasthebasicunknownquantity,itiscalledthedisplacementmethod;whenthenodalforceisselectedasthebasicunknownquantity,itiscalledtheforcemethod;Whenapartofthenodalforceandapartofthenodaldisplacementareregardedasthebasicunknownquantity,itiscalledthehybridmethod.Thedisplacementmethodiseasytorealizethecalculationautomation,sothedisplacementmethodisthemostwidelyusedinthefiniteelementmethod.

Whenthedisplacementmethodisused,aftertheobjectorstructureisdiscretized,thetotalphysicalquantitiesoftheelement,suchasdisplacement,strainandstress,canberepresentedbythenodedisplacement.Atthistime,someapproximatefunctionsthatcanapproximatetheoriginalfunctioncanbeusedtodescribethedisplacementdistributionintheelement.Usually,inthefiniteelementmethod,weexpressthedisplacementasasimplefunctionofcoordinatevariables.Thisfunctioniscalledthedisplacementmodeordisplacementfunction.

Analyzujte mechanické vlastnosti

Accordingtotheelement’smaterialproperties,shape,size,numberofnodes,positionandmeaning,etc.,findouttherelationshipbetweentheelementnodeforceandthenodedisplacement.ThisisAkeystepinunitanalysis.Atthistime,itisnecessarytoapplythegeometricequationsandphysicalequationsinelasticmechanicstoestablishtheequationsofforceanddisplacement,soastoderivetheelementstiffnessmatrix,whichisoneofthebasicstepsofthefiniteelementmethod.

Ekvivalentní nodalforce

Aftertheobjectisdiscretized,itisassumedthattheforceistransferredfromoneelementtoanotherthroughthenodes.However,fortheactualcontinuum,theforceistransferredfromthecommonedgeoftheunittoanotherunit.Therefore,thesurfaceforce,volumeforceandconcentratedforceactingontheelementboundaryneedtobeequivalentlymovedtothenode,thatis,theequivalentnodalforceisusedtoreplacealltheforcesactingontheelement.

Elementgroupset

Definice

Usingtheequilibriumconditionsandboundaryconditionsofstructuralmechanicstoreconnecteachelementaccordingtotheoriginalstructuretoformanoverallfiniteelementequation.

Význam

Kisthestiffnessmatrixoftheoverallstructure;qisthenodaldisplacementarray;fistheloadarray.

Řešit

Řešitthefiniteelementequationtogetthedisplacement.Here,theappropriatecalculationmethodcanbeselectedaccordingtothespecificcharacteristicsoftheequations.

Throughtheaboveanalysis,itcanbeseenthatthebasicideaof​​thefiniteelementmethodis"onedivisionandoneintegration",thedivisionisforunitanalysis,andthecombinationisforthecomprehensiveanalysisoftheoverallstructure.

Rozvojoverview

In1943,couranttookapiecewisecontinuousfunctiondefinedonatriangulardomaininhispaper,andusedtheprincipleofminimumpotentialenergytostudySt.Venant’storsionproblem.

V roce 1960 použil ve svých papírech na rovinnou elasticitu název "FiniteElementMethod".

In1965,FengKangpublishedthepaper"DifferenceSchemeBasedontheVariationalPrinciple".Thispaperisthemainbasisfortheinternationalacademiccommunitytorecognizetheindependentdevelopmentofthefiniteelementmethodinmycountry.

In1970,withthedevelopmentofcomputersandsoftware,finiteelementsdeveloped.

In1975,XieQianquanpublishedthepaper"FiniteElementMethodforThree-DimensionalElasticProblems",markingthatChinesescholarsindependentlydevelopedfiniteelementmethodsandfiniteelementmethodsthatcanbeappliedtothree-dimensionalpracticeinisolation.engineeringsoftware.Thearticlealsotooktheleadintheworldtoobtainthesuperconvergenceresultsofthree-dimensionalfiniteelement.

Zapojený obsah

Thetheorybehindthefiniteelement,theprincipleofunitdivision,theselectionandcoordinationofshapefunctions.

Metohodina konečných prvků

numericalcalculationmethodsandtheirerrors,convergenceandstability.

