邊界元法中奇異積分問題的研究及其在固體力學中的應用.pdf

1、中國科學技術(shù)大學博士學位論文邊界元法中奇異積分問題的研究及其在固體力學中的應用姓名：牛忠榮申請學位級別：博士專業(yè)：固體力學指導教師：王秀喜2001.7.1里型堂墊查_大堂墮圭堂些堡塞：望墨垂鯊魚墨堡坌囹墅盟塹窒墨基壟壁墮查堂墮生旦一一——ABSTRACTInthisthesis，thepresentsituationanddevelopmentoftheboundaryelementmethods(BEMs)isbrieflyrevie

2、wedThereexiststhedifficultyoftheevaluationofthehypersingularintegralsandnearlyhypersingularintegralsintheBEMs，whichhavebeendisturbingtheapplicationsoftheBEMsinengineeringThenearlysingularintegralsoccurintheBIEswhenasourc

3、epointiSclosetoanintegrationelement(ascomparedtoitssize)butnotontheelementForthenearlysingularintegralslntwo—dimensionalBEMs1inearisoparametricelementswithtwonodesareusedThen，theconceptofapproachdegreeisdefined，whichisus

4、edtodescribepossibleinfluenceofsingularityoftheintegralsBymeansofsomeintegralformulations，thenearlysingularintegralsareledtothesumofanalyticalpartsandnonsingularintegralsbyusingintegrationbypartsTheprocedureistemedthereg

5、ularizationalgorithmConsiderthetriangularelementswitllthreenodesforthfee’dimensionalBEMsBvtheintroductionofthepolarC00rdinates(P，0)intheplaneofeachtriangularelement，asemianalyticalalgorithmisdesignedforevaluatingthenearl

6、ystronglysingularandhypersingularintegralsThenearlysingularsurfaceintegralsontheelementaretransformedtoaseriesoflineintegralsalongthecontouroftheelementwithintegrationbypartsThenstandardGaussianquadraturecanprovideveryac

7、curateevaluationoftheresultinglineintegralsFortheriseofhigherorderelements，thesubdivisionWaysareproposed，ie，utilizingsomelinearelements(fortwodimensionaiBEMs)orsometriangularelements(forthree—dimensionalBEMs)insteadofthe

8、originalelementonlywhenthenearlysingularintegralsontheelementneedtobedeterminedTheresultsofthenumericalinvestigationsillustratetheaccuracyandeffectivenessoftheregularizationalgorithmandsemianalyticalalgorithmTheregulariz

9、ationalgorithmandsemianalyticalalgorithmareappliedtotwodimensionalandthree—dimensionalelasticityproblemsThenearlystronglyandhypersingularintegralsontheboundaryelementsaredirectlycalculatedAsaresult，thedisplacementsandstr

10、essesatthepointsclosetotheboundaryareobtainedThepresentmethodsaresimple，easyjnuseandaccurateMoreover，theregularizationalgorithmisalsosuccessfulforcomputingthenearlyhypersingularintegralsintheBEMSofpotentialproblemsForalo

11、ngtimethereiSanopinionthattheBEMsaredifficultfortheanalysisofthinandnarrowdomainsInfactitiSbecauseofthepuzzleofnearlysingularintegralsThepresentregularizationalgorithmisalsousedtocomputethenearlysingularintegralsinBIEsof

12、elasticityproblemswhenthesourcepointisontheboundaryThisshowsthatBEMsaresuitabletodealwiththethin—walledstructuresandcompositestructuresDerivativeboundaryintegralequationsusuallycontainHadamardfinitepartintegralswhoseeval

13、uationisalsodifficultalthoughtheoriginalproblemsarenotsingularFortwo—dimensionalelasticity，theauthortakestheoperators毛and∈Ⅳ(permutationsymbols)toactonthedisplacementderivativeBIEsThen，theboundarydisplacements，tractionsan