Finite Elements : Computational Engineering Sciences

289 Pages·2012·3.354 MB·English

by  A Baker

Finite Elements
,,
Computational
Engineering Sciences

Finite Elements
,,
Computational
Engineering Sciences
A. J. Baker
ProfessorEmeritus
TheUniversityofTennessee
USA
Thiseditionfirstpublished2012
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particularpedagogicalapproachorparticularuseoftheMATLAB software.

LibraryofCongressCataloguing-in-PublicationData
Baker,A.J.,1936-
Finiteelements:computationalengineeringsciences/A.J.Baker.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-119-94050-0(cloth)
1. Finiteelementmethod. I. Title.
TA347.F5B34232012
620.001051825–dc23
2012011745
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:9781119940500
Setin10/12.5pt, Palatino-RomanbyThomsonDigital,Noida,India
YogiBerraisquoted,
“Ifyoucometoaforkintheroad,takeit,”
soIdidandendeduphere.

Contents
Preface xi
AbouttheAuthor xv
Notations xvii
1 TheComputationalEngineeringSciences:anintroduction 1
1.1 EngineeringSimulation 1
1.2 AProblem-SolvingEnvironment 3
1.3 WeakFormulationEssence 4
1.4 DecisionsonFormingWSN 6
1.5 DiscreteWShImplementations 8

1.6 ChapterSummary 10
References 11
2 ProblemStatements:intheengineeringsciences 13
2.1 EngineeringSimulation 13
2.2 ContinuumMechanicsViewpoint 14
2.3 ContinuumConservationPrincipleForms 14
2.4 ConstitutiveClosureforConservationPrinciplePDEs 16
2.5 EngineeringScienceContinuumMechanics 20
References 21
3 SomeIntroductoryMaterial:PDEs,BCs,solutions,discreteconcepts 23
3.1 ExampleLinearHeatConductionSolutions 23
3.2 MultidimensionalPDEs,SeparationofVariables 24
3.3 MathematicalFoundationEssenceforGWSN 28
3.4 ALegacyFDConstruction 29
3.5 AnFDApproximateSolution 31
3.6 LagrangeInterpolationPolynomials 32
viii Contents
3.7 ChapterSummary 33
Exercises 34
References 34
4 HeatConduction:anFEweakstatementtutorial 35
4.1 ASteadyHeatConductionExample 35
4.2 WeakFormApproximation,ErrorExtremization 36
4.3 GWSNDiscreteImplementation,FETrialSpaceBasis 38
4.4 FiniteElementMatrixStatements 40
4.5 Assemblyof{WS} toformAlgebraicGWSh 42
e
4.6 SolutionAccuracy,ErrorDistribution 44
4.7 Convergence,BoundaryHeatFlux 45
4.8 ChapterSummary 46
Exercises 46
Reference 46
5 SteadyHeatTransfer,n¼1:GWShimplementedwith
{Nk(za)},1(cid:2)k(cid:2)3,accuracy,convergence,nonlinearity,templates 47
5.1 Introduction 47
5.2 SteadyHeatTransfer,n¼1 48
5.3 FEk¼1TrialSpaceBasisMatrixLibrary 50
5.4 Object-OrientedGWShProgramming 53
5.5 HigherCompletenessDegreeTrialSpaceBases 56
5.6 GlobalTheory,AsymptoticErrorEstimate 59
5.7 NonsmoothData,TheoryGe neralization 63
5.8 Temperature-DependentConductivity,Nonlinearity 65
5.9 StaticCondensation,p-Elements 68
5.10 ChapterSummary 70
Exercises 72
ComputerLabs 72
References 73
6 EngineeringSciences,n¼1:GWSh{Nk(za)}
implementationsinthecomputationalengineeringsciences 75
6.1 Introduction 75
6.2 TheEuler–BernoulliBeamEquation 76
6.3 Euler–BernoulliBeamTheoryGWShReformulation 81
6.4 TimoshenkoBeamTheory 87
6.5 MechanicalVibrationsofaBeam 92
6.6 FluidMechanics,PotentialFlow 100
6.7 ElectromagneticPlaneWavePropagation 104
6.8 Convection–RadiationFinnedCylinderHeatTransfer 105
6.9 ChapterSummary 113