A Tour of Nonlinear Analysis

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1、.2ATourofNonlinearAnalysis2–1Chapter2:ATOUROFNONLINEARANALYSIS2–2TABLEOFCONTENTSPage§2.1.Introduction2–3§2.2.EquilibriumPathandResponseDiagrams2–3§2.2.1.Load-deflectionresponse.............2–3§2.2.2.Terminology.................2–3§2.3.SpecialEquilibriumPoints2–4§2.3.1.Criticalpoints...........

2、......2–4§2.3.2.Turningpoints................2–5§2.3.3.Failurepoints.................2–5§2.4.LinearResponse2–5§2.5.TangentStiffnessandStability2–6§2.6.GeneralizedResponse2–7§2.7.ResponseFlavors2–8§2.8.EngineeringApplications2–9§2.9.SourcesofNonlinearities2–9§2.10.GeometricNonlinearity2–11§2.1

3、1.MaterialNonlinearity2–12§2.12.ForceBCNonlinearity2–13§2.13.DisplacementBCNonlinearity2–14§2.Exercises......................2–152–22–3§2.2EQUILIBRIUMPATHANDRESPONSEDIAGRAMS§2.1.IntroductionThischapterreviewsnonlinearstructuralproblemsbylookingatthemanifestationandphysicalsourcesofnonlinearbe

4、havior.Webeginbyintroducingresponseasapictorialcharacterizationofnonlinearityofastructuralsystem.Responseisagraphicalrepresentationofthefundamentalconceptofequilibriumpath.Thisconceptpermeatestheentirecoursebecauseofbothitsintrinsicphysicalvalueandthefactthatincrementalsolutionmethods(mention

5、edinChapter1)arebasedonit.Finally,nonlinearitiesareclassifiedaccordingtotheirsourceinthemathematicalmodelofcon-tinuummechanicsandcorrelatedwiththephysicalsystem.Examplesofthesenonlinearitiesinpracticalengineeringapplicationsaregiven.§2.2.EquilibriumPathandResponseDiagramsTheconceptofequilibriu

6、mpathplaysacentralroleinexplainingthemysteriesofnonlinearstructuralanalysis.Thisconceptlendsitselftographicalrepresentationintheformofresponsediagrams.Themostwidelyusedformofthesepicturesistheload-deflectionresponsediagram.Throughthisrepresentationmanykeyconceptscanbeillustratedandinterpretedi

7、nphysical,mathematicalorcomputationalterms.§2.2.1.Load-deflectionresponseThegrossoroverallstaticbehaviorofmanystructurescanbecharacterizedbyaload-deflectionorforce-displacementresponse.Theresponseisusuallydrawnintwodimensionsasax-yplotasillustr