Introductiontocalculation
English:FiniteElement
Thefiniteelementmethodisamoderncalculationmethodthathasdevelopedrapidlywiththedevelopmentofelectroniccomputers.Itisaneffectivenumericalanalysismethodfirstappliedinthefieldofcontinuummechanics-thestaticanddynamiccharacteristicsanalysisofaircraftstructuresinthe1950s,andthenitwasquicklyandwidelyusedtosolvecontinuityproblemssuchasheatconduction,electromagneticfields,andfluidmechanics.
Methods
Thethinkingandmethodsoffiniteelementmethodanalysisandcalculationcanbesummarizedasfollows:
Discretizationofobjects
Discreteintoacalculationmodelcomposedofvariouselements,thisstepiscalledelementdivision.Afterdiscretization,theelementandtheelementareconnectedwitheachotherbyusingelementnodes;thesetting,natureandnumberofelementnodesshouldbedeterminedbythenatureoftheproblem,theneedtodescribethedeformationformandthecalculationaccuracy(generally,themoredetailedthedivisionoftheelementistodescribethedeformation.Themoreaccurate,theclosertotheactualdeformation,butthegreatertheamountofcalculation).Therefore,thestructureanalyzedinthefiniteelementisnolongertheoriginalobjectorstructure,butadiscreteobjectconnectedinacertainwaywithmanyelementsofthenewmaterial.Inthisway,theresultsobtainedbyfiniteelementanalysisandcalculationareonlyapproximate.Ifthenumberofdivisionunitsisverylargeandreasonable,theresultobtainedisconsistentwiththeactualsituation.
Selectthedisplacementmode
Inthefiniteelementmethod,whenthenodaldisplacementisselectedasthebasicunknownquantity,itiscalledthedisplacementmethod;whenthenodalforceisselectedasthebasicunknownquantity,itiscalledtheforcemethod;Whenapartofthenodalforceandapartofthenodaldisplacementareregardedasthebasicunknownquantity,itiscalledthehybridmethod.Thedisplacementmethodiseasytorealizethecalculationautomation,sothedisplacementmethodisthemostwidelyusedinthefiniteelementmethod.
Whenthedisplacementmethodisused,aftertheobjectorstructureisdiscretized,thetotalphysicalquantitiesoftheelement,suchasdisplacement,strainandstress,canberepresentedbythenodedisplacement.Atthistime,someapproximatefunctionsthatcanapproximatetheoriginalfunctioncanbeusedtodescribethedisplacementdistributionintheelement.Usually,inthefiniteelementmethod,weexpressthedisplacementasasimplefunctionofcoordinatevariables.Thisfunctioniscalledthedisplacementmodeordisplacementfunction.
Analyzethemechanicalproperties
Accordingtotheelement’smaterialproperties,shape,size,numberofnodes,positionandmeaning,etc.,findouttherelationshipbetweentheelementnodeforceandthenodedisplacement.ThisisAkeystepinunitanalysis.Atthistime,itisnecessarytoapplythegeometricequationsandphysicalequationsinelasticmechanicstoestablishtheequationsofforceanddisplacement,soastoderivetheelementstiffnessmatrix,whichisoneofthebasicstepsofthefiniteelementmethod.
Equivalentnodalforce
Aftertheobjectisdiscretized,itisassumedthattheforceistransferredfromoneelementtoanotherthroughthenodes.However,fortheactualcontinuum,theforceistransferredfromthecommonedgeoftheunittoanotherunit.Therefore,thesurfaceforce,volumeforceandconcentratedforceactingontheelementboundaryneedtobeequivalentlymovedtothenode,thatis,theequivalentnodalforceisusedtoreplacealltheforcesactingontheelement.
Elementgroupset
Definition
Usingtheequilibriumconditionsandboundaryconditionsofstructuralmechanicstoreconnecteachelementaccordingtotheoriginalstructuretoformanoverallfiniteelementequation.
Meaning
Kisthestiffnessmatrixoftheoverallstructure;qisthenodaldisplacementarray;fistheloadarray.
Solve
Solvethefiniteelementequationtogetthedisplacement.Here,theappropriatecalculationmethodcanbeselectedaccordingtothespecificcharacteristicsoftheequations.
Throughtheaboveanalysis,itcanbeseenthatthebasicideaofthefiniteelementmethodis"onedivisionandoneintegration",thedivisionisforunitanalysis,andthecombinationisforthecomprehensiveanalysisoftheoverallstructure.
Developmentoverview
In1943,couranttookapiecewisecontinuousfunctiondefinedonatriangulardomaininhispaper,andusedtheprincipleofminimumpotentialenergytostudySt.Venant’storsionproblem.
In1960,cloughusedthename"FiniteElementMethod"inhispaperonplaneelasticity.
In1965,FengKangpublishedthepaper"DifferenceSchemeBasedontheVariationalPrinciple".Thispaperisthemainbasisfortheinternationalacademiccommunitytorecognizetheindependentdevelopmentofthefiniteelementmethodinmycountry.
In1970,withthedevelopmentofcomputersandsoftware,finiteelementsdeveloped.
In1975,XieQianquanpublishedthepaper"FiniteElementMethodforThree-DimensionalElasticProblems",markingthatChinesescholarsindependentlydevelopedfiniteelementmethodsandfiniteelementmethodsthatcanbeappliedtothree-dimensionalpracticeinisolation.engineeringsoftware.Thearticlealsotooktheleadintheworldtoobtainthesuperconvergenceresultsofthree-dimensionalfiniteelement.
Contentsinvolved
Thetheorybehindthefiniteelement,theprincipleofunitdivision,theselectionandcoordinationofshapefunctions.
Thefiniteelementmethodinvolves
numericalcalculationmethodsandtheirerrors,convergenceandstability.
Scopeofapplication
Solidmechanics,fluidmechanics,heatconduction,electromagnetics,acoustics,biomechanics
Solvingsituation
Pole,Elastic(linearandnonlinear),elastoplasticorplasticproblems(includingstaticanddynamicproblems)composedofvariouselementssuchasbeams,plates,shells,andblocks.Itcansolvevariousfielddistributionproblems(steadystateandtransientproblemsoffluidfield,temperaturefield,electromagneticfield,etc.),waterflowpipelines,circuits,lubrication,noise,andsolid,fluid,andtemperatureinteractionproblems.
Development
Overview:
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.
Domesticdevelopmentmileage
China'sCAEtechnologyresearch,developmentandapplicationcanbesaidtobeupsanddowns,anditisonaverydifficultdevelopmentroad.ThelateMr.FengKang,afamouscomputationalmathematicianinmycountry,putforwardthebasicideaofthefiniteelementmethodinthe1950s,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,becauseinreallifewecanseethatthecompletesetoftechnology,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.