有限元误差分析

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1、Chapter7ErrorAnalysisTherearevarioussourcesoferrorsinfiniteelementanalysis.Erroranalysishasbecomeindispensableintoday’sengineeringapplicationoffiniteelementsoftware.Inthischapter,wewilldiscussthematurebasisoferroranalysisforlinearstaticanalysisusingfiniteelem

2、ents.§1SourcesoferrorTheerroroffiniteelementresultsmayariseatanyproceduresoffiniteelementanalysis.Agoodandmatureuseroffiniteelementmethodshouldbeawareoftheallpossibleerrorsourcesinthefiniteelementanalysis.Generally,possiblemajorsourcesoferrorcanbeputintothefo

3、llowingcategories1)ModelingerrorItreferstothedifferencebetweenaphysicalsystemanditsmathematicalmodel.Itshouldbekeptatanacceptabledegree.Otherwise,themathematicalmodelneedberevised.Usually,simplificationsareintroducedintothemathematicalmodel.Inthemodel,forinst

4、ance,probablysmallholesandothergeometricirregularitiesinthestructureareneglected;loadsaresimplified;boundaryconditionsareidealizedasbytreatingacomponentwithrelativelylargestiffnessasrigid.Quiteoftenatwo-dimensionalproblemisstudied,ignoringitsthree-dimensional

5、characteristic;astaticanalysisisperformed,ignoringthedynamiccharacter.2)DiscretizationerrorThemathematicalmodelhasinfinitenumberofdof,butfinitedofareusedinfiniteelementanalysis.Thefiniteelementsolutionisaffectedbythenumberofelementsinthemodel,thedofpernode,th

6、enumericalintegrationrule,andetc.Actually,thiskindoferrorhasbeendiscussedatthefirstsectionoflastchapter.3)TruncationerrororroundingerrorItreferstolossofinformationduetotruncationorroundingofnumberstofitafinitecomputerwordlength.4)AccumulationerrorThiskindofer

7、rorariseswhenglobalequationsaresolvedrepeatedlyasinnonlinearordynamicproblems.Thetermnumericalerroristhecombinedresultoftruncation(orrounding)errorandaccumulationerror.Inthischapter,emphasisismainlyplacedondiscretizationerrorandnumericalerror.Theaboveclassifi

8、cationexcludespossibleusererrorandbugs.Usererrorreferstomistakesmadeusersafteraneffectivemodelhasbeenestablished.Bugsareprogrammingerrorsembeddedinfiniteelementanalysissoftware.Someofthem