外文翻译机械结构的可靠性优化设计Word文档下载推荐.docx
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外文翻译机械结构的可靠性优化设计Word文档下载推荐.docx
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secondmomentmethods,fulldistributionmethods),Lackingasinglemethod,
individualsarelikelytoadoptseparatestrategiesforhandlingtheuncertaintyintheirparticularproblems,Thissuggeststhepossibilityofdifferentreliabilitypredictionsinsimilarstructuraldesignsituations,Then,therearedivergingopinionsonmany
basicissues,fromtheverydefinitionofreliability-basedoptimization,includingthedefinitionoftheoptimumsolution,theobjectivefunctionandtheconstraints,toitsapplicationinstructuraldesignpractice,Thereisaneedtoformallyconsiderthese
itessinthemergerofpresentstructuraloptimizationresearchwithreliability-baseddesignphilosophy。
Ingeneral,anoptimizationproblemcanbestatedasfollows,Minimize
subjecttotheconstraints
whereXisan-dimensionalvectorcalledthedesignvector,f(X)iscalledthe
objectivefunctionand,"
k(X)and}i(X)are,respectively,theinequalityandequalityconstraints,Thenumberofvariablesnandthenumberofconstraints,Lneednotbe
relatedinanyway,Thus,Lcouldbelessthan,equaltoorgreaterthanninagivenmathematicalprogrammingproblem,Insomeproblems,thevalueofLmightbe
zerowhichmeanstherearenoconstraintsontheproblem,Suchtypeofproblemsare
called"
unconstrained"
optimizationproblems,ThoseproblemsforwhichLisnot
equaltozeroareknownas"
constrained"
optimizationproblems。
Traditionallythedesignerassumestheloadingonanelementandthestrengthofthatelementtobeasinglevaluedcharacteristicordesignvalue,Perhapsitisequal
tosomemaximum(orminimum)anticipatedornominalvalue,Safetyisassuredby
introducingafactorofsafety,greaterthanone,usuallyappliedasareductionfactortostrength。
Probabilisticdesignispropose:
asanalternativetotheconventionalapproachwiththepromiseofproducing"
betterengineered"
systems,eachfactorinthedesign
processcanbedefinedandtreatedasarandomvariable,Usingmethod-ologyfrom
probabilistictheory,thedesignerdefinestheappropriatelimitstateandcomputestheprobabilityoffailureP}oftheelement,Thebasicdesignrequirementisthat,where
pfisthemaximumallowableprobabilityoffailure。
Advantagesofadoptingtheprobabilisticdesignapproacharewelldocumented(Wu,1984),Basicallytheargumentsforprobabilisticdesigncenteraroundthefactthat,relativetotheconventionalapproach,a)riskisamoremeaningfulindexofstructuralperformance,andb)areliabilityapproachtodesignofasys-tomcantendtoproducean"
optimum"
designbyensuringauniformriskinallcomponents。
Optimization,whichmaybeconsideredacomponentofoperationsresearch,istheprocessofobtainingthebestresultbyfindingconditionsthatproducethemaximumorminimumvalueofafunction,Table1,1illustratesareaofoperations
research。
Mathematicalprogrammingtechniques,alsoknownasoptimizationmethods,areusefulinfindingtheminimum(ormaximum)ofafunctionofseveralvariablesunderaprescribedsetofconstraints,Rao(1979)presentedadefinitionanddescriptionofsomeofthevariousmethodsofmathematicalprogramming,Stochas-ticprocess
techniquescanbeusedtoanalyzeproblemswhicharedescribedbyasetofrandomvariables,Statisticalmethodsenableonetoanalyzetheexperimentaldataandbuildempiricalmodelstoobtainthemostaccuraterepresentationsofphysicalbehavior。
OriginsofoptimizationtheorycanbetracedtothedaysofNewton,La-grangeandCauchyinthe1800'
x,TheapplicationofdifferentialcalculustooptimizationwaspossiblebecauseofthecontributionsofNewtonandLeibnitz,Thefoundationsof
calculusofvariationswerelaidbyBernoulli,Euler,LagrangeandWeirstrass,The
methodofoptimizationforconstrainedproblems,whichinvolvestheadditionofunknownmultipliersbecameknownbythenameitsinventor,La-grange,Cauchy
presentedthefirstapplicationofthesteepestdescentmethodtosolveminimizationproblems。
Inspiteoftheseearlycontributions,verylittleprogresswasmadeuntilthemiddle
ofthetwentiethGentry,whenhigh-speeddigitalcomputersmadetheimplementationofoptimizationprocedurespossibleandstimulate,dfurtherresearchonnewmethods,Spectacularadvancesfollowed,producingam;
}sssiveliteratureonoptimizationtechniques,Thisadvancementalsoresultedintheemergenceofseveralwell-definednewareasinoptimizationtheory。
ItisinterestingtonotethatmajordevelopmentsintheareaofnumericalmethodsofunconstrainedoptimizationhavebeenmadeintheTTnitedKingdomonlyinthe1960'
x,ThedevelopmentofthesimplexmethodbyDantzig(1947)forlinearprogrammingandtheannunciationoftheprincipleofoptimalitybyBellman(195?
