Bofang Zhu

The Finite Element Method (eBook, ePUB)

Fundamentals and Applications in Civil, Hydraulic, Mechanical and Aeronautical Engineering

• Format: ePub

Produktbeschreibung

A comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines. Written by a renowned author and academician with the Chinese Academy of Engineering, The Finite Element Method would appeal to researchers looking to understand how the fundamentals of the FEM can be applied in other disciplines. Researchers and graduate students studying hydraulic, mechanical and civil engineering will find it a practical reference text.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 880
• Erscheinungstermin: 20. März 2018
• Englisch
• ISBN-13: 9781119107347
• Artikelnr.: 52555061

Autorenporträt

About the Author Bofang Zhu, China Institute of Water Resources and Hydropower Research, Chinese Academy of Engineering, China

Inhaltsangabe

Preface xxiii

About the Author xxv

1 Introduction to Finite ElementMethod andMatrix Analysis of Truss 1

1.1 Introduction to Finite Element Method 1

1.2 Truss Analysis Overview 5

1.3 Stiffness Matrix of Horizontal Bar Element 8

1.4 Stiffness Matrix of Inclined Bar Element 10

1.5 Coordinate Transformation 11

1.6 Nodal Equilibrium Equation and Global Stiffness Matrix 14

1.7 Treatment of Boundary Conditions 15

Bibliography 23

2 Plane Problems in Theory of Elasticity 25

2.1 Discretization of Continuous Medium 25

2.2 Displacement Function 28

2.3 Element Strain 30

2.4 Initial Strain 31

2.5 Element Stress 32

2.6 Equivalent Nodal Force and Element Stiffness Matrix 35

2.7 Nodal Loads 40

2.8 Nodal Equilibrium Equation and Global Stiffness Matrix 43

2.9 Establish the Global Stiffness Matrix by the Coding Method 48

2.10 Calculation Example 51

Bibliography 51

3 Element Analysis 53

3.1 Principle of Virtual Displacement 53

3.2 Element Displacement 56

3.3 Element Strain and Stress 57

3.4 Nodal Force and Element Stiffness Matrix 57

3.5 Nodal Load 59

3.6 Application Examples of the Principle of Virtual Displacements: Beam Element 61

3.7 Strain Energy and Complementary Strain Energy 64

3.8 Principle of Minimum Potential Energy 65

3.9 Minimum Complementary Energy Principle 69

3.10 Hybrid Element 70

3.11 Hybrid Element Example: Plane Rectangular Element 73

3.12 Mixed Energy Principle 75

3.13 Composite Element 77

Bibliography 79

4 Global Analysis 81

4.1 Nodal Equilibrium Equation 81

4.2 Application of the Principle of Minimum Potential Energy 82

4.3 The Low Limit Property of the Solution of Minimum Potential Energy 84

4.4 The Convergence of Solutions 85

4.5 Analysis of the Substructure 88

Bibliography 91

5 High-Order Element of Plane Problem 93

5.1 Rectangular Elements 93

5.2 Area Coordinates 97

5.3 High-Order Triangular Element 100

Bibliography 104

6 Axisymmetrical Problems in Theory of Elasticity 105

6.1 Stresses Due to Axisymmetrical Loads 105

6.2 Antisymmetrical Load 110

Bibliography 114

7 Spatial Problems in Theory of Elasticity 115

7.1 Constant Strain Tetrahedral Elements 115

7.2 Volume Coordinates 121

7.3 High-Order Tetrahedral Elements 122

Bibliography 124

8 Shape Function, Coordinate Transformation, Isoparametric Element, and Infinite Element 125

8.1 Definition of Shape Functions 125

8.2 One-Dimensional Shape Functions 126

8.3 Two-Dimensional Shape Function 127

8.4 Three-Dimensional Shape Function 130

8.5 Coordinate Transformation 136

8.6 Displacement Function 145

8.7 Element Strain 147

8.8 Stiffness Matrix 151

8.9 Nodal Loads 153

8.10 Degradation of Isoparametric Elements 155

8.11 Numerical Integration 161

8.13 Stress Refinement and Stress Smoothing 168

8.14 Elemental Form and Layout 173

8.15 Inconsistent Elements 176

8.16 Patch Test 179

8.17 Triangular, Tetrahedral, and Prismatic Curved-Side Elements 183

8.18 Vector Computation in Isoparametric Elements 187

8.19 Numerical Examples of Isoparametric Elements 191

8.20 Infinite Elements 192
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