結(jié)構(gòu)穩(wěn)定分析中基于有限元方程的突變理論建模方法.pdf

1、同濟(jì)大學(xué)土木工程學(xué)院博士學(xué)位論文結(jié)構(gòu)穩(wěn)定分析中基于有限元方程的突變理論建模方法姓名：王天英申請(qǐng)學(xué)位級(jí)別：博士專(zhuān)業(yè)：結(jié)構(gòu)工程指導(dǎo)教師：鄧長(zhǎng)根20080728ABSTRACTABSTRACTCatastropheTheory(CT)isapowerfulmathematicaltooltosolvenonlinearproblems，butinitsapplicationinstructuralstabilityanalysis，forta

2、kingpotentialenergyfunctionasthebasis，itisdifficultforCTtobeappliedtocomplexcontinuoussystemsordiscreteoneswithlotsofdegreesoffreedomInordertoexploittheapplicationofCTinstructuralstabilityanalysis，thispaperpresentsanewid

3、eaofusingnon—energymethodtoestablishcatastrophicmodelsinordertobuildbridgebetweentheanalyticalmethodCTandnumericalmethodfiniteelementmethod(FEM)Asaresult，CTCanbeappliedtononlinearstabilityanalysisofgeneralelasticconserva

4、tivesystemswithmultipleparametervariablesandgeneralizedcoordinatesTheresearchresultscanbeusedinstructuralpostbucklinganalysis，oVimizationandpassivebucklingcontrol，andSOOilTheresearchworkandmainconclusionsinthisPaperaresk

5、etchedasfollowsFirstly，onthepremisethatthecoordinatesofthecriticalpointaregiven，ageneraldiscriminantforclassifyingsimplecriticalpointsofimperfectstructuressubjectedtoconservativeloadingwithsmallinitialgeometricimperfecti

6、onsisputforwardwithperturbationmethodbasedonthecriticalequilibriumconditionsThentheclassificationofsimplecriticalpointsisrefinedlystudiedusingthediscriminantFurthermore，therelationshipsbetweensimplecriticalpointsandbasic

7、catastrophesareestablishedInaddition，basedonfundamentalprincipleofloading—perturbationmethodtoshiftequilibriumpath，foursteploadingunloadingproceduretopinpointthebifurcationpointbetweentheinitialequilibriumpathandthebranc

8、hingoneandtracethebranchpathsusinggeneralsoftwareforfiniteelementanalysisispresentedSecondly，thegeneralquantitativerelationshipbetweenstructuralsecantstiffnessmatrixandtangentstiffnessmatrixexpressedbyTaylorseriesexpress