Finite Elements Method Summary Sheets

conditions

Equilibrates degreed freedom
boundary
equations
constitutive
compatibility minimumnumberd independent

Xa 0
coordinates
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3Basiolaris only
enforcedapproximately

1 Equilibrium forcesinanelementandwholestructuemustsumtozeroth

2 Compatibility displacementsandstrainsmustbe
continuous exceptacrosscracks


3 MaterialLaws velatestressesandstrains

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nodaldisplacements
substitutingexpressionsin

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disactisingthedomainintoall nonoverlapping
elements


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elements
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10StepstorsolvingaFEProblein
1 Definedisplacementrelationship ontheelement u CN Eu
2 Evaluatestraindisplacementrelationship E CBIEu
3 Definematerialpropertymatrix CDT
4 Evaluatestressdisplacementrelationship 0 473CBIEu

5 Determineelementstiffnessmatrixandforcevectors CkEu Ep3
6 Transformnodalvariablestoglobalonesifnecessary CITCHET EU CTFEp
7 Assembleglobalstiffnessmatrixandloadvector K2andEP3
8 Apply kinematicboundaryconditions
9 Solveforunknowndisplacementsandreactions EU3 LK EP
10 Backsubstituteforelementstresses 0 4731133TIEU

, FiniteElementsfora 2 DimensionalRod
2

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