Finite Elements - A J Baker

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Résumé :
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Preface viii

Notation xi

1 COMPUTATIONAL ENGINEERING SCIENCE 1

1.1 Engineering simulation 1

1.2 A problem solving environment 2

1.3 Problem statements in engineering 4

1.4 Decisions on forming WS N 6

1.5 Discrete approximate WS h implementation 8

1.6 Chapter summary 9

1.7 Chapter references 10

2 PROBLEM STATEMENTS 11

2.1 Engineering simulation 11

2.2 Continuum mechanics viewpoint 12

2.3 Continuum conservation law forms 12

2.4 Constitutive closure for conservation law PDEs 14

2.5 Engineering science continuum mechanics 18

2.6 Chapter references 20

3 SOME INTRODUCTORY MATERIAL 21

3.1 Introduction 21

3.2 Multi-dimensional PDEs, separation of variables 22

3.3 Theoretical foundations, GWS h 27

3.4 A legacy FD construction 28

3.5 An FD approximate solution 30

3.6 Lagrange interpolation polynomials 31

3.7 Chapter summary 32

3.8 Exercises 34

3.9 Chapter references 34

4 HEAT CONDUCTION35

4.1 A steady heat conduction example 35

4.2 Weak form approximation, error minimization 37

4.3 GWS N discrete implementation, FE basis38

4.4 Finite element matrix statement 41

4.5 Assembly of {WS}_e to form algebraic GWS h 43

4.6 Solution accuracy, error distribution 45

4.7 Convergence, boundary heat flux 47

4.8 Chapter summary 47

4.9 Exercises 48

4.10 Chapter reference 48

5 STEADY HEAT TRANSFER, n =149

5.1 Introduction 49

5.2 Steady heat transfer, n = 1 50

5.3 FE k = 1 trial space basis matrix library 52

5.4 Object-oriented GWS h programming 55

5.5 Higher completeness degree trial space bases58

5.6 Global theory, asymptotic error estimate 62

5.7 Non-smooth data, theory generalization 66

5.8 Temperature dependent conductivity, non-linearity 69

5.9 Static condensation, p-elements 72

5.10 Chapter summary 75

5.11 Exercises 76

5.12 Computer labs 77

5.13 Chapter references 78

6 ENGINEERING SCIENCES, n =1 79

6.1 Introduction 79

6.2 The Euler-Bernoulli beam equation 80

6.3 Euler-Bernoulli beam theory GWS h reformulation 85

6.4 The Timoshenko beam theory 92

6.5 Mechanical vibrations of a beam 99

6.6 Fluid mechanics, potential flow 106

6.7 Electromagnetic plane wave propagation110

6.8 Convective-radiative finned cylinder heat transfer 112

6.9 Chapter summary 120

6.10 Exercises122

6.10 Computer labs 123

6.11 Chapter references 124

7 STEADY HEAT TRANSFER, n > 1 125

7.1 Introduction 125

7.2 Multi-dimensional FE bases and DOF 126

7.3 Multi-dimensional FE operations 129

7.4 The NC k = 1,2 basis FE matrix library 132

7.5 NC basis {WS}_e template, accuracy, convergence 136

7.6 The tensor product basis element family 139

7.7 Gauss numerical quadrature, k = 1 TP basis library 141

7.8 Convection-radiation BC GWS h implementation 146

7.9 Linear basis GWS h template unification?150

7.10 Accuracy, convergence revisited 152

7.11 Chapter summary 153

7.12 Exercises155

7.13 Computer labs 155

7.14 Chapter references 156

8 FINITE DIFFERENCES OF OPINION 159

8.1 The FD-FE correlation159

8.2 The FV-FE correlation162

8.3 Chapter summary 167

8.4 Exercises168

9 CONVECTION-DIFFUSION, n = 1...