Rozsah aplikace

Mechanika pevných látek, mechanika tekutin, vedení tepla, elektromagnetické pole, akustika, biomechanika

Řešení situace

Pól,Elastický (lineární a nelineární),elastoplastickéneboplasticképroblémy(včetně statickýchadynamickýchproblémů)složený z různých prvků,jako jsou nosníky, desky, skořepiny a bloky.Může vyřešit různé problémy s distribucí pole (problémy v ustáleném stavu a přechodné,problémyproudění,bezteplotnípoleateplotnípole,teplotní pole,pevné.

Rozvoj

Přehled:

Withtherapiddevelopmentofcomputertechnology,intheengineeringfield,finiteelementanalysis(FEA)Itisincreasinglyusedforsimulationtosolverealengineeringproblems.Overtheyears,moreandmoreengineers,appliedmathematiciansandphysicistshaveprovedthatthismethodofsolvingpartialdifferentialequations(PDE)cansolvemanyphysicalphenomena.Thesepartialdifferentialequationscanbeusedtodescribetheflow,electromagneticfieldandstructure.Mechanicsandsoon.Thefiniteelementmethodisusedtoconvertthesewell-knownmathematicalequationsintoapproximatedigitalimages.

Earlyfiniteelementsfocusedonacertainprofessionalfield,suchasstressorfatigue,but,generallyspeaking,physicalphenomenadonotexistalone.Forexample,aslongasmovementwillgenerateheat,andheatinturnaffectssomematerialproperties,suchaselectricalconductivity,chemicalreactionrate,fluidviscosityandsoon.Thiskindofcouplingofphysicalsystemsiswhatwecallmultiphysics,andanalysisismuchmorecomplicatedthananalyzingasinglephysicalfieldalone.Obviously,weneedamultiphysicsanalysistool.

Beforethe1990s,duetothelackofcomputerresources,multi-physicssimulationonlystayedatthetheoreticalstage,andfiniteelementmodelingwasalsolimitedtothesimulationofasinglephysicalfield,themostcommonbeingSimulationofmechanics,heattransfer,fluidsandelectromagneticfields.Itseemsthatthefateoffiniteelementsimulationisthesimulationofasinglephysicalfield.

Thissituationhasbeguntochange.Afterdecadesofhardwork,thedevelopmentofcomputationalsciencehasprovideduswithmoredexterous,concise,andfasteralgorithms,andmorepowerfulhardwareconfigurations,makingfiniteelementsimulationofmulti-physicspossible.Theemergingfiniteelementmethodprovidesanewopportunityformulti-physicsanalysisandsatisfiesengineers'needsforsolvingrealphysicalsystems.Thefutureoffiniteelementliesinmultiphysicssolving.

Thousandsofwordsareendless.Thefollowingcanonlyshowsomepotentialapplicationsofmultiphysicsfiniteelementanalysisinthefuturethroughafewexamples.

Piezoacoustictransducercanconvertelectriccurrentintoacousticpressurefield,orviceversa,convertsoundfieldintoelectriccurrentfield.Thiskindofdeviceisgenerallyusedinsoundsourcedevicesinairorliquid,suchasphasedarraymicrophones,ultrasoundbioimaging,sonarsensors,acousticbiotherapy,etc.Itcanalsobeusedinsomemechanicaldevicessuchasinkjetsandpiezoelectrics.Motoretc.

Piezoelectricloudspeakersinvolvethreedifferentphysicalfields:structurefield,electricfieldandsoundfieldinfluid.Onlysoftwarewithmultiphysicsanalysiscapabilitiescansolvethismodel.

PZT5-Hcrystalisusedaspiezoelectricmaterial,whichiswidelyusedinpiezoelectricsensors.Attheinterfacebetweentheairandthecrystal,thesoundfieldboundaryconditionissettothepressureequaltothenormalaccelerationofthestructurefield,sothatthepressurecanbetransmittedtotheair.Inaddition,thecrystaldomainwillbedeformedduetotheinfluenceofairpressureonit.Thesimulationstudiesthepropagationofsoundwavesgeneratedbythecrystalafterapplyingacurrentwithanamplitudeof200Vandanoscillationfrequencyof300KHz.Thedescriptionofthismodelanditsperfectresultsshowthatunderanycomplexmodel,wecanuseaseriesofmathematicalmodelstoexpressandthensolve.

