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1、NonlinearFiniteElementAnalysisofStructuresStrengthenedwithCarbonFibreReinforcedPolymer:AComparisonStudyX.S.Yang,J.M.Lees,andC.T.MorleyDepartmentofEngineering,UniversityofCambridgeTrumpingtonStreet,CambridgeCB21PZ,UKxy227@eng.cam.ac.ukAbstract.Modellingcrackpropagationin
2、fracturemechanicsisaverychallengingtask.Di?erentmethodsareusuallyrobustunderdi?erentconditionsandthereisnouniversallye?cientnumericalmethodfordy-namicfracturesimulations.Mostavailablemethodsarecomputation-allyextensiveandusuallyrequirefrequentremeshing.Thiscomparisonstu
3、dyfocusesonthreemajormethods:thediscreteelementmethod,theadaptive?xedcrackmethodandtheelement-freeGalerkinmethod.Byimplementingthesemethodstostudya2Dconcretebeamwithreinforce-mentofcarbon-?brereinforcedpolymerstraps,wehaveshownthatforsimulationsofalimitednumberofcracks,
4、?xedcrackmethodgivesthebestresults.Formultiplecrossovercracks,thediscreteelementmethodismoresuitable,whileformoderatenumberofelements,theelement-freeGalerkinmethodaresuperior.However,forlargenumberofelements,?xedcrackmethodismoste?cient.Comparisonswillbegiveninde-tails.
5、Inaddition,newalgorithmsarestillhighlyneededforthee?cientsimulationsofdynamiccrackpropagations.1IntroductionThetechniqueofstrengtheningreinforcedconcretestructureusingcarbon?bre-reinforcedpolymer(CFRP)ispromisingandcanhaveimportantapplicationsinmanyareas.However,anunder
6、standingofthebehaviourandin?uenceoftheFRPcompositesystemiscrucialfortheproperdesignofstructuralreinforcementstrategiesininfrastructuresuchasbridgesandbuildings[6,7].Thecomputersimulationisancost-e?ectivewayofimprovingsuchanunderstanding.Insimulatingthefractureandcrackgr
7、owth,therearethreemajorparadigms:discreteelementmethods,smearedcrackmethodsandelement-freeGalerkinmethods.Thediscreteelementmethodhastheadvantageoftracingeachindi-vidualcrackwithanirregulargeometry.Inordertodothis,substantialremesh-ingisrequiredtoaccommodatethearbitrary
8、geometryandboundariesalongthenewlycreatedcracksandthusextensivecomputationisrequiredwhichisusuallytime-consumi
