Finite Elements Method Summary Sheets

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Summary

Finite Elements Method Summary Sheets

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18 pages

2021/2022

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Preview 3 out of 18 pages

Summary notes on entire content of Finite Elements Method (FEM) module, covering the fundamentals of finite element theory that can be applied to analysing structural, fluid, and thermodynamics problems. Hand-written, coloured notes, with images, graphs, equations, derivations, and relevant tips. Topics include: - Fundamentals of FEM/FEA - Shape functions - Beam finite element methods - Numerical methods - Triangle and quadrilateral elements - Stress, strain, and distortion analysis

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conditions

Equilibrates degreed freedom
boundary
equations
constitutive
compatibility minimumnumberd independent

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coordinates
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t inFEneuseallpossibled

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3Basiolaris only
enforcedapproximately

1 Equilibrium forcesinanelementandwholestructuemustsumtozeroth

2 Compatibility displacementsandstrainsmustbe
continuous exceptacrosscracks

3 MaterialLaws velatestressesandstrains

Princintualwork prescript'sindicatesa virtualquantity

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iii i
utetffutdstffutbd
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.EE
Swi Swe edx
se
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algebraic
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to i Shape Functions uW W3Eu3

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favirtua d.paoementslswoi

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, termsofrealandvirtual
nodaldisplacements
substitutingexpressionsin

CBI
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FBI DV u
CBI E NITE 8 ENI'Idst fNIkdVt fuB5EDEod

ffBTCD3CB3dVEu3 NITEtfgNItdstfgnfbdvtf.veBILDTEodV
EF E3 Fo
Ck FB
disactisingthedomainintoall nonoverlapping
elements

I
elements
Eu EEEEEEEFI EF 03 Ek Eu EP

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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step 5 skipped 433433

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Document information

Study: Unknown
Uploaded on: March 27, 2025
Number of pages: 18
Written in: 2021/2022
Type: Summary

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