)fordynamicprogrammingproblemspavedthewa,;
f}=developmentofthemethods
ofconstrainedoptimization,TheworkbyKuhnandTucker(1951)onnecessaryand
xuflicientconditionsfortheoptimalxolutionofprogrammingproblemslaidfoundationsforlaterresearchinnonlinearprogramming,theoptimizationareaofthisthesis。
Althoughnosingletechniquehasbeenfoundtobeuniversallyapplicablefornonlinearprogramming,theworksbyCacrol(1961)andFiaccoandMcCormic(1968)suggestedpracticalsolutionsbyemployingwell-knowntechniquesofunconxtrainedoptimization,GeometricprogrammingwasdevelopedbyDufhn,ZenerandPeterson(1960),Gomory(1963)pioneeredworkinintegerprogramming,whichisatthistimeanexcitingandrapidlydevelopingareaofoptimizationresearch,Many
"
real-world"
applicationscanbecastinthiscategoryofproblem,Dantzig(1955)and
CharnelandCooper(1959)developedstochasticprogrammingtechniquesandsolvedproblemsbyassumingdesignparameterstobeindependentandnormallydistributed。
Techniquesofnonlinearprogramming,employedinthisstudy,canbecategorized
1,one-dimensionalminimizationmethod
2,unconstrainedmultivariableminimization
A,gradientbasedmethod
B,nongradientbasedmethod
3,constrainedmultivariableminimization
B,gradientbasedmethod
Thegradientbasedmethodsrequirefunctionandderivativeevaluationswhilethenongradientbasedmethodsrequirefunctionevaluationsonly,Ingeneral,onewould
expectthegradientmethodstobemoreeffecti;
re,duetotheaddedinformationprovided,However,ifanalyticalderivativesareavailable,thequestionofwhetherasearchtechniqueshouldbeusedatallispresented,Ifnumericalderivative
approximationsareutilized,theefficiencyofthegradientbasedmethodsshouldbeapproximatelythesameasthatofnongradientbasedmethods,Gradientbased
methodsincorporatingnumericalderivativeswouldbeexpectedtopresentsomenumericalproblemsinthevicinityoftheoptimum,i,e,,approximationstoslopes
wouldbecomesmall,Fig,1,1showsthe$owchartofgeneraliterativeschemeofoptimization(Rao,1979),
Noclaimismadethatsomemethodsarebetterthananyothers,Amethod
workswellononeproblemmayperformverypoorlyonanotherproblemofthesamegeneraltype,Onlyaftermuchexperienceusingallthemethodscanonejudgewhichmethodwouldbebetterforaparticularproblem(KuestersndMize,1973).
Firstattemptstoapplyprobabilisticandstatisticalconceptsinstructuralanalysisdatebacktothebeginningofthiscentury,However,thesubjectaidnotreceive
muchattentionuntilaftertheWorldWarII,InOctober1945,ahistoricpaperwritten
byA,M,Freudenthalentitled"
TheSafetyofStructures"
appearedintheproceedingsoftheAmericanSocietyofCivilEngineers,Thepublication
ofthispapermarkedthegenesisofstructuralreliabilityintheU,S,A,,Professor
F:
eudenthalcontinuedformanyyearstobeintheforefrontofstructuralreliabilityandriskanalysis,
Duringthe1960'
stherewasrapidgrowthofacademicinterestinstruc-totalreliabilitytheory,Classicaltheorybecamewelldevelopedandwidelyknown
throughafewinfluentialpublicationssuchasthatofFreudenthal,Garrelts,andShi-nouzuka(1966),Pugsley(1966),KececiogluandCormier(1964),Ferry-BorgesandCastenheta(1971,andHaugen(1968),However,professionalacceptancewas
lowforseveralreasons,Probabilisticdesignseemedcumbersome,thetheory,
particularlysystemanalysis,seemedmathematicallyintractible,Littledatawere
available,andmodelingerrorwasanissuewhichneededtobeaddressed,
Buttherewereearlyeffortstocircumventtheselimitations,Turkstra(l070)
Yr}}ntedstructuraldesignasaproblemofdecisionmakingunderuncertaintyandrisk,Lind,Turkstra,andWright(1965)definedtheproblemofrationaldesignofacodeasfindingasetofbestvaluesoftheloadandresistancefactors,Cornell(1967)
suggestedtheuseofasecondmomentformat,andsubsequentlyit
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