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1、CHAPTERFIVEOptimalPlasticDesignofBeams:AllowanceforSelfweight,BoundedSpatialGradients(Niordson-Constraints)andLinearSegments5.1INTRODUCTORYREMARKSIndesigningaero-spaceandnavalstructures,weight-minimizationisofpri•maryimportancesinceanyreductioninthestructuralmass
2、resultsinim•provedaccelerationandfueleconomy.Inthecaseofimmobileterrestrialstructures,suchasbuildingsandbridges,theleast-weightcriterionisoflesserimportancebecauseavarietyofpracticalconsiderationsrestrictthedesigntobeadopted.Notableexceptionsarelong-spanstructure
3、sfortworeasons:first,atlongerspansasignificantproportionofthetotalloadisduetoself•weight(deadload);second,evensmalldesignchangescanresultinseveralhundredpercentextrastructuralweightifthespanisinthevicinityofthespanningcapacity[see,forexample,RozvanyandWang,(1984)
4、andFig.1.12intheIntroduction].However,fortheoptimizationoflong-spanstructurestoberealistic,itisessentialtotakethemostsignificantloadcomponent,namelyselfweight,intoconsideration.Itwillbeseeninthenextsectionthatallowanceforselfweightinstructuraloptimizationbecomesr
5、elativelysimpleifstatic-kinematicoptimalitycriteriaareemployed.Unconstrainedandsimplifiedstructuraloptimizationoftenresultsinanunrealisticdistributionofthecross-sectionalareaforbeamsandgrid-likestructures(orofthethicknessforplatesandshells),includingsuddenchanges
6、inthecross-sectionalarea,vanishingcross-sections,impulse-likeconcentra•tionsoflocallyinfiniteintensityandribsoftheoreticallyinfinitesimalspacing205G.I.N.Rozvany,StructuralDesignviaOptimalityCriteria©KluwerAcademicPublishers1989ChapterFivePlasticDesign:Sel/weighta
7、ndGeometricalConstraints(inplatesandshells).Thesepropertiesoftheoreticalleast-weightsolutionswerediscussedextensivelyinaposthumouspaperbyPrager(1981).Un•usualfeaturesofleast-weightplatesweretreatedanalyticallybyRozvany,Olhoff,ChengandTaylor(1982),seealsoFig.I.11i
8、ntheIntroduction.Suchanomaliesinthesolutioncanrenderadesignunpracticalandmay,asNiordson(1983a,1983b)pointedout,alsoviolatefundamentalassumptionsoftheunderlying
