OptimalDesignofFilament-WoundCompositeToroids413

OptimalDesignofFilament2WoundCompositeToroids

LeiZu,SotirisKoussios,AdriaanBeukers

DesignandProductionofCompositeStructures,FacultyofAerospaceEngineeringDelftUniversityofTechnology,Kluyverweg1,2629HSDelft,TheNetherlands

Abstract:Compositetoroidshaveemergedasanattractivealternativeinmanyindustrialfieldswherespace2saving,weightreductionandnon2driftofcenterofmassarerequired.Thispaperaimstodeter2minetheoptimalwindingtrajectoriesforgeodesicallyoverwoundtoroidalpressurevessels,andtodem2onstratethefavorableperformanceofthepresentdesignmethod.Withthecontinuumtheo2ryandthegeodesicwindinglaw,theequationsthatonto2rusarederived.Thegeneralcriteriaforavoidingaformulated,basedondifferentialgeometry.Next,theattheequatorareconsideredasthedesignvariables,tactsastheobjectivefunction.Theoptimalgeodesictrelativebendingradii,aredeterminedtoevaluatetheeffectontheoftoroids.Thestressfieldismodeledusingclassicallaminationtheoryandthe2Wutensortheoryisemployedasthefailurecriterionforanindividuallayer.Re2sultsshowthattheoptimizationalgorithmisefficientandconvergenttostablesolutionswhiletheop2timalwindingpathobtaineddoessatisfytherequirementsforthemanufacturingprocess.Resultsalsoindicatethatfilament2woundtoroidsdesignedusingthepresentmethodshowbetterperformance,mainlytriggeredbymaximumutilizationofthelaminatestrengthascomparedtoconventionalgeodes2ics2basedtoroids.Therecommendeddesign2orientedmethodcaneasilybeappliedduringpreliminarydimensioningandoptimizationoffilament2woundtoroidalpressurevessels.

Keywords:Compositepressurevessels;Filamentwinding;Toroids;Geodesicwinding;Classicallam2inationtheory

Documentcode:A　　ArticleID:100124381(2009)Suppl220413207

efficiency,new2fashionedconfiguration,andlowas2

INTRODUCTION

Optimalfilamentarycompositepressurevesselsprovidesignificantadvantagesascomparedtotheirsteel2basedcounterparts.Thefilamentwindingtech2niqueiswidelyusedforthemanufacturingofFRPproducts.Itisaprocessbywhichcontinuousreinfor2cingfibersarepreciselypositionedinapredeterminedpatternonarotatingmandreltoformaclosedshape.TheprocessisnormallyCNCcontrolledtopermithighlyautomatedproduction.Continuousfiberscanbeorientedtomatchthedirectionandmagnitudeofstressesinalaminatedstructure,allowingoptimalre2inforcementloading.Morerecently,compositeto2roidalstructuresshowgreatpotentialforapplicationsinavarietyofindustriesbecauseoftheirstructural

pectratio.Thetoroidbelongstotheclassofdoublycurvedcomponents,andisaninterestingalternativeforspaceshavinglimitedheight.Itcanberegardedasabent,endlesscylinderthatsavesontheneedformaterialintheendcaps.Asashape,itisthusatleastasstructurallyefficientasacylinder.Sofar,filament2woundconvexbodieshavebeenstudiedformanyyearsandthedesignandproductionofaxisym2metricallywoundpartssuchascylinders,spheresanddomeshasbecamerelativelysimpleandma2

ture[1-4].Inwindinganaxisymmetricallyconvexbody,abasicfiberpathisrepeatedcontinuouslybyindexingthewindingaxis,opposedtoatorus,whichisadoubly2closedbodyhavingaconvex2concavesur2face.Moreover,forhighappliedloads,toroidalpressurevesselsdemandbetterstructuralefficiency