Fuzzy structural analysis based on fundamental reliability concepts

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1、ComputersandStructures112-113(2012)183–192ContentslistsavailableatSciVerseScienceDirectComputersandStructuresjournalhomepage:www.elsevier.com/locate/compstrucFuzzystructuralanalysisbasedonfundamentalreliabilityconceptsJorgeE.Hurtado⇑,DiegoA.Alvarez,JulianaRamírezUniversidadNacionaldeColombia,S

2、edeManizales,Apartado127,Manizales,ColombiaarticleinfoabstractArticlehistory:FuzzystructuralanalysisisorientedtoestimatethemembershipfunctionofanoutputstructuralvariableReceived20March2012giventhemembershipfunctionsoftheinputones,whicharediscretizedinso-calleda-cutlevels.SuchanAccepted19August

3、2012estimationrequiresthesolutionoftwooptimizationproblemsforeachofthem.Inthispaperanalterna-tiveapproachispresented.Itconsistsinsolvingasingleoptimizationproblemfortheentireproblem,whichisthatofFORM(first-orderreliabilityanalysis).ItisshownthatFORMsolutionhasavaluableKeywords:property,namelyth

4、atitallowsorganizingtheorderstatisticsoftheoutputvariablealongthedesignFuzzystructuralanalysispointvector.ThispropertyisexploitedbyanonlinearprojectionofalargeamountofstandardGaussianStructuralreliabilitynumbers,truncatedaccordingtothemembershipfunctions,ontoabi-dimensionalspace.Fromthismap-In

5、tervalanalysisReliabilityplotpingthesamplesnecessaryfordirectlysolvingtheoptimizationproblemsareeasilydrawnusingtwoOrderstatisticscurves,whoseequationsarederivedfromasimilartransformationofthesecond-orderapproximationofthelimitstatefunction.Adetailedstructuralexampleshowsthatthedesiredmembersh

6、ipfunctionoftheresponsecanbeaccuratelyestimatedbytheproposedmethod.Ó2012ElsevierLtd.Allrightsreserved.1.Introductionavailableandonlysomeapproximatemodelisused.Inthesecondcase,thebasicvariablescanbeclassifiedintotwogroups:episte-Theanalysisofuncertaintyspreadinstructuralengineeringhasmicuncertai

7、ntyandaleatoryuncertainty;ontheonehand,theepi-mainlybeencarriedoutwiththetoolsofclassicalprobabilitythe-stemicorreducibleuncertaintyarisesduetothelackofknowledgeoryinthelast50years(seee.g.[1–5]).Thisapproach,however,isabouttheparameters