method for nonlinear dynamics英文学习材料

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1、AppliedandComputationalMechanics5(2011)1520NewimplicitmethodforanalysisofproblemsinnonlinearstructuraldynamicsA.A.Gholampoura,∗,M.GhassemiehaaSchoolofCivilEngineering,UniversityofTehran,Tehran,IranReceived13October2010;receivedinrevisedform2May2011AbstractInthispaperanewmethodispropo

2、sedfordirecttimeintegrationofnonlinearstructuraldynamicsproblems.IntheproposedmethodtheorderoftimeintegrationschemeishigherthantheconventionalNewmarksfamilyofmethods.Thismethodassumessecondordervariationoftheaccelerationateachtimestep.Twovariableparametersareusedtoincreasethestabilit

3、yandaccuracyofthemethod.Theresultobtainedfromthisnewhigherordermethodiscomparedwithtwoimplicitmethods;namelytheWilson-θandtheNewmarksaverageaccelerationmethods.c2011UniversityofWestBohemia.Allrightsreserved.Keywords:directtimeintegration,nonlinearstructuraldynamics,secondorderaccele

4、ration,implicitmethod1.IntroductionProblemsinthetheoryofvibrationaredividedintwocategories;wavepropagationproblemsandinertiaproblems,whichthelatteriscalledstructuraldynamics.Intheseproblems,gov-erningfieldequationisasecondorderdifferentialequation[1,2].Fornonlinearsystems,itisusuallye

5、xpectedtosolveequationsofmotionnumerically[2].Inthetimeintegrationmethods,timeisdividedtoseveraltimestepsandanalgorithmisusedtopredictthevaluesofdisplace-ment,velocityoraccelerationateachtimebasedonpreviousvalue.Thealgorithmisbasedonanassumptionforvariationofdisplacementineachtimeste

6、pandsatisfyingtheequationofmotioninselecteddiscretetimes.Infactitisaformoffinitedifferencesolutionfordifferentialequations[211].Innonlinearanalysis,stiffnessiscalculatedatthebeginningofeachtimestepandthenre-sponseiscalculatedattheendofthistimestepwithassumingthatstiffnessisconstantthr

7、ough-outthestep.Thereforenonlinearityisconsideredbycontinuouslyupdatingthestiffness.Cal-culatedresponseswillbeconsideredattheendofeachtimestepastheinitialconditionsfornexttimestep.Thereforesystemnonlinearitybehaviorisreplacedwithaseriesofconsecutiveapproximatelinearcharacteristics[1,

8、2,5,8].Insom