Finite Element Analysis for Design Engineers
portes grátis
Finite Element Analysis for Design Engineers
Kurowski, Paul M
SAE International
12/2022
287
Dura
Inglês
9781468605358
15 a 20 dias
Descrição não disponível.
Preface xix
Chapter 1
Introduction 1
1.1. What Is Finite Element Analysis? 1
1.2. What Is the Place of FEA among Other Tools of
Computer-Aided Engineering? 2
1.3. Fields of Application of FEA and Mechanism Analysis 2
1.4. Fields of Application of FEA and CFD 4
1.5. What Is "FEA for Design Engineers"? 4
1.6. Note on Hands-On Exercises 5
Chapter 2
From CAD Model to Results of FEA 7
2.1. Formulation of the Mathematical Model 7
2.2. Selecting the Numerical Method to Solve the
Mathematical Model 10
2.2.1. Selected Numerical Methods in CAE 10
2.2.2. Reasons for the Dominance of FEM 10
2.3. FEA Model 11
2.3.1. Meshing 11
2.3.2. Formulation of FE Equations 12
2.3.3. Errors in FEA Results 13
2.4. Verification and Validation of FEA Results 14
Chapter 3
Fundamental Concepts of FEA 17
3.1. Formulation of a Finite Element 17
3.1.1. Closer Look at Finite Element 17
3.1.2. Requirements to be Satisfied by Displacement Interpolation
Function 20
3.1.3. Artificial Restraints 20
3.2. Choices of Discretization 22
3.3. Types of Finite Elements 23
3.3.1. Element Dimensionality 23
3.3.2. Element Shape 28
3.3.3. Element Order and Element Type 29
3.3.4. Summary of Commonly Used Elements 30
3.3.5. Element Modeling Capabilities 31
Chapter 4
Controlling Discretization Errors 33
4.1. Presenting Stress Results 34
4.2. Types of Convergence Analysis 36
4.2.1. h Convergence by Global Mesh Refinement 36
4.2.2. h Convergence by Local Mesh Refinement 40
4.2.3. Adaptive h Convergence 42
4.2.4. p Convergence Process 44
4.2.5. Choice of Convergence Process 46
4.3. Discretization Error 46
4.3.1. Convergence Error 47
4.3.2. Solution Error 47
4.4. Problems with Convergence 48
4.4.1. Stress Singularity 48
4.4.2. Displacement Singularity 54
4.5. Hands-On Exercises 58
4.5.1. HOLLOW PLATE 58
Description 58
Objective 58
Procedure 59
4.5.2. L BRACKET01 60
Description 60
Objective 60
Procedure 60
Contents ix
4.5.3. WEDGE 61
Description 61
Objective 61
Procedure 61
Chapter 5
Finite Element Mesh 65
5.1. Meshing Techniques 65
5.1.1. Manual Meshing 65
5.1.2. Semi-automatic Meshing 66
5.1.3. Automatic Meshing 67
5.2. Mesh Compatibility 69
5.2.1. Compatible Elements 70
5.2.2. Incompatible Elements 70
5.2.3. Forced Compatibility 71
5.3. Common Meshing Problems 73
5.3.1. Element Distortion 73
5.3.2. Mesh Adequacy 75
5.3.3. Element Mapping to Geometry 76
5.3.4. Incorrect Conversion to Shell Model 78
5.4. Hands-On Exercises 79
5.4.1. BRACKET01 79
Description 79
Objective 79
Procedure 79
5.4.2. CANTILEVER 80
Description 80
Objective 80
Procedure 80
Chapter 6
Modeling Process 83
6.1. Modeling Steps 84
6.1.1. Definition of the Objective of Analysis 84
6.1.2. Selection of the Units of Measurement 84
6.1.3. Geometry Preparation 85
6.1.4. Defining Material Properties 85
6.1.5. Defining Boundary Conditions 86
Contentsx
6.2. Selected Modeling Techniques 87
6.2.1. Mirror Symmetry and Anti-symmetry Boundary Conditions 87
6.2.2. Axial Symmetry 92
6.2.3. Cyclic Symmetry 92
6.2.4. Realignment of Degrees of Freedom 94
6.2.5. Using Point Restraints to Eliminate Rigid Body Motions 95
6.3. Hands-On Exercises 96
6.3.1. BRACKET02-Mirror Symmetry BC 96
Description 96
Objective 96
Procedure 96
6.3.2. BRACKET02-Anti-symmetry BC 97
Description 97
Objective 97
Procedure 97
6.3.3. BRACKET02-Mirror Symmetry and Anti-symmetry BC 98
Description 98
Objective 98
Procedure 98
6.3.4. SHAFT01 99
Description 99
Objective 99
Procedure 99
6.3.5. PRESSURE TANK 100
Description 100
Objective 100
Procedure 100
6.3.6. RING 101
Description 101
Objective 101
Procedure 101
6.3.7. LINK01 102
Description 102
Objective 102
Procedure 103
Chapter 7
Nonlinear Geometry Analysis 105
7.1. Classification of Different Types of Nonlinearities 105
7.2. Geometric Nonlinearity 106
