REFINED TOPOLOGY OPTIMIZATION SCHEMES FOR CONCEPTUAL DESIGN OF STRUCTURES

Abstract

Structural topologyoptimizationhasplayedanimportantroleinrecentimprovementsinengineering and constructionsectors,includingthecrucialtransportationinfrastructure.Theinventionandex- ploitation ofinnovativemathematicalapproachestoengineeringchallengesresultedinthecreation of uniquestructuralsystems.Furthermore,duetothecontinualdevelopmentofnewtoolsandthe constant expansionincomputingcapability,today’sarchitectsandengineershaveaccesstoawide range ofskills.Despiteextensivestudy,thekeybarrierstothewiderimplementationoftopology optimization processesincludechallengesindevelopingsophisticatedmultiphysicsalgorithms,high processing costs,manufacturinglimits,andsoon.Thisstudyaimstosolvesomedifficultiesrelated to algorithmicdevelopmentandcomputingefficiencyandapplythemtoimprovetheperformanceof buildingandbridgestructures. In chaptertwo,topologyoptimizationisrevisitedinthecontextofnonlinearityanddynamicload- ing. TheprimaryfocusisonintegratinggeometricnonlinearitythroughtheTotalLagrangianfor- mulation. AnadditionalquadratictermintheGreen-Lagrangianstrainensuresthepropermodeling of largedeformationstrain,complementingthehyperelasticSt.Venantmaterialmodel.Thestudy employsthedensity-basedtopologyoptimizationmethod,whichpenalizesintermediatedensities.A notable challengearisesfromthepronounceddistortionoflow-densityelements,resultinginnumeri- cal instability.Toaddressthisissue,awell-establishedelementremovaltechniqueisutilized,wherein low-densityelementsareexcludedfromtheconvergencecriteria.Despitealltheseadvancements, topology evolutionthroughdesignvariableupdatingschemesmayleadtoslowerconvergenceoreven divergence.Themaincontributionofthisstudyliesinrevisingthepopularoptimalitycriteriaupdate scheme andmakingsomeimportantmodificationstoit.Specifically,thewayofhandlingtheLagrange multiplier andtheupdatingstepsofthedesignvariablehasbeenmodifiedbasedontheconditional convexlinearizationapproach.Theresultsshowpromisingconvergenceratesandoptimizedshapes. Chapter threediscussesthedynamicresponsetopologyoptimizationprocess.Bothtime-domain and frequency-domaincasestudieshavebeenpresented.Adjointsensitivitieshavebeenusedforall of theobjectivefunctions,namelydynamiccompliance,eigenvalues,andmodalcompliance.Appli- cations tolateralload-resistingframestructuresofbuildingssubjectedtogroundexcitationhavebeen showninadditiontooptimizingtheeigenvaluetoimprovedynamicbehavior.Finally,theoptimized shape ofbridgesuperstructureshapesundermovingvehicularloadinghasbeenstudied.Ithasbeen realized thatdespitethereductioniniterations,thefiniteelementsolverstilltakeshugecomputational time withtherefinementofthegeometry.Thesolutioninthisdirectionhasbeenattemptedinour second researchobjective.