C1 static-kinematic optimality criteria

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1、CHAPTERONEStatic-KinematicOptimalityCriteria1.1AIMSTheaimofthischapteristoprovidethereaderwithacomprehensivelistofoptimalitycriteriaforbothplasticandelasticdesign.ThesecriteriacanberegardedasextensionsofthePrager-Shield(1967)conditionandarecalled"static-kinematic"becausetheyallrequirestaticallyad

2、missiblestressfieldsandkinematicallyadmissiblestrainfields.Aswillbeexplained,kinematicadmissibilityisnotanoriginalprerequisiteofplasticdesign(basedonthelowerboundtheoremofplasticlimitanalysis)andhenceitcanbe'regardedasanadditionaloptimalitycondition.ThePrager-Shieldconditionitselfhasbeenredefined

3、andgeneralizedbytheauthorandhisassociates,bytheintroductionofthegradientoperator9andthroughextensionstonon•convexanddiscontinuousspecificcostfunctions.Finally,itshouldbenotedthatequivalentsofthePrager-ShieldconditioncanbederivedfromtheoriesofMasur(1970),Mroz(1963),Save(1972)orPragerandTaylor(1968

4、).BeforediscussingthetheoreticalframeworkofthePrager-approachtostructuraloptimization,asimpleexamplewillbepresentedwithaviewtoillustratingmostofthefundamentalconceptstobetreatedmoresystemati•callylaterinthisbook.ImportantNotefortheNon-SpecialistReader.WhilsttheIntroduc•toryexample(Section1.2)andb

5、ackgroundinformation(Sections1.3-1.7andthefirstpartofSection1.8)areessentialfortheunderstandingofsubsequentchapters,thelatterpartofthischapterismeanttobeareferencetextwithaviewtoenablingthereadertolookuptheappropriateoptimalitycriteriaforparticularclassesofproblems.Thenon-specialistreaderwould,th

6、erefore,probablyfinditeasierifhe/sheignoredthisreferencepartofChapterOne21G.I.N.Rozvany,StructuralDesignviaOptimalityCriteria©KluwerAcademicPublishers1989ChapterOneStatic-KinematicOptimalityCriteria(Section1.9onwards)duringthefirstreadingofthebookandacquiredabet•tercomprehensionoftheprinciplesinv

7、olvedbyworkinghis/herwaythroughthesolvedproblemsinthesubsequentchapters.Shouldthereaderrequireinformationaboutaparticularclassofoptimalityconditions,thereisusuallyacross-reference(indicatedby.)inthischaptertosubsequent