Contents xi
7.3. Membrane Stress Stiffening 112
7.4. Contact 117
7.5. Hands-On Exercises 122
7.5.1. CANTILEVER BEAM 122
Description 122
Objective 123
Procedure 123
7.5.2. SHAFT02 123
Description 123
Objective 123
Procedure 123
7.5.3. ROUND PLATE01 123
Description 123
Objective 124
Procedure 124
7.5.4. LINK02 124
Description 124
Objective 124
Procedure 124
7.5.5. SLIDING SUPPORT 125
Description 125
Objective 125
Procedure 125
7.5.6. CLAMP01 125
Description 125
Objective 125
Procedure 125
7.5.7. CLAMP02 126
Description 126
Objective 126
Procedure 126
Chapter 8
Nonlinear Material Analysis 129
8.1. Review of Nonlinear Material Models 129
8.2. Use of Nonlinear Material to Control Stress Singularity 132
8.3. Other Types of Nonlinearities 134
8.4. Hands-On Exercises 134
8.4.1. BRACKET NL 134
Objective 135
Contentsxii
Procedure 135
8.4.2. L BRACKET02 135
Description 135
Objective 135
Procedure 135
Chapter 9
Modal Analysis 139
9.1. Differences between Modal and
Static Analysis 139
9.2. Interpretation of Displacement and Stress Results in
Modal Analysis 140
9.3. Modal Analysis with Rigid Body Motions 141
9.4. Importance of Supports in Modal Analysis 143
9.5. Applications of Modal Analysis 144
9.5.1. Finding Modal Frequencies and Associated Shapes of Vibration 144
9.5.2. Locating "Weak Spots" in Structure 145
9.5.3. Modal Analysis Provides Input to Vibration Analysis 146
9.6. Pre-stress Modal Analysis 146
9.7. Symmetry and Anti-symmetry Boundary Conditions in
Modal Analysis 148
9.8. Convergence of Modal Frequencies 149
9.9. Meshing Consideration for Modal Analysis 150
9.10. Hands-On Exercises 150
9.10.1. TUNING FORK 150
Description 150
Objective 150
Procedure 150
Comments 150
9.10.2. BOX 151
Description 151
Objective 151
Procedure 151
Comments 151
9.10.3. AIRPLANE 151
Description 151
Objective 151
Procedure 151
Comments 152
Contents xiii
9.10.4. BALL 152
Description 152
Objective 152
Procedure 152
Comments 152
9.10.5. LINK03 152
Description 152
Objective 152
Procedure 152
Comments 153
9.10.6. HELICOPTER BLADE 153
Description 153
Objective 153
Procedure 153
Comments 153
9.10.7. COLUMN 154
Description 154
Objective 154
Procedure 154
Comments 155
9.10.8. BRACKET03 155
Description 155
Objective 155
Procedure 155
Comments 156
Chapter 1 0
Buckling Analysis 159
10.1. Linear Buckling Analysis 160
10.2. Convergence of Results in Linear Buckling Analysis 163
10.3. Nonlinear Buckling Analysis 163
10.4. Controlling an Onset of Buckling in Nonlinear Buckling
Analysis 174
10.5. Summary 175
10.6. Hands-On Exercises 176
10.6.1. NOTCHED COLUMN - Free End 176
Description 176
Objective 176
Procedure 176
Comments 177
Contentsxiv
10.6.2. NOTCHED COLUMN - Sliding End 177
Procedure 177
10.6.3. ROUND PLATE02 177
Description 177
Objective 177
Procedure 177
Comments 178
10.6.4. CURVED COLUMN 178
Objective 178
10.6.5. STAND 178
Description 178
Objective 178
Procedure 178
Comments 179
10.6.6. CURVED SHEET 179
Description 179
Objective 179
Procedure 179
Chapter 1 1
Vibration Analysis 181
11.1. Modal Superposition Method 181
11.2. Time Response Analysis 183
11.3. Frequency Response Analysis 186
11.4. Nonlinear Vibration Analysis 190
11.5. Hands-On Exercises 192
11.5.1. HAMMER - Impulse Load 192
Description 192
Objective 192
Procedure 192
Comments 193
11.5.2. HAMMER - Beating 193
Description 193
Objective 193
Procedure 193
Comments 194
11.5.3. ELBOW PIPE 194
Description 194
Objective 194
Procedure 194
Comments 194
Contents xv
11.5.4. CENTRIFUGE 194
Description 194
Objective 195
Procedure 195
Comments 195
11.5.5. PLANK 195
Description 195
Objective 195
Procedure 195
Comments 196
Chapter 1 2
Thermal Analysis 199
12.1. Heat Flow by Conduction 200
12.2. Heat Flow by Convection 201
12.3. Heat Transfer by Radiation 203
12.4. Modeling Considerations in Thermal Analysis 204
12.5. Challenges in Thermal Analysis 206
12.6. Hands-On Exercises 207
12.6.1. BRACKET04 207
Description 207
Objective 207
