trefftz有限元理论与相关数值方法分析

《trefftz有限元理论与相关数值方法分析》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、RESEARCHONTREFFTZFINITEELEMENTTHEORYANDRELATEDNUMERICALMETHODSABSTRACTAsanewefficientnumericalmethod,TheTrefftzElementMethodinheritedtheadvantagesoftraditionalFiniteElementMethodandBoundaryElementMethod,andabandonedsomeoftheirshortcomings.Therefore,theTrefftzElementMethoda

2、regraduallytakenseriouslybothathomeandabroad.ThispaperisdividedintothreepartstostudytheTrefftzFiniteElementMethodandtherelatednumericaltechnology.Inthefirstpart,theTrefftzFiniteElementMethodisusedtosolvetheproblemofsteadyseepageoffreesurface.Thispaperproposedamethodcombini

3、ngadaptivemeshingtechnologyandTrefftzFiniteElementMethod,whichcaneffectivelymakeupfortheproblemthatthetraditionElementMethodcouldleadtolessaccuracyundertheconditionofmeshdistortion.Numericalresultsshowagoodagreementwithexperimentsolutionsoranalyticalsolutions.Inthesecondpa

4、rt,theTrefftzElementMethodisusedtosolvethepotentialproblemsoforthotropicaxisymmetric.Theproblemshaveawideapplicationinengineering,butingeneralitisathree-dimensionalproblem.Thispartonlystudythesituationthatthesolvingdomainandtheexternalloadareaxisymmetric.Firstofall,weassum

5、edtwoindependentpotentialinterpolationmode:inter-elementpotentialfieldandframepotentialfield,thenapplythemodifiedvariationalfunctionandGaussiandivergencetheoremtoeliminateregionalintegration.Finallywegetanelementstiffnessequationonlycontainedboundaryintegrationaccordingtov

6、aluetheorem.NumericalresultshaveagoodagreementwithanalyticalsolutionsorABAQUSresults.Inthethreepart,theTrefftzFiniteElementMethodisusedtosolvetheproblemofaxisymmetricpoissonequation.Theradialbasisfunction(RBF)dependonlyontheII万方数据Euclideandistancebetweenfieldpointandrefere

7、ncepoint(sometimesthecenterpointofelement),sotheyareisotropicandcanbeeasilyusedinmulti-dimensionaldiscretedatainterpolation.Thereforeweproposedamethodusingradialbasisfunctionapproximation,togetelementstiffnessequationoftheproblemcombinedmodifiedvariationalfunction.Numerica

8、lresultsshowagoodagreementwithexactsolutions.KEYWORDS：Trefftzfiniteelementmethod,adaptive