边界元简介BEMppt课件.ppt

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1、BoundaryElementMethod(BEM)ZoranIlievskiWednesday28thJune,2006HG6.96(TU/e)1TalkOverviewTheideaofBEManditsadvantagesThe2DpotentialproblemNumericalimplementation2IdeaofBEM3IdeaofBEM4AdvantagesofBEM1)Reductionofproblemdimensionby1Lessdatapreparationtime.Easiertochangetheappliedmesh.Usefulforproblemst

2、hatrequirere-meshing.5AdvantagesofBEM2)HighAccuracyStressesareaccurateastherearenoapproximationsimposedonthesolutionininteriordomainpoints.Suitableformodelingproblemsofrapidlychangingstresses.6AdvantagesofBEM3)LesscomputertimeandstorageForthesamelevelofaccuracyasothermethodsBEMuseslessnumberofnod

3、esandelements.7AdvantagesofBEM4)Filteroutunwantedinformation.Internalpointsofthedomainareoptional.Focusonparticularinternalregion.Furtherreducescomputertime.8AdvantagesofBEMReductionofproblemdimensionby1.HighAccuracy.Lesscomputertimeandstorage.Filteroutunwantedinformationandsofocusonsectionofthe

4、domainyouareinterestedin.BEMisanattractiveoption.9The2DpotentialproblemWherecanBEMbeapplied?Twoimportantfunctions.Descriptionofthedomain.Mappingofhighertolowerdimensions.SatisfactionoftheLaplaceequationsandhowtodealwithasingularity.Theboundaryintegralequation(BIE)10The2DpotentialproblemWherecan

5、BEMbeapplied?WhereanypotentialproblemisgovernedbyadifferentialequationthatsatisfiestheLaplaceequation.(oranyotherbehaviorthathasarelatedfundamentalsolution)e.g.ThefollowingcanbeanalyzedwiththeLaplaceequation:fluidflow,torsionofbars,diffusionandsteadystateheatconduction.11The2DpotentialproblemThe

6、Laplaceequationfor2DLaplacianoperatorPotentialfunctionCartesiancoordinateaxis12The2DpotentialproblemTwoimportantfunctions.Thefunctiondescribingthepropertyunderanalysis.e.g.heat.(Unknown)ThefundamentalsolutionoftheLaplaceequation.(Thesearewellknown)13The2DpotentialproblemFundamentalsolutionofthe2D

7、LaplaceequationforaconcentratedsourcepointatpisWhereDescriptionofthedomain14The2DpotentialproblemMappingofhighertolowerdimensionsBoundaryofanydomainisofadimension1lessthanofthedomain.InBEMtheproblemismovedfromwithinth