高性能六面體組合雜交元研究.pdf

1、西北工業(yè)大學(xué)碩士學(xué)位論文高性能六面體組合雜交元研究姓名：袁占斌申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：聶玉峰20050301AbstractWhenwesolvepracticalproblemsitisnottheidealwaystousehighorderelementoruseveryfinegrids.Notonlythecomputercantbeartheburdenbutalsotheerrorwillbegreate

2、rafterlongtimestransmitting.Soengineersandmathematiciansnevergiveupeffortstofindthebestschemewhoseprecisionishighbutcostislow.Inthisthesisfirstlythedevelopmentprocedureofquadrilateralhighperformanceelementisreviewedandth

3、econclusionsarerecalledthattheenforcedstrainschemeandmultifieldvariationalprinciplemustbeusedinordertogainhighperformanceanditsknownthattheBabuskaBrezziconditionisanobstacleformixedandhybridelementsavoidingthisconditioni

4、snotasighofahighperformanceelementmethod.Forafixeddisplacementfieldhowtoconstructacorrespondingstressfieldisthekeytoimprovetheperformance.Foratwodimensionalelasticityproblemenergycompatibleconditionisfoundasthecrucialrea

5、sonfromCH(O1).AndlatertheequivalencerelationshipbetweenenergycompatibleconditionandorthogonalconditioninCH(01)isproved.ThenalongtheapporachofquadrilateralcombinedhybridelementCH(01)thestressmodesconstrainedbysocalledener

6、gycompatibleconditionorthogonalityconditionandweakequilibriumconditionrespectivelywithWilsonbubblesareexplicitexpressed.Itisobtainedthattwostressmodesrestrictedbyenergycompatibleconditionandorthogonalityconditionarenotth

7、esameforgeneralgrids.Onlywhenregularmeshesareusedthetwoconditionsarethesameandweakequilibriumconditioncanbesatisfiedautomatic.AsthemeshessatisfyBconditionthediferencebetweenthemisahigherorderinfinitesimal.Alloftheseconcl

8、usionsarebasedonadetailanalysisofthegeometricparametersusedbythetrilineartransformation.Asystemof8nodeshexahedronelementsbasedonabovestressspaceanddiferentdisplacementspaceareconstructedtosolve3dimensionalproblemAndtheir

9、performancesaretestedthroughsomenumericalexamples.Thedatashowthattheeffectoftheadjustofcombinedparameter“amonginterval(01)isnotnotableforthenumericalresultsforelementsconstructedbyincompatibledisplacementandaboveconstrai

10、nedstressandthebestresultisgainedasaequalstooneforelementsconstrainedbycompatibledisplacementandconstrainedstress.Keywords:CombinedhybridvariationalprincipleHighperformanceelementEnergycompatibleconditionorthogonalitycon