结构稳定理论之钢结构设计论文英文版

GraduateCourseWorkSteelStructureStabilityDesignSchool:ChinaUniversityofMiningName:LiuFeiStudentID:TSP130604088Grade:2013FinishDate:2014.1.1AbstractSteelstructurehasadvantagesoflightweight,highstrengthandhighdegreeofindustryalization,whichhasbeenwidelyusedintheconstructionengineering.Weoftenhearthistheaccidentcasecausedbyitsinstabilityandfailureofstructureofcasualtiesandpropertylosses,andthecauseofthefailureisusuallycausedbystructuredesignflaws.Thispapersaystheexperiencesinthedesignofstabilityofsteelstructurethroughthesummaryofthestabilityofsteelstructuredesignoftheconcept,principle,analysismethodandcombinationwithengineeringpractice.Keywords:steelstructure;stabilitydesign;detailstructureSteelStructureStabilityDesignStructurallystablesystemswereintroducedbyAleksandrAndronovandLevPontryaginin1937underthenamesystèmesgrossières,orroughsystems.Theyannouncedacharacterizationofroughsystemsintheplane,theAndronov–Pontryagincriterion.Inthiscase,structurallystablesystemsaretypical,theyformanopendensesetinthespaceofallsystemsendowedwithappropriatetopology.Inhigherdimensions,thisisnolongertrue,indicatingthattypicaldynamicscanbeverycomplex(cfstrangeattractor).AnimportantclassofstructurallystablesystemsinarbitrarydimensionsisgivenbyAnosovdiffeomorphismsandflows.Inmathematics,structuralstabilityisafundamentalpropertyofadynamicalsystemwhichmeansthatthequalitativebehaviorofthetrajectoriesisunaffectedbyC1-smallperturbations.Examplesofsuchqualitativepropertiesarenumbersoffixedpointsandperiodicorbits(butnottheirperiods).UnlikeLyapunovstability,whichconsidersperturbationsofinitialconditionsforafixedsystem,structuralstabilitydealswithperturbationsofthesystemitself.Variantsofthisnotionapplytosystemsofordinarydifferentialequations,vectorfieldsonsmoothmanifoldsandflowsgeneratedbythem,anddiffeomorphisms.Thestabilityisoneofthecontentwhichneedstobeaddressedinthedesignofsteelstructureengineering.Threearemoreengineeringaccidentcaseduetothesteelstructureinstabilityinthereallife.Forexample,thestadium,inthecityofHartford92mby110mtotheplaneofspacetrussstructure,suddenlyfellonthegroundin1978.Thereasonisthecompressivebarbucklinginstability;13.2mby18.0msteeltruss,in1988,lackofstabilityofthewebmembercollapsedinconstructionprocessinChina;OnJanuary3,2010intheafternoon,38msteelstructurebridgeinKunmingNewacrosssuddenlycollapsed,killingsevenpeople,8peopleseriouslyinjured,26peopleslightlyinjured.Thereasonisthatthebridgesteelstructuresupportingsystemisoutofstability,suddenlyabridgecollapsingdownto8mtall.Wecanseefromtheabovecase,theusualcauseofinstabilityandfailureofsteelstructureistheunreasonablestructuraldesign,structuraldesigndefects.Tofundamentallypreventsuchaccidents,stabilityofsteelstructuredesignisthekey.Structuralstabilityofthesystemprovidesajustificationforapplyingthequalitativetheoryofdynamicalsystemstoanalysisofconcretephysicalsystems.TheideaofsuchqualitativeanalysisgoesbacktotheworkofHenriPoincaréonthethree-bodyproblemincelestialmechanics.Aroundthesametime,AleksandrLyapunovrigorouslyinvestigatedstabilityofsmallperturbationsofanindividualsystem.Inpractice,theevolutionlawofthesystem(i.e.thedifferentialequations)isneverknownexactly,duetothepresenceofvarioussmallinteractions.Itis,therefore,crucialtoknowthatbasicfeaturesofthedynamicsarethesameforanysmallperturbationofthemodelsystem,whoseevolutionisgovernedbyacertainknownphysicallaw.QualitativeanalysiswasfurtherdevelopedbyGeorgeBirkhoffinthe1920s,butwasfirstformalizedwithintroductionoftheconceptofroughsystembyAndronovandPontryaginin1937.ThiswasimmediatelyappliedtoanalysisofphysicalsystemswithoscillationsbyAndronov,Witt,andKhaikin.ThetermstructuralstabilityisduetoSolomonLefschetz,whooversawtranslationoftheirmonographintoEnglish.IdeasofstructuralstabilityweretakenupbyStephenSmaleandhisschoolinthe1960sinthecontextofhyperbolicdynamics.Earlier,MarstonMorseandHasslerWhitneyinitiatedandRenéThomdevelopedaparalleltheoryofstabilityfordifferentiablemaps,whichformsakeypartofsingularitytheory.Thomenvisagedapplicationsofthistheorytobiologicalsystems.BothSmaleandThomworkedindirectcontactwithMaurícioPeixoto,whodevelopedPeixoto'stheoreminthelate1950's.WhenSmalestartedtodevelopthetheoryofhyperbolicdynamicalsystems,hehopedthatstructurallystablesystemswouldbetypical.Thiswouldhavebeenconsistentwiththesituationinlowdimensions:dimensiontwoforflowsanddimensiononefordiffeomorphisms.However,hesoonfoundexamplesofvectorfieldsonhigher-dimensionalmanifoldsthatcannotbemadestructurallystablebyanarbitrarilysmallperturbation(suchexampleshavebeenlaterconstructedonmanifoldsofdimensionthree).Thismeansthatinhigherdimensions,structurallystablesystemsarenotdense.Inaddition,astructurallystablesystemmayhavetransversalhomoclinictrajectoriesofhyperbolicsaddleclosedorbitsandinfinitelymanyperiodicorbits,eventhoughthephasespaceiscompact.Theclosesthigher-dimensionalanalogueofstructurallystablesystemsconsideredbyAndronovandPontryaginisgivenbytheMorse–Smalesystems.Structuretheoryofstabilitystudywasconductedonthemathematicalmodeloftheideal,andthea