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时间:2020-04-21
《非线性解析概要-Abaqus 6.9 Nonlinearity.doc》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、8. NonlinearityThischapterdiscussesnonlinearstructuralanalysisinAbaqus.Thedifferencesbetweenlinearandnonlinearanalysesaresummarizedbelow.LinearanalysisAlltheanalysesdiscussedsofarhavebeenlinear:thereisalinearrelationshipbetweentheappliedloadsandtheresponseofthesystem.Forexample,ifalin
2、earspringextendsstaticallyby1 munderaloadof10 N,itwillextendby2 mwhenaloadof20 Nisapplied.ThismeansthatinalinearAbaqus/Standard analysistheflexibilityofthestructureneedonlybecalculatedonce(byassemblingthestiffnessmatrixandinvertingit).Thelinearresponseofthestructuretootherloadcasescan
3、befoundbymultiplyingthenewvectorofloadsbytheinvertedstiffnessmatrix.Furthermore,thestructure'sresponsetovariousloadcasescanbescaledbyconstantsand/orsuperimposedononeanothertodetermineitsresponsetoacompletelynewloadcase,providedthatthenewloadcaseisthesum(ormultiple)ofpreviousones.Thisp
4、rincipleofsuperpositionofloadcasesassumesthatthesameboundaryconditionsareusedforalltheloadcases.Abaqus/Standardusestheprincipleofsuperpositionofloadcasesinlineardynamicssimulations,whicharediscussedinChapter7,“LinearDynamics.”NonlinearanalysisAnonlinearstructuralproblemisoneinwhichthe
5、structure'sstiffnesschangesasitdeforms.Allphysicalstructuresarenonlinear.Linearanalysisisaconvenientapproximationthatisoftenadequatefordesignpurposes.Itisobviouslyinadequateformanystructuralsimulationsincludingmanufacturingprocesses,suchasforgingorstamping;crashanalyses;andanalysesofr
6、ubbercomponents,suchastiresorenginemounts.Asimpleexampleisaspringwithanonlinearstiffeningresponse(seeFigure8–1).Figure8–1Linearandnonlinearspringcharacteristics.34Sincethestiffnessisnowdependentonthedisplacement,theinitialflexibilitycannolongerbemultipliedbytheappliedloadtocalculateth
7、espring'sdisplacementforanyload.Inanonlinearimplicitanalysisthestiffnessmatrixofthestructurehastobeassembledandinvertedmanytimesduringthecourseoftheanalysis,makingitmuchmoreexpensivetosolvethanalinearimplicitanalysis.Inanexplicitanalysistheincreasedcostofanonlinearanalysisisduetoreduc
8、tions
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