邊界元法中奇異積分問題的研究及其在固體力學(xué)中的應(yīng)用.pdf

1、中國科學(xué)技術(shù)大學(xué)博士學(xué)位論文邊界元法中奇異積分問題的研究及其在固體力學(xué)中的應(yīng)用姓名：牛忠榮申請學(xué)位級別：博士專業(yè)：固體力學(xué)指導(dǎo)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