非线性解析概要-Abaqus 6.9 Nonlinearity.doc

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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