Anotheradvantageofmulti-physicsmodelingisthatinschool,studentsintuitivelyobtainsomephenomenathatwerenotseenbefore,andthesimpleandeasy-to-understandexpressionshavealsowonthefavorofstudents.ThisisjustwhatDr.KrishanKumarBhatiafeltwhenheintroducedmodelingandanalysistoolstoseniorgraduatesatRowanUniversityinGlassboro,NewYork,whenheintroducedthemodelingandanalysistools.Hisstudent'stopicwashowtocooltheengineboxofamotorcycle.Dr.Bhatiataughtthemhowtousetheconceptof"design-manufacture-test"tojudge,find,andsolveproblems.Ifthereisnoapplicationofcomputersimulation,thismethodisunimaginableintheclassroom,becausethecostistoolarge.

COMSOLMultiphysicshasanexcellentuserinterfacethatallowsstudentstoeasilysetupheattransferproblemsandquicklygettheresultstheyneed."Mygoalistoenableeverystudenttounderstandpartialdifferentialequations.Whentheyencountersuchaproblemnexttime,theywon'tworryaboutitanymore,"saidDr.Bhatia."Thisdoesnotrequireknowledgeoftoomanyanalyticaltools.Inotherwords,thestudentsallreflect'thismodelingtoolisgreat'".

Manyoutstandinghigh-techengineeringcompanieshaveseenthatmultiphysicsmodelingcanhelpthemstaycompetitive.Multiphysicsmodelingtoolsallowengineerstoperformmorevirtualanalysisinsteadofphysicaltestingeverytime.Inthisway,theycanoptimizetheproductquicklyandeconomically.IntheMedradInnovationsGroupinIndonesia,aresearchteamledbyDr.JohnKalafutusesmultiphysicsanalysistoolstostudytheinjectionprocessofbloodcellsinaslendersyringe.Thisisanon-Newtonianfluidandhasahighshear.Cutrate.

Throughthisresearch,MedradengineershavecreatedanoveldevicecalledVanguardDxAngiographicCatheter.Comparedwiththetraditionalcatheterswithsharpnozzles,thenewcatheterswithdivergentnozzlesmakethecontrastagentmoreevenlydistributed.ContrastagentsarespecialmaterialsthatshowthediseasedorgansmoreclearlywhentakingX-rayphotographs.

Anotherproblemisthattraditionalcathetersmaycausethecontrastagenttoproduceagreatspeedduringuse,whichmaydamagebloodvessels.Pioneerangiographycathetersreducetheimpactofcontrastagentsonbloodvesselsandminimizethepossibilityofvasculardamage.

Thekeyissueishowtodesignthenozzleshapeoftheductsothatitcanoptimizethefluidvelocityandreducestructuraldeformation.Kalafut'sresearchteamusesmultiphysicsmodelingmethodstocoupletheforcesgeneratedbylaminarflowtostress-strainanalysis,andthenconductfluid-structurecouplinganalysisonvariousnozzleshapesandlayouts."Oneofourtraineesestablisheddifferentnozzlelayoutsfordifferentfluidareasandanalyzedthem,"saidDr.Kalafut."Weusetheseanalysisresultstoevaluatethefeasibilityofthesenewideas,therebyreducingthenumberofphysicalmodelmanufacturing."

Frictionstirwelding(FSW),sinceitspatentapplicationin1991,hasbeenwidelyusedinweldingaluminumalloys.Theaviationindustryisthefirsttoadoptthesetechnologiesandisstudyinghowtousethemtoreducemanufacturingcosts.Intheprocessoffrictionstirwelding,acylindricaltoolwithashoulderandastirringheadisrotatedandinsertedintothejointoftwopiecesofmetal.Therotatingshoulderandmixingheadareusedtogenerateheat,butthisheatisnotenoughtomeltthemetal.Conversely,thesoftenedandplasticmetalwillformasolidbarrierthatwillpreventtheformationofoxygen-oxidizedmetalandairbubbles.Theactionofcrushing,stirringandsqueezingcanmakethestructureoftheweldseambetterthantheoriginalmetalstructure,andthestrengthcanevenbedoubled.Thisweldingdevicecanevenbeusedforweldingdifferenttypesofaluminumalloys.

Airbus(AirBus)hasfundedalotofresearchonfrictionstirwelding.Beforemanufacturersmadelarge-scaleinvestmentandreorganizationofproductionlines,Dr.PaulColegroveofCranfieldUniversityusedmultiphysicsanalysistoolstohelpthemunderstandtheprocess.

