C8 the theory of optimal layouts and a brief review of its applications

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1、CHAPTEREIGHTTheTheoryofOptimalLayoutsandaBriefReviewofitsApplications"Mostoftheliteratureonstructuraloptimizationisconcernedwiththeoptimalchoiceofcross-sectionaldimensions.Whenthelayoutaswellasthecross-sectionaldimensionsareatthechoiceofthedesigner,struturaloptimiz

2、ationbecomesamuchmorechallengingproblem."(PragerandRozvany,1971).8.1INTRODUCTORYREMARKSThetheoryofoptimallayoutsforstructuralsystems,developedinthelateseventiesbyPragerandtheauthorandextendedconsiderablyinrecentyearsbytheauthor'sresearchgroup,isoneofthemostusefulap

3、plicationsofstatic-kinematicoptimalitycriteria.Firstthegeneraltheoryisoutlinedandillustratedwithintroductoryexamples,thenthedifferencebetween"classi•cal"and"advanced"layouttheoriesisexplainedandfinallyabriefreviewofsomerecentapplicationsisgiveninthischapter.Layouto

4、ptimizationin•volvesnotonlytheselectionofthecross-sectionaldimensionsandtheshapeofcentroidalaxesandmiddlesurfacesbutalsotheoptimalchoiceofthetopography(topology),spatialsequenceandconnectivityofmembers(com•ponents)andjointsinastructuralsystem.Thebasicideaoflayoutop

5、timizationviastatic-kinematicoptimalitycri•teriawasproposedaroundtheturnofthecenturybyMichell(1904).Apartfrombeingperhapsintellectuallythemostchallengingareaofstructuralop•timization,optimallayouttheoryhasimportantpracticalimplications.AsexplainedthroughFig.1.12int

6、heIntroduction,theselectionofthebeststructurallayoutcaninvolvemuchmoresubstantialsavingsthananopti•mizationprocedurerestrictedtocross-sectionaldimensions.323G.I.N.Rozvany,StructuralDesignviaOptimalityCriteria©KluwerAcademicPublishers1989ChapterEightOptimalLayoutThe

7、oryanditsApplicationspp(a)(b)Fig.8.1Exampleofastructuraluniverse:pin-jointedframe.8.2THECONCEPTOFSTRUCTURALUNIVERSEWedefinethe"structuraluniverse"astheunionofallfeasible(orpotentialorcandidate)members(elements)inastructuraldesignproblem.Sincestatic•kinematicoptimal

8、itycriteriafurnishastrainrequirement(usuallyinequality)alsoforvanishingcross-sections(i.e.non-optimalmembers),itsfulfilmentfortheentirestructural