Procedure 207
Comments 207
12.6.2. HEAT SINK 207
Description 207
Objective 207
Procedure 207
Comments 208
12.6.3. CHANNEL 208
Description 208
Objective 208
Procedure 208
Comments 208
12.6.4. SPACE HEATER 209
Description 209
Objective 209
Procedure 209
Comments 209
Contentsxvi
Chapter 1 3
Implementation of Finite Element Analysis in
the Design Process 211
13.1. Differences between CAD and FEA Geometry 211
13.1.1. Defeaturing 212
13.1.2. Idealization 213
13.1.3. Cleanup 214
13.2. Common Meshing Problems 216
13.3. Mesh Adequacy 218
13.4. Integration of CAD and FEA Programs 219
13.4.1. Stand-Alone FEA Programs 219
13.4.2. FEA Programs Integrated with CAD 219
13.4.3. Computer Aided Engineering (CAE) Programs 219
13.5. FEA Implementation 220
13.5.1. Positioning of CAD and FEA Activities 220
13.5.2. Personnel Training 221
13.5.3. FEA Program Selection 223
13.5.4. Hardware Selection 225
13.5.5. Building Confidence in FEA 225
13.5.6. Return on Investment 226
13.6. FEA Project 226
13.6.1. Before FEA Project Starts 227
13.6.2. Establish the Scope of Analysis 227
13.6.3. Create the Mathematical Model 227
13.6.4. Create the Finite Element Model and Solve It 228
13.6.5. Review the Results 228
13.6.6. Presentation of the Results 229
13.6.7. FEA Report 230
13.6.8. Project Documentation and Backups 231
13.6.9. Contracting Out FEA Services 231
13.6.10. Common Errors in Management of FEA Projects 232
Chapter 1 4
Summary 235
14.1. FEA Quiz 235
14.2. Frequently Asked Questions 238
Contents xvii
Chapter 1 5
FEA Resources 249
Chapter 1 6
Glossary 253
Chapter 1 7
List of Exercises 259
Index 261
About the Author 265
Chapter 1
Introduction 1
1.1. What Is Finite Element Analysis? 1
1.2. What Is the Place of FEA among Other Tools of
Computer-Aided Engineering? 2
1.3. Fields of Application of FEA and Mechanism Analysis 2
1.4. Fields of Application of FEA and CFD 4
1.5. What Is "FEA for Design Engineers"? 4
1.6. Note on Hands-On Exercises 5
Chapter 2
From CAD Model to Results of FEA 7
2.1. Formulation of the Mathematical Model 7
2.2. Selecting the Numerical Method to Solve the
Mathematical Model 10
2.2.1. Selected Numerical Methods in CAE 10
2.2.2. Reasons for the Dominance of FEM 10
2.3. FEA Model 11
2.3.1. Meshing 11
2.3.2. Formulation of FE Equations 12
2.3.3. Errors in FEA Results 13
2.4. Verification and Validation of FEA Results 14
Chapter 3
Fundamental Concepts of FEA 17
3.1. Formulation of a Finite Element 17
3.1.1. Closer Look at Finite Element 17
3.1.2. Requirements to be Satisfied by Displacement Interpolation
Function 20
3.1.3. Artificial Restraints 20
3.2. Choices of Discretization 22
3.3. Types of Finite Elements 23
3.3.1. Element Dimensionality 23
3.3.2. Element Shape 28
3.3.3. Element Order and Element Type 29
3.3.4. Summary of Commonly Used Elements 30
3.3.5. Element Modeling Capabilities 31
Chapter 4
Controlling Discretization Errors 33
4.1. Presenting Stress Results 34
4.2. Types of Convergence Analysis 36
4.2.1. h Convergence by Global Mesh Refinement 36
4.2.2. h Convergence by Local Mesh Refinement 40
4.2.3. Adaptive h Convergence 42
4.2.4. p Convergence Process 44
4.2.5. Choice of Convergence Process 46
4.3. Discretization Error 46
4.3.1. Convergence Error 47
4.3.2. Solution Error 47
4.4. Problems with Convergence 48
4.4.1. Stress Singularity 48
4.4.2. Displacement Singularity 54
4.5. Hands-On Exercises 58
4.5.1. HOLLOW PLATE 58
Description 58
Objective 58
Procedure 59
4.5.2. L BRACKET01 60
Description 60
Objective 60
Procedure 60
Contents ix
4.5.3. WEDGE 61
Description 61
Objective 61
Procedure 61
Chapter 5
Finite Element Mesh 65
5.1. Meshing Techniques 65
5.1.1. Manual Meshing 65
5.1.2. Semi-automatic Meshing 66
5.1.3. Automatic Meshing 67
5.2. Mesh Compatibility 69
5.2.1. Compatible Elements 70
5.2.2. Incompatible Elements 70
5.2.3. Forced Compatibility 71
5.3. Common Meshing Problems 73
5.3.1. Element Distortion 73
5.3.2. Mesh Adequacy 75
5.3.3. Element Mapping to Geometry 76