Thefirstresearchresultisamathematicalmodeloffrictionstirwelding,whichallowsAirbusengineersto"seethrough"theweldtochecktemperaturedistributionandmicrostructurechanges.Dr.ColegroveandhisresearchteamalsowroteasimulationtoolwithagraphicalinterfacesothatAirbusengineerscandirectlyextractthethermalpropertiesofthematerialandtheultimatestrengthoftheweld.

Inthisfrictionstirweldingsimulationprocess,three-dimensionalheattransferanalysisandtwo-dimensionalaxisymmetriceddycurrentsimulationarecoupled.Theheattransferanalysiscalculatestheheatdistributionofthestructureaftertheheatfluxisappliedtothesurfaceofthetool.Thedisplacementofthetool,thethermalboundaryconditions,andthethermalpropertiesoftheweldingmaterialcanbeextracted.Next,thethree-dimensionalheatdistributionatthetoolsurfaceismappedtothetwo-dimensionalmodel.Thecoupledmodelcancalculatetheinteractionbetweenheatandfluidduringprocessing.

Couplingtheelectromagnetic,electricalresistance,andheattransferbehaviorofthesubstraterequiresatruemultiphysicsanalysistool.Atypicalapplicationisintheprocessofsemiconductorprocessingandannealing.Thereisahotwallfurnaceusinginductionheating,whichisusedtogrowsemiconductorwafers,whichisakeytechnologyintheelectronicsindustry.

Forexample,emerycanreplaceagraphitereceiverinahightemperatureenvironmentof2,000°C.Thereceiverisheatedbyaradiofrequencydevicewithapowercloseto10KW.Tomaintainauniformtemperatureinthefurnaceatsuchahightemperature,thedesignofthefurnacecavityisveryimportant.Afteranalysisbymulti-physicsanalysistools,itisfoundthatheatismainlytransmittedthroughradiation.Inthemodel,youcanseenotonlythetemperaturedistributiononthesurfaceofthewafer,butalsothetemperaturedistributiononthequartztubeofthefurnace.

Incircuitdesign,animportantaspectthataffectsmaterialselectionisthedurabilityandservicelifeofthematerial.Thetrendofminiaturizationofelectricalapplianceshasledtotherapiddevelopmentofelectroniccomponentsthatcanbemountedoncircuitboards.Asweallknow,theresistorsandothercomponentsmountedonthecircuitboardwillgeneratealotofheat,whichmaycausecracksinthesolderfeetofthecomponents,andfinallycausetheentirecircuitboardtobescrapped.

Multi-physicsanalysistoolscananalyzetheheattransferoftheentirecircuitboard,structuralstresschangesanddeformationduetotemperaturerise.Thiscanbeusedtoimprovetherationalityofthecircuitboarddesignandtherationalityofmaterialselection.

Theimprovementofcomputercapabilitieshasmadefiniteelementanalysisarealityfromsingle-fieldanalysistomulti-fieldanalysis.Inthenextfewyears,multi-physicsanalysistoolswillshocktheacademicandengineeringcircles.Themonotonous"design-check"designmethodwillgraduallybeeliminated,virtualmodelingtechnologywillmakeyourmindgofurther,andsimulationwillignitethesparkofinnovation.

