基于偶應力理論的無網(wǎng)格法.pdf

1、山東大學碩士學位論文基于偶應力理論的無網(wǎng)格法姓名：張瑞霞申請學位級別：碩士專業(yè)：固體力學指導教師：王錫平20050520山東大掌碩士學位論文一ABSTRACThIordertoexplainthesizeeffectformaterialsinthescaleofmicronmetersthestraingradienttheorywasdevelopedBasedontheanalysisandarrangementofpresent

2、straingradienttheoriesandelement—freemethods，theelasticitycouplestresstheoryiscombinedwithEFGM(ElementFreeGalerkinMethod)inthispaperanddevelopedanewelement—freemethodMATLABprogramsarecompiled0nthismethod，togetherwithsome

3、experiments，proveditsfeasibilityandefficiencyThemainresearchcontentandconclusionarestatedasfollowed：ThemechanicscharacterofcouplestresstheoryisanalyzedsystemicallyEquationofbalance，equationofmotionequationofcompatibility

4、andconstitutionequationofcouplestresstheoryarederivedinbothplanestraindeformationandplanestressdeformationFortheconvenienceofdiscussingelasticitycouplestresstheoryinplanestressdeformationisstudiedinthepaperAnewelementfre

5、emethodisderivedwiththeelasticitycouplestresstheorycombinedwithEFGMThedevelopmentoftheelementfreemethodsduringrecentyearsisstudied，andtheresearchprogressinelementfreemethodsisdiscussedindetailinthispaperEFGM，whichisbased

6、onthemovingleastsquaresmethod，isnotconstrainedbytheconnectivitybetweeuBodesandelemeutsinthefiuiteelenxen^methodItcanfreelydistributenodesandintegrationsubdomainsaccordingtotheactualgeometryanditcanapplytheproperbasisfunc

7、tionaccordingtothepossibledisplacementfunction，haveagoodcomputationalprecisionMATLABprogramsarecompiledtovalidatesomeexperimentsTodealwithstressconcentrationproblems，theproblemsofthecircularholeinafieldofuniformtensionor

8、inafieldoftensionorcompressionsintwoperpendiculardirectionsaresolvedThecomputationalprecisionofMLS(MovingLeastSquares)basedelementfreemethodisanalyzed，somecommonlyusedweightfunctionsarestudiedAtthesametimetheeffectofthec

9、ompactsupportonthecomputationalprecisionisstudiedWhencouplestressmustbeconsidered，thestressconcentrationfactordecreasesandincreaseswitha／l(holeradius／characteristiclength)increases，andfinallyitapproachesclassicalanswerTh