5.3.4. Incorrect Conversion to Shell Model 78
5.4. Hands-On Exercises 79
5.4.1. BRACKET01 79
Description 79
Objective 79
Procedure 79
5.4.2. CANTILEVER 80
Description 80
Objective 80
Procedure 80
Chapter 6
Modeling Process 83
6.1. Modeling Steps 84
6.1.1. Definition of the Objective of Analysis 84
6.1.2. Selection of the Units of Measurement 84
6.1.3. Geometry Preparation 85
6.1.4. Defining Material Properties 85
6.1.5. Defining Boundary Conditions 86
Contentsx
6.2. Selected Modeling Techniques 87
6.2.1. Mirror Symmetry and Anti-symmetry Boundary Conditions 87
6.2.2. Axial Symmetry 92
6.2.3. Cyclic Symmetry 92
6.2.4. Realignment of Degrees of Freedom 94
6.2.5. Using Point Restraints to Eliminate Rigid Body Motions 95
6.3. Hands-On Exercises 96
6.3.1. BRACKET02-Mirror Symmetry BC 96
Description 96
Objective 96
Procedure 96
6.3.2. BRACKET02-Anti-symmetry BC 97
Description 97
Objective 97
Procedure 97
6.3.3. BRACKET02-Mirror Symmetry and Anti-symmetry BC 98
Description 98
Objective 98
Procedure 98
6.3.4. SHAFT01 99
Description 99
Objective 99
Procedure 99
6.3.5. PRESSURE TANK 100
Description 100
Objective 100
Procedure 100
6.3.6. RING 101
Description 101
Objective 101
Procedure 101
6.3.7. LINK01 102
Description 102
Objective 102
Procedure 103
Chapter 7
Nonlinear Geometry Analysis 105
7.1. Classification of Different Types of Nonlinearities 105
7.2. Geometric Nonlinearity 106
Contents xi
7.3. Membrane Stress Stiffening 112
7.4. Contact 117
7.5. Hands-On Exercises 122
7.5.1. CANTILEVER BEAM 122
Description 122
Objective 123
Procedure 123
7.5.2. SHAFT02 123
Description 123
Objective 123
Procedure 123
7.5.3. ROUND PLATE01 123
Description 123
Objective 124
Procedure 124
7.5.4. LINK02 124
Description 124
Objective 124
Procedure 124
7.5.5. SLIDING SUPPORT 125
Description 125
Objective 125
Procedure 125
7.5.6. CLAMP01 125
Description 125
Objective 125
Procedure 125
7.5.7. CLAMP02 126
Description 126
Objective 126
Procedure 126
Chapter 8
Nonlinear Material Analysis 129
8.1. Review of Nonlinear Material Models 129
8.2. Use of Nonlinear Material to Control Stress Singularity 132
8.3. Other Types of Nonlinearities 134
8.4. Hands-On Exercises 134
8.4.1. BRACKET NL 134
Objective 135
Contentsxii
Procedure 135
8.4.2. L BRACKET02 135
Description 135
Objective 135
Procedure 135
Chapter 9
Modal Analysis 139
9.1. Differences between Modal and
Static Analysis 139
9.2. Interpretation of Displacement and Stress Results in
Modal Analysis 140
9.3. Modal Analysis with Rigid Body Motions 141
9.4. Importance of Supports in Modal Analysis 143
9.5. Applications of Modal Analysis 144
9.5.1. Finding Modal Frequencies and Associated Shapes of Vibration 144
9.5.2. Locating "Weak Spots" in Structure 145
9.5.3. Modal Analysis Provides Input to Vibration Analysis 146
9.6. Pre-stress Modal Analysis 146
9.7. Symmetry and Anti-symmetry Boundary Conditions in
Modal Analysis 148
9.8. Convergence of Modal Frequencies 149
9.9. Meshing Consideration for Modal Analysis 150
9.10. Hands-On Exercises 150
9.10.1. TUNING FORK 150
Description 150
Objective 150
Procedure 150
Comments 150
9.10.2. BOX 151
Description 151
Objective 151
Procedure 151
Comments 151
9.10.3. AIRPLANE 151
Description 151
Objective 151
Procedure 151
Comments 152
Contents xiii
9.10.4. BALL 152
Description 152
Objective 152
Procedure 152
Comments 152
9.10.5. LINK03 152
Description 152
Objective 152
Procedure 152
Comments 153
9.10.6. HELICOPTER BLADE 153
Description 153
Objective 153
Procedure 153
Comments 153
9.10.7. COLUMN 154
Description 154
Objective 154
Procedure 154
Comments 155
9.10.8. BRACKET03 155
Description 155
Objective 155
Procedure 155
Comments 156
Chapter 1 0
Buckling Analysis 159
10.1. Linear Buckling Analysis 160
10.2. Convergence of Results in Linear Buckling Analysis 163
10.3. Nonlinear Buckling Analysis 163
10.4. Controlling an Onset of Buckling in Nonlinear Buckling
Analysis 174
10.5. Summary 175
10.6. Hands-On Exercises 176