Since2000,alotofresearchhasbeendoneonthenumericalsolutionofnonlinearstructuralproblemsathomeandabroad.TheappearanceofthemodifiedNewton-Raphsoniterativemethodprovidesaguaranteeforensuringthecalculationaccuracy.However,itisstilldifficulttofindthelimitpointwiththismethodforsolvingtheultimatestrengthofthestructure.Wright&Gaylorddevelopedanimaginaryspringmethodtoensurethepositivedefinitenessofthestructuralstiffnessmatrixoftherearultimatestrengthregion,anditwassuccessfullyappliedtotheanalysisofframestructures.Berganetal.proposedthecurrentstiffnessparametermethodtorestrainthebalanceiterationofthecriticalregionandthencrossthelimitpoint.Batozproposedadisplacementcontrolmethod,whichreversedtheinternalforceofthestructurebyapplyingaknowndisplacementchangeprocess,soastocrossthelimitpointtoobtainthepost-ultimatestrengthresponseofthestructure.Riksfirstproposedthearclengthcontrolmethod,whichwasimprovedbyCrisfield,Ramm,Powell,andSimonsin1981,andcombinedwiththemodifiedNewton-Raphsonmethodtosuccessfullyachievethe"stepjump"inthelimitequilibriumpathafterthesolution."(Snap-through)question.GaoSuheetal.studiedtherelationshipbetweenmeshdensityandfiniteelementsolutionaccuracy.Throughtheanalysisandcomparisonofthecalculationresultsandaccuratesolutionsofthefiniteelementmechanicalmodelsofdifferentmeshdensitiesanddifferentelementtypes,exploretheinternalrelationshipbetweentheelementmeshingandtheaccuracyofthefiniteelementsolution,inordertoensurethatthefiniteelementsolutionmeetstheactualaccuracyrequirementsoftheengineeringUnderthepremiseofdeterminingthereasonablemeshdensity,andimprovingtheefficiencyoffiniteelementanalysis,ausefulexplorationiscarriedout.Theresearchprovesthatforthesharpcornersofthegeometryandtheareaswithlargestressandstrainchanges,higher-orderelementsshouldbeselectedinthefiniteelementanalysis,andtheelementmeshdensityshouldbeincreasedappropriately.Inthisway,theshapeoftheelementcanbeensured,andatthesametime,thesolutionprecision,accuracyandconvergencespeedcanbeimproved.Whenthemeshisautomaticallydivided,priorityisgiventotheselectionofhigher-orderelements.Inthegriddivisionandpreliminarysolution,itshouldbesimplifiedfirstandthencomplicated,coarsefirstandthenrefined.Becauseengineeringstructuresgenerallyhavethecharacteristicsofrepeatedsymmetryoraxisymmetric,mirrorsymmetry,etc.,inordertoimprovetheefficiencyofthesolution,thecharacteristicsofrepetitionandsymmetryshouldbefullyutilized,andsub-structuresorsymmetricmodelsshouldbeadoptedtoimprovetheefficiencyandaccuracyofthesolution.

Domácí rozvoj najeté kilometry

China'sCAEtechnologyresearch,developmentandapplicationcanbesaidtobeupsanddowns,anditisonaverydifficultdevelopmentroad.ThelateMr.FengKang,afamouscomputationalmathematicianinmycountry,putforwardthebasicideaof​​thefiniteelementmethodinthe1950s,whichisalmostsynchronizedwithforeigncountries.Inthemid-1960s,someunitsandscholarslearningfiniteelementmethodsalsoappearedinChina.However,duetothelimitationsofcomputerhardwareconditions,andtheinfluenceofpoliticalandsocialenvironmentssuchastheCulturalRevolution,China’sCAEtechnologyhasbeenimpactedforalongtime.Respondingtothenationalcall,researchersdevotedthemselvestothecalculationofstressandstrainofhydropowerdams.Finally,XieQianquanandLiJianhuaoftheHunanInstituteofComputingTechnologyindependentlyinventedChina’sthree-dimensionallimitedinisolationfromforeigncountries.Themeta-methodandengineeringsoftwareweresuccessfullyappliedtotheYellowRiverConservancyCommission’sengineeringprojectin1973,andthearticle“FiniteElementMethodforThree-DimensionalElasticityProblems”waspublishedin1975,andthenappliedtothewholecountryfromthe1970stothefirsthalfofthe1980s.Thecalculationoflargedamshassavedthecountryalotofmoney;itisworthemphasizingthat,accordingtothisarticlethathasbeenrigorouslyreviewed,thethree-dimensionalfiniteelementprogramthatXieQianquanandLiJianhuaworkedtogetherwassuccessfullydebuggedin1972andusedintheYellowRiverConservancyCommissionin1973.Project,thefootnoteonthefirstpageofthepaperclearlypointedout:Thisarticlewassubmittedin1973,finalizedin1974,andofficiallypublishedin1975.Itisavailableinchronologicalorder.Theydiscoveredthesuperconvergenceofthree-dimensionalfiniteelementin1973,whichisfaraheadofforeigncountries.Experts,theconclusionthattheyfirstdiscoveredsuperconvergencein3Dfiniteelementintheworldwaspubliclyacknowledgedbytheworld-renownedfiniteelementexpertMICHALKRIZEKinacademicpapers.ThisisthefirstdiscoveryinChinathathassurpassedforeigncountriesinthefieldoffiniteelement..In2000,LiJianhuaandXieQianquandiscoveredtheinvisibilitycloakforthefirsttimeintheworld,anditwasaachievabledouble-layerinvisibilitycloakthatdidnotexceedthespeedoflight.Itnotonlycontinuedtomaintainaleadingpositioninthefieldofcomputingscience,butalsotooktheleadintheworldtoproposeasuper-scientific.concept.

