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1、Chapter9ShakedownandSafetyAssessmentNestorZouainFederalUniversityofRiodeJaneiro,RiodeJaneiro,BrazilHistorically(Melan,1938;Neal,1950;Drucker,Prager1Introduction291andGreenberg,1951;Koiter,1960;KonigandMaier,¨1981),thewordshakedown,introducedinthe1940sby2BasicNotation294W.Prager(Symonds,2000),
2、becamesynonymouswith3ClassicalStaticandKinematicShakedownelasticadaptationinthepresenceofvariableloadings,Formulations296thatis,asafestabilizedphenomenon,oftenduetosome4ExtremumPrinciplesforElasticShakedown299limitedplasticdeformation(orequivalently,duetothe5DiscreteModelsforElasticShakedown3
3、01residualstressdistributionassociatedwithinelasticstrains).6PreventingAlternatingPlasticity304Inthischapter,thewordshakedown,wheneverusedwithout7PreventingSimpleMechanismsofadjective,meanselasticshakedown.IncrementalCollapse304Ontheotherhand,concerningthefailureanalysisof8ExtensionsConcernin
4、gHardeningandductilestructures,thetermsalternatingplasticityandincre-TemperatureEffects307mentalcollapse,besidesplasticcollapse,havebecome9OtherExtensionsofShakedownTheory310widelyusedtoidentifyfailuremodesundervariableload-10AnAlgorithmforShakedownAnalysis312ings.Astructureundergoesalternati
5、ngplasticity,often11NumericalProceduresforShakedowncalledplasticshakedown,whenthe?uctuatingloadingpro-Analysis316gramproduces,afteranyarbitrarilylargetime,someplasticdeformationaswellasasubsequentvanishingofthenet12Applications321deformation.Thisinducesfailureduetolow-cyclefatigue.13Conclusio
6、ns330Likewise,thestructurefailsbyincrementalcollapsewhenReferences331plasticdeformations(percycle)accumulateintheformofacompatiblestraindistributionthatleadstoexcessiveinelas-ticdeformation.1INTRODUCTIONThemainsubjectsofthischapterarethevariationalformulationsforthecomputationofasafetyfactori
7、nManyengineersandresearchershavecontributedtoidentifyshakedownanalysis,thenumericalproceduresavailabletotheessentialfeaturesintypicalfailurephenomenarelatedimplementthisanalysis,andanintroductoryviewonthetoinelasticstructuresormachinecomponen