10.6.1. NOTCHED COLUMN - Free End 176
Description 176
Objective 176
Procedure 176
Comments 177
Contentsxiv
10.6.2. NOTCHED COLUMN - Sliding End 177
Procedure 177
10.6.3. ROUND PLATE02 177
Description 177
Objective 177
Procedure 177
Comments 178
10.6.4. CURVED COLUMN 178
Objective 178
10.6.5. STAND 178
Description 178
Objective 178
Procedure 178
Comments 179
10.6.6. CURVED SHEET 179
Description 179
Objective 179
Procedure 179
Chapter 1 1
Vibration Analysis 181
11.1. Modal Superposition Method 181
11.2. Time Response Analysis 183
11.3. Frequency Response Analysis 186
11.4. Nonlinear Vibration Analysis 190
11.5. Hands-On Exercises 192
11.5.1. HAMMER - Impulse Load 192
Description 192
Objective 192
Procedure 192
Comments 193
11.5.2. HAMMER - Beating 193
Description 193
Objective 193
Procedure 193
Comments 194
11.5.3. ELBOW PIPE 194
Description 194
Objective 194
Procedure 194
Comments 194
Contents xv
11.5.4. CENTRIFUGE 194
Description 194
Objective 195
Procedure 195
Comments 195
11.5.5. PLANK 195
Description 195
Objective 195
Procedure 195
Comments 196
Chapter 1 2
Thermal Analysis 199
12.1. Heat Flow by Conduction 200
12.2. Heat Flow by Convection 201
12.3. Heat Transfer by Radiation 203
12.4. Modeling Considerations in Thermal Analysis 204
12.5. Challenges in Thermal Analysis 206
12.6. Hands-On Exercises 207
12.6.1. BRACKET04 207
Description 207
Objective 207
Procedure 207
Comments 207
12.6.2. HEAT SINK 207
Description 207
Objective 207
Procedure 207
Comments 208
12.6.3. CHANNEL 208
Description 208
Objective 208
Procedure 208
Comments 208
12.6.4. SPACE HEATER 209
Description 209
Objective 209
Procedure 209
Comments 209
Contentsxvi
Chapter 1 3
Implementation of Finite Element Analysis in
the Design Process 211
13.1. Differences between CAD and FEA Geometry 211
13.1.1. Defeaturing 212
13.1.2. Idealization 213
13.1.3. Cleanup 214
13.2. Common Meshing Problems 216
13.3. Mesh Adequacy 218
13.4. Integration of CAD and FEA Programs 219
13.4.1. Stand-Alone FEA Programs 219
13.4.2. FEA Programs Integrated with CAD 219
13.4.3. Computer Aided Engineering (CAE) Programs 219
13.5. FEA Implementation 220
13.5.1. Positioning of CAD and FEA Activities 220
13.5.2. Personnel Training 221
13.5.3. FEA Program Selection 223
13.5.4. Hardware Selection 225
13.5.5. Building Confidence in FEA 225
13.5.6. Return on Investment 226
13.6. FEA Project 226
13.6.1. Before FEA Project Starts 227
13.6.2. Establish the Scope of Analysis 227
13.6.3. Create the Mathematical Model 227
13.6.4. Create the Finite Element Model and Solve It 228
13.6.5. Review the Results 228
13.6.6. Presentation of the Results 229
13.6.7. FEA Report 230
13.6.8. Project Documentation and Backups 231
13.6.9. Contracting Out FEA Services 231
13.6.10. Common Errors in Management of FEA Projects 232
Chapter 1 4
Summary 235
14.1. FEA Quiz 235
14.2. Frequently Asked Questions 238
Contents xvii
Chapter 1 5
FEA Resources 249
Chapter 1 6
Glossary 253
Chapter 1 7
List of Exercises 259
Index 261
About the Author 265
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element analysis; design; CAD; CAM; CAE; CAM and CAE; engineering
Preface xix
Chapter 1
Introduction 1
1.1. What Is Finite Element Analysis? 1
1.2. What Is the Place of FEA among Other Tools of
Computer-Aided Engineering? 2
1.3. Fields of Application of FEA and Mechanism Analysis 2
1.4. Fields of Application of FEA and CFD 4
1.5. What Is "FEA for Design Engineers"? 4
1.6. Note on Hands-On Exercises 5
Chapter 2
From CAD Model to Results of FEA 7
2.1. Formulation of the Mathematical Model 7
2.2. Selecting the Numerical Method to Solve the
Mathematical Model 10
2.2.1. Selected Numerical Methods in CAE 10
2.2.2. Reasons for the Dominance of FEM 10
2.3. FEA Model 11
2.3.1. Meshing 11
2.3.2. Formulation of FE Equations 12
2.3.3. Errors in FEA Results 13
2.4. Verification and Validation of FEA Results 14
Chapter 3
Fundamental Concepts of FEA 17
3.1. Formulation of a Finite Element 17