Inthemid-1970s,DalianUniversityofTechnologydevelopedDDJ,JIGFEXfiniteelementanalysissoftwareandDDDUstructuraloptimizationsoftware;ProfessorLiMingruiofBeijingAgriculturalUniversitydevelopedFEMsoftware;mid-1980s,PekingUniversityProfessorYuanMingwuThroughthetransplantationandmajortransformationofforeignSAPsoftware,SAP-84wasdeveloped;duetotheneedsoftheaviationindustry,theMinistryofAviationIndustrybegantoorganizethedevelopmentofHAJIF(I,II,III),YIDOYU,COMPASS,Andwonmanynationalawardsandsoon.Comparedwithsimilarforeignproducts,thesedomesticCAEsoftwarehasmanycharacteristicsincorealgorithmsandseveralfunctions,reflectingtheachievementsofChinesescholarsincomputationalmechanicsresearch,andfullyconsideringtheactualconditionsofcomputerhardwareinmycountry.Ithasplayedanimportantroleinconstructionandengineeringstructuredesignandhasawiderangeofapplications.

Sincethe1990s,thecountryhasincreaseditsopeningupandalargenumberofforeignsoftwarehasfloodedintotheChinesemarket,whichhasacceleratedthepromotionofCAEtechnologyinmycountry,whichundoubtedlyimprovedthedesignlevelofmycountry'sequipmentmanufacturingindustry.Atthesametime,ourself-developedsoftwareisstronglychallenged.Inparticular,piratedforeignsoftwarehasdealtagreatblowtomycountry'sself-developedCAEsoftware.Foraperiodoftime,thevoiceofself-developedCAEsoftwarewashardlyheard,andtheeffortsofrelevantmanagementdepartmentstosupportthedevelopmentofdomesticsoftwarehavedroppedsharply.ThedepartmentsthatsupportbasicresearchbelievethatCAEsoftwaredevelopmentcannotraisebasicscientificissues.Thedepartmentsthatsupportscientificandtechnologicalresearchandhigh-techdevelopmentbelievethatCAEsoftwaredevelopmentmusttaketheroadofmarketizationandfindfundsinthemarket.Self-developedCAEsoftwarehasencounteredmanydifficultiesinhuman,financialandmaterialresources.

CAEsoftwareconcentratestheresearchresultsoftechnologyandscience,andthesituationfacedbyself-developedCAEsoftwareissimilartothatoftechnologyandscienceinmycountry.Attherecentconferenceoftheacademiciansofthetwoacademies,ComradeHuJintaoemphasizedthetendencyofignoringtechnologyandscience,whichgaveusgreatencouragement.Infact,theachievementsofthesesoftwareswithindependentintellectualpropertyrightsinourcountryareindelible.Thesesoftwaresnotonlysolvealargenumberofproblemsraisedbythecountry’seconomicconstruction,butalsoproducedirectandindirecteconomicbenefits.TheresearchandapplicationprocesshascultivatedalargenumberofTalentsengagedinCAER&Dandapplication;theexistenceofthesesoftwarehasalsobrokenthebarriersofWesterncountriestous,forcingforeignproductstodrasticallyreduceprices,andtheyhavedirectlyorindirectlycontributedtothecountry’sGDPthatcannotbeunderestimated.

ThedilemmafacedbydomesticCAEsoftwaredevelopmentistheepitomeofthedilemmafacedbymostofthetechnologiesandproductsofourcountry’sindependentintellectualpropertyrights;inthefieldoftechnicaleconomicsinmycountry,someexpertsbelievethatsincethereformandopeningThemaincontributionofeconomicgrowthcomesfromopeningup,ratherthantechnologicalinnovationwithindependentintellectualpropertyrights,thelatter'scontributiontoGDPisverysmall.Suchastatementmayhaveabasis,becauseinreallifewe​​canseethatthecompletesetoftechnology,completesetofproductionlineequipmentandlarge-scalesoftwareusedbyalargenumberofdomesticenterprisesareimportedfromabroad.TheproductionprocessandtheintellectualpropertyrightsofmanyproductsareOfaforeigncompany.Facedwiththecompletesetsoftechnologies,equipment,productsandmarketexpansionexperiencedevelopedbyWesterndevelopedcountriesformanyyears,althoughourindependentinnovationtechnologicalachievementsaretechnicallysuperiortoeachother,theyoftenlacksufficienteconomicadvantagestoeliminateeachother.Suchastatementshouldarouseourscientificandtechnologicalworkersandmanagementdepartmentstoreflectonhowtoaccelerateourtechnologicalinnovationactivitieswithindependentintellectualpropertyrights,andhowtotransformtheseachievementsintorealproductivityassoonaspossible.However,weshouldemphasizethatitisveryone-sidedtomeasurethecontributionofChina’sscientificandtechnologicalprogresstothecountry’seconomicconstructionandsocialprogressbyitsdirectcontributiontoGDP;Innovation.AsComradeJiangZeminpointedout,innovationisthesoulofanation.

