流形方法的理論與應(yīng)用研究.pdf

1、重慶大學博士學位論文流形方法的理論與應(yīng)用研究姓名：蔡永昌申請學位級別：博士專業(yè)：固體力學指導(dǎo)教師：張湘?zhèn)?001.3.1●ABSTRACTThemanifoldmethod(MM)，aprosperousnumericalmethodbasedonthefinitecover，isaveryflexiblenumericalanalysismethodwhichcanuniformlydealwithcalculatingproblem

2、softhewidelyusedfiniteelementmethod(FEM)，discontinuousdeformationanalysis(DDA)andanalyticmethodThemainworksofthisdissertationaretoadoptthestandardrectangle，thetraditionalfiniteelementsandtheoverlappingsectorstoconstructt

3、hecoversysteminMM，andapplyMMtothelinearanalysisoftwodimensionalcontinuousbodysandthesimutationofopencrackpropagationFirstofa11，therectangularmeshesarechosenasthecoversystemofMMSomepivotaltechniquesinMMsuchastheimplemetio

4、nofessentialboundaryconditions，theselectionofweightfunctions，thecomputationmethodofhighprecisionstress，thenumericalintegrationofmanifoldelementandtheinfluenceofthehigh—orderdisplacementfunctionsarediscussedindetailBecaus

5、ethestandardrectangularmeshesareuniformlyusedforcomplexbodys，thismethodhastheadvantagesofeasyimplementing，applyingandincorporatingwiththeCADtechnologyFortheproposedtheoryandmethod，theobjectedorientedprogrammingisintroduc

6、edintotheprogramdesigninginMMByabstractingthefinitecoversystemofMMasindependentdataclassesthedesignandimplementionoftheobjectsaboutMMarestudiedinwhichtheobjectsaremanagedbytechniquesoftreestructureForcomplexareawitharbit

7、raryshapethecoversystemofMMhavebeenautomaticallygeneratedbyusingtheseobjectsandtreesByapplyingcontourintegralmethodandhigh—orderdisplacementfunctionsofMMweobtaintheaccuratestressintensityfactorsofmixed—modecrackThen，theo

8、pencrackpropagationofthemixedmodeIand11issimulatedbymeansoftheoriesoflinearelasticfracturemechanicsThisprovidesasimpleandeffectivenumericalwayforcrackevolvementstudyingInaddition，basedonthetheoryofmanifoldcoverandmovingl

9、eastsquares(MLS)，animprovedformulationoftheelementfreemethod(IEFM)isintroducedTheproposedmethodcanavoidtheelementmeshingandsimplifytheconstructionofapproximationsinthefieldbyusingthediscretecircleandsectorcoversIEFMcanal