3.1.1. Closer Look at Finite Element 17
3.1.2. Requirements to be Satisfied by Displacement Interpolation
Function 20
3.1.3. Artificial Restraints 20
3.2. Choices of Discretization 22
3.3. Types of Finite Elements 23
3.3.1. Element Dimensionality 23
3.3.2. Element Shape 28
3.3.3. Element Order and Element Type 29
3.3.4. Summary of Commonly Used Elements 30
3.3.5. Element Modeling Capabilities 31
Chapter 4
Controlling Discretization Errors 33
4.1. Presenting Stress Results 34
4.2. Types of Convergence Analysis 36
4.2.1. h Convergence by Global Mesh Refinement 36
4.2.2. h Convergence by Local Mesh Refinement 40
4.2.3. Adaptive h Convergence 42
4.2.4. p Convergence Process 44
4.2.5. Choice of Convergence Process 46
4.3. Discretization Error 46
4.3.1. Convergence Error 47
4.3.2. Solution Error 47
4.4. Problems with Convergence 48
4.4.1. Stress Singularity 48
4.4.2. Displacement Singularity 54
4.5. Hands-On Exercises 58
4.5.1. HOLLOW PLATE 58
Description 58
Objective 58
Procedure 59
4.5.2. L BRACKET01 60
Description 60
Objective 60
Procedure 60
Contents ix
4.5.3. WEDGE 61
Description 61
Objective 61
Procedure 61
Chapter 5
Finite Element Mesh 65
5.1. Meshing Techniques 65
5.1.1. Manual Meshing 65
5.1.2. Semi-automatic Meshing 66
5.1.3. Automatic Meshing 67
5.2. Mesh Compatibility 69
5.2.1. Compatible Elements 70
5.2.2. Incompatible Elements 70
5.2.3. Forced Compatibility 71
5.3. Common Meshing Problems 73
5.3.1. Element Distortion 73
5.3.2. Mesh Adequacy 75
5.3.3. Element Mapping to Geometry 76
5.3.4. Incorrect Conversion to Shell Model 78
5.4. Hands-On Exercises 79
5.4.1. BRACKET01 79
Description 79
Objective 79
Procedure 79
5.4.2. CANTILEVER 80
Description 80
Objective 80
Procedure 80
Chapter 6
Modeling Process 83
6.1. Modeling Steps 84
6.1.1. Definition of the Objective of Analysis 84
6.1.2. Selection of the Units of Measurement 84
6.1.3. Geometry Preparation 85
6.1.4. Defining Material Properties 85
6.1.5. Defining Boundary Conditions 86
Contentsx
6.2. Selected Modeling Techniques 87
6.2.1. Mirror Symmetry and Anti-symmetry Boundary Conditions 87
6.2.2. Axial Symmetry 92
6.2.3. Cyclic Symmetry 92
6.2.4. Realignment of Degrees of Freedom 94
6.2.5. Using Point Restraints to Eliminate Rigid Body Motions 95
6.3. Hands-On Exercises 96
6.3.1. BRACKET02-Mirror Symmetry BC 96
Description 96
Objective 96
Procedure 96
6.3.2. BRACKET02-Anti-symmetry BC 97
Description 97
Objective 97
Procedure 97
6.3.3. BRACKET02-Mirror Symmetry and Anti-symmetry BC 98
Description 98
Objective 98
Procedure 98
6.3.4. SHAFT01 99
Description 99
Objective 99
Procedure 99
6.3.5. PRESSURE TANK 100
Description 100
Objective 100
Procedure 100
6.3.6. RING 101
Description 101
Objective 101
Procedure 101
6.3.7. LINK01 102
Description 102
Objective 102
Procedure 103
Chapter 7
Nonlinear Geometry Analysis 105
7.1. Classification of Different Types of Nonlinearities 105
7.2. Geometric Nonlinearity 106
Contents xi
7.3. Membrane Stress Stiffening 112
7.4. Contact 117
7.5. Hands-On Exercises 122
7.5.1. CANTILEVER BEAM 122
Description 122
Objective 123
Procedure 123
7.5.2. SHAFT02 123
Description 123
Objective 123
Procedure 123
7.5.3. ROUND PLATE01 123
Description 123
Objective 124
Procedure 124
7.5.4. LINK02 124
Description 124
Objective 124
Procedure 124
7.5.5. SLIDING SUPPORT 125
Description 125
Objective 125
Procedure 125
7.5.6. CLAMP01 125
Description 125
Objective 125
Procedure 125
7.5.7. CLAMP02 126
Description 126
Objective 126
Procedure 126
Chapter 8
Nonlinear Material Analysis 129
8.1. Review of Nonlinear Material Models 129
8.2. Use of Nonlinear Material to Control Stress Singularity 132
8.3. Other Types of Nonlinearities 134
8.4. Hands-On Exercises 134
8.4.1. BRACKET NL 134
Objective 135
Contentsxii
Procedure 135
8.4.2. L BRACKET02 135
Description 135
Objective 135
Procedure 135
Chapter 9
Modal Analysis 139
9.1. Differences between Modal and
Static Analysis 139