Fortunately,despitethemanydifficulties,agroupofresearchteamsdedicatedtoCAEtechnologystill"survived"inChina.Thechiefscientistofmeta-computingandtheresearcherLiangGuopingfromtheInstituteofMathematicsandSystemsScienceoftheChineseAcademyofSciences,aftereightyearsofpainstakingresearch,createdaninternationallyadvancedfiniteelementprogramautomaticgenerationsystem(FEPG).FEPGadoptsthecomponent-basedideaandtheadvancedsoftwaredesignoffiniteelementlanguage,whichprovidesanextremelypowerfultoolforsolvingfiniteelementproblemsinvariousfieldsandvariousaspects.UsingFEPG,itcanbecompletedinafewdaysorevenhours.Programminglaborthatcanonlybecompletedinmonthsorevenyears.FEPGisoneofthefewCAEsoftwarethat"survived".ThisisalsoduetothefactthatFEPGsoftwareismoreflexibleandcansolvemanyfiniteelementproblemsthatforeigncommercialsoftwarecannotsolve.FEPGsoftwareismorepractical,buteasiertousethanforeigncommercialsoftware.Poor,thisisalsoafactorthatmakesitdifficultformanyprimaryuserstolearnFEPG.Afteryearsofaccumulation,therearemorethan300researchinstitutesandenterprisesintheindustry.IthasbecomethelargestfiniteelementsoftwareplatforminChina.However,comparedwiththedegreeofforeignsoftwaremarketization,thereisstillacertaingap,andsomeworkneedstobedoneintermsofsoftwareeaseofuse.

Inordertoprovidedomesticuserswithanapplication-orientedfiniteelementanalysissystem,Dr.QianHuashanoftheoriginalFEPGteamorganizedandestablishedBeijingSupercomputingTechnologyCo.,Ltd.anddevelopedthesupercomputingfiniteelementanalysissystemSciFEA.SciFEAsoftwarehasformedaseriesofversionsofstand-aloneversion,networkversion(iSciFEA),clusterparallelversion,andGPUparallelversion(SciFEA-GPU).Therearenearly500officialusersofSciFEAsoftwareinChina,andmorethan20,000trialusershavedownloadedthem.SciFEAdiscardsthetraditionalCAEsoftwarecomplexstructuresystemdesignmodel,andadoptsanindependentmoduledevelopmentmethodthatdirectlyfacesuserneeds.Theusualcomputingfunctionsoftheprojectarealreadyavailable,andtheexpansionofthecomputingmodelneedsfurtherdevelopment.

InadditiontoFEPGsoftwareandSciFEAsoftware,whicharerelativelylarge-scale,thePKPMsoftwareofChinaArchitectureDesignandResearchInstitutealsohasawiderangeofapplicationsinthefieldofarchitecture,whilethesoftwareofDalianUniversityofTechnologymainlysolvesstructuraloptimization;therearealsosomeothersDomesticfiniteelementsoftware,thefiniteelementdevelopedbyChinaAgriculturalUniversityfocusesonthecalculationofbeams,platesandshells,butitsdevelopmentisslowanditisdifficulttoseeitstracesinthemarket.TheUnitedStatesmadesimulationcalculationoneofthefivebasicindustriesinthefutureplaninthe2011plan,whichshowstheinfluenceoffiniteelementonthedevelopmentofsociety,whilemostofourcountryusesforeignfiniteelementsoftware,andinsomemilitaryindustryorThecutting-edgefiniteelementanalysismoduleisstrictlyrestrictedfromexporttoChina.Thisrequiresdomesticfiniteelementsoftwarewithindependentintellectualpropertyrights.

Thefiniteelementmethodoffluidmechanicsincludesvelocitypressuremethod,flowfunction-vortexfunctionmethodandflowfunctionmethod.