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Finite Elements Method Summary Sheets

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27-03-2025

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2021/2022

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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Written for

Institution: Imperial College London (ICL)
Study: Unknown
Course: Finite Elements Method

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Document information

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

Subjects

finite elements
fem
fea
mathematics
engineering
physics
numerical

Content preview

conditions

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boundary
equations
constitutive
compatibility minimumnumberd independent

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coordinates
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t inFEneuseallpossibled

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enforcedapproximately

1 Equilibrium forcesinanelementandwholestructuemustsumtozeroth

2 Compatibility displacementsandstrainsmustbe
continuous exceptacrosscracks

3 MaterialLaws velatestressesandstrains

Princintualwork prescript'sindicatesa virtualquantity

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disactisingthedomainintoall nonoverlapping
elements

I
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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
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Finite Elements Method Summary Sheets

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