9.2. Interpretation of Displacement and Stress Results in
Modal Analysis 140
9.3. Modal Analysis with Rigid Body Motions 141
9.4. Importance of Supports in Modal Analysis 143
9.5. Applications of Modal Analysis 144
9.5.1. Finding Modal Frequencies and Associated Shapes of Vibration 144
9.5.2. Locating "Weak Spots" in Structure 145
9.5.3. Modal Analysis Provides Input to Vibration Analysis 146
9.6. Pre-stress Modal Analysis 146
9.7. Symmetry and Anti-symmetry Boundary Conditions in
Modal Analysis 148
9.8. Convergence of Modal Frequencies 149
9.9. Meshing Consideration for Modal Analysis 150
9.10. Hands-On Exercises 150
9.10.1. TUNING FORK 150
Description 150
Objective 150
Procedure 150
Comments 150
9.10.2. BOX 151
Description 151
Objective 151
Procedure 151
Comments 151
9.10.3. AIRPLANE 151
Description 151
Objective 151
Procedure 151
Comments 152
Contents xiii
9.10.4. BALL 152
Description 152
Objective 152
Procedure 152
Comments 152
9.10.5. LINK03 152
Description 152
Objective 152
Procedure 152
Comments 153
9.10.6. HELICOPTER BLADE 153
Description 153
Objective 153
Procedure 153
Comments 153
9.10.7. COLUMN 154
Description 154
Objective 154
Procedure 154
Comments 155
9.10.8. BRACKET03 155
Description 155
Objective 155
Procedure 155
Comments 156
Chapter 1 0
Buckling Analysis 159
10.1. Linear Buckling Analysis 160
10.2. Convergence of Results in Linear Buckling Analysis 163
10.3. Nonlinear Buckling Analysis 163
10.4. Controlling an Onset of Buckling in Nonlinear Buckling
Analysis 174
10.5. Summary 175
10.6. Hands-On Exercises 176
10.6.1. NOTCHED COLUMN - Free End 176
Description 176
Objective 176
Procedure 176
Comments 177
Contentsxiv
10.6.2. NOTCHED COLUMN - Sliding End 177
Procedure 177
10.6.3. ROUND PLATE02 177
Description 177
Objective 177
Procedure 177
Comments 178
10.6.4. CURVED COLUMN 178
Objective 178
10.6.5. STAND 178
Description 178
Objective 178
Procedure 178
Comments 179
10.6.6. CURVED SHEET 179
Description 179
Objective 179
Procedure 179
Chapter 1 1
Vibration Analysis 181
11.1. Modal Superposition Method 181
11.2. Time Response Analysis 183
11.3. Frequency Response Analysis 186
11.4. Nonlinear Vibration Analysis 190
11.5. Hands-On Exercises 192
11.5.1. HAMMER - Impulse Load 192
Description 192
Objective 192
Procedure 192
Comments 193
11.5.2. HAMMER - Beating 193
Description 193
Objective 193
Procedure 193
Comments 194
11.5.3. ELBOW PIPE 194
Description 194
Objective 194
Procedure 194
Comments 194
Contents xv
11.5.4. CENTRIFUGE 194
Description 194
Objective 195
Procedure 195
Comments 195
11.5.5. PLANK 195
Description 195
Objective 195
Procedure 195
Comments 196
Chapter 1 2
Thermal Analysis 199
12.1. Heat Flow by Conduction 200
12.2. Heat Flow by Convection 201
12.3. Heat Transfer by Radiation 203
12.4. Modeling Considerations in Thermal Analysis 204
12.5. Challenges in Thermal Analysis 206
12.6. Hands-On Exercises 207
12.6.1. BRACKET04 207
Description 207
Objective 207
Procedure 207
Comments 207
12.6.2. HEAT SINK 207
Description 207
Objective 207
Procedure 207
Comments 208
12.6.3. CHANNEL 208
Description 208
Objective 208
Procedure 208
Comments 208
12.6.4. SPACE HEATER 209
Description 209
Objective 209
Procedure 209
Comments 209
Contentsxvi
Chapter 1 3
Implementation of Finite Element Analysis in
the Design Process 211
13.1. Differences between CAD and FEA Geometry 211
13.1.1. Defeaturing 212
13.1.2. Idealization 213
13.1.3. Cleanup 214
13.2. Common Meshing Problems 216
13.3. Mesh Adequacy 218
13.4. Integration of CAD and FEA Programs 219
13.4.1. Stand-Alone FEA Programs 219
13.4.2. FEA Programs Integrated with CAD 219
13.4.3. Computer Aided Engineering (CAE) Programs 219
13.5. FEA Implementation 220
13.5.1. Positioning of CAD and FEA Activities 220
13.5.2. Personnel Training 221
13.5.3. FEA Program Selection 223
13.5.4. Hardware Selection 225
13.5.5. Building Confidence in FEA 225
13.5.6. Return on Investment 226
13.6. FEA Project 226
13.6.1. Before FEA Project Starts 227
