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NFEM.Ch05.PDF
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NFEM.Ch05.pdf
Finite Element Formulation for Beam, Plate, Shell Element
.5 CriticalPoints andRelated Properties 51Chapter5:CRITICALPOINTSANDRELATEDPROPERTIES52 TABLEOFCONTENTS Page §5.1.ClassicationofCriticalPoints53 §5.2.LimitPointSensors56 §5.3.*TurningPoints56 §5.4.*DerivativesofEnergyFunctions56 §5.5.*EnergyIncrements58 §5.Exercises......................510 5253§5.1CLASSIFICATIONOFCRITICALPOINTS ThisChapterprovidesadditionalmaterialonpropertiesoftheone-parameterforceresidualequa- tions.Itbeginswithastudyofcriticalpoints,whichareclassiedintolimitandbifurcationpoints. Limitpoint“sensors” andturningpointsarebrieydescribed.Thesectionconcludeswithsome mathematicalderivationsforconservativesystems,whichwillbeofuseinChaptersdealingwith incrementa
.5 CriticalPoints andRelated Properties 51Chapter5:CRITICALPOINTSANDRELATEDPROPERTIES52 TABLEOFCONTENTS Page §5.1.ClassicationofCriticalPoints53 §5.2.LimitPointSensors56 §5.3.*TurningPoints56 §5.4.*DerivativesofEnergyFunctions56 §5.5.*EnergyIncrements58 §5.Exercises......................510 5253§5.1CLASSIFICATIONOFCRITICALPOINTS ThisChapterprovidesadditionalmaterialonpropertiesoftheone-parameterforceresidualequa- tions.Itbeginswithastudyofcriticalpoints,whichareclassiedintolimitandbifurcationpoints. Limitpoint“sensors” andturningpointsarebrieydescribed.Thesectionconcludeswithsome mathematicalderivationsforconservativesystems,whichwillbeofuseinChaptersdealingwith incrementa
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