13.6.2. Establish the Scope of Analysis 227
13.6.3. Create the Mathematical Model 227
13.6.4. Create the Finite Element Model and Solve It 228
13.6.5. Review the Results 228
13.6.6. Presentation of the Results 229
13.6.7. FEA Report 230
13.6.8. Project Documentation and Backups 231
13.6.9. Contracting Out FEA Services 231
13.6.10. Common Errors in Management of FEA Projects 232
Chapter 1 4
Summary 235
14.1. FEA Quiz 235
14.2. Frequently Asked Questions 238
Contents xvii
Chapter 1 5
FEA Resources 249
Chapter 1 6
Glossary 253
Chapter 1 7
List of Exercises 259
Index 261
About the Author 265
Chapter 1
Introduction 1
1.1. What Is Finite Element Analysis? 1
1.2. What Is the Place of FEA among Other Tools of
Computer-Aided Engineering? 2
1.3. Fields of Application of FEA and Mechanism Analysis 2
1.4. Fields of Application of FEA and CFD 4
1.5. What Is "FEA for Design Engineers"? 4
1.6. Note on Hands-On Exercises 5
Chapter 2
From CAD Model to Results of FEA 7
2.1. Formulation of the Mathematical Model 7
2.2. Selecting the Numerical Method to Solve the
Mathematical Model 10
2.2.1. Selected Numerical Methods in CAE 10
2.2.2. Reasons for the Dominance of FEM 10
2.3. FEA Model 11
2.3.1. Meshing 11
2.3.2. Formulation of FE Equations 12
2.3.3. Errors in FEA Results 13
2.4. Verification and Validation of FEA Results 14
Chapter 3
Fundamental Concepts of FEA 17
3.1. Formulation of a Finite Element 17
3.1.1. Closer Look at Finite Element 17
3.1.2. Requirements to be Satisfied by Displacement Interpolation
Function 20
3.1.3. Artificial Restraints 20
3.2. Choices of Discretization 22
3.3. Types of Finite Elements 23
3.3.1. Element Dimensionality 23
3.3.2. Element Shape 28
3.3.3. Element Order and Element Type 29
3.3.4. Summary of Commonly Used Elements 30
3.3.5. Element Modeling Capabilities 31
Chapter 4
Controlling Discretization Errors 33
4.1. Presenting Stress Results 34
4.2. Types of Convergence Analysis 36
4.2.1. h Convergence by Global Mesh Refinement 36
4.2.2. h Convergence by Local Mesh Refinement 40
4.2.3. Adaptive h Convergence 42
4.2.4. p Convergence Process 44
4.2.5. Choice of Convergence Process 46
4.3. Discretization Error 46
4.3.1. Convergence Error 47
4.3.2. Solution Error 47
4.4. Problems with Convergence 48
4.4.1. Stress Singularity 48
4.4.2. Displacement Singularity 54
4.5. Hands-On Exercises 58
4.5.1. HOLLOW PLATE 58
Description 58
Objective 58
Procedure 59
4.5.2. L BRACKET01 60
Description 60
Objective 60
Procedure 60
Contents ix
4.5.3. WEDGE 61
Description 61
Objective 61
Procedure 61
Chapter 5
Finite Element Mesh 65
5.1. Meshing Techniques 65
5.1.1. Manual Meshing 65
5.1.2. Semi-automatic Meshing 66
5.1.3. Automatic Meshing 67
5.2. Mesh Compatibility 69
5.2.1. Compatible Elements 70
5.2.2. Incompatible Elements 70
5.2.3. Forced Compatibility 71
5.3. Common Meshing Problems 73
5.3.1. Element Distortion 73
5.3.2. Mesh Adequacy 75
5.3.3. Element Mapping to Geometry 76
5.3.4. Incorrect Conversion to Shell Model 78
5.4. Hands-On Exercises 79
5.4.1. BRACKET01 79
Description 79
Objective 79
Procedure 79
5.4.2. CANTILEVER 80
Description 80
Objective 80
Procedure 80
Chapter 6
Modeling Process 83
6.1. Modeling Steps 84
6.1.1. Definition of the Objective of Analysis 84
6.1.2. Selection of the Units of Measurement 84
6.1.3. Geometry Preparation 85
6.1.4. Defining Material Properties 85
6.1.5. Defining Boundary Conditions 86
Contentsx
6.2. Selected Modeling Techniques 87
6.2.1. Mirror Symmetry and Anti-symmetry Boundary Conditions 87
6.2.2. Axial Symmetry 92
6.2.3. Cyclic Symmetry 92
6.2.4. Realignment of Degrees of Freedom 94
6.2.5. Using Point Restraints to Eliminate Rigid Body Motions 95
6.3. Hands-On Exercises 96
6.3.1. BRACKET02-Mirror Symmetry BC 96
Description 96
Objective 96
Procedure 96
6.3.2. BRACKET02-Anti-symmetry BC 97
Description 97
Objective 97
Procedure 97
6.3.3. BRACKET02-Mirror Symmetry and Anti-symmetry BC 98
Description 98
Objective 98
Procedure 98
6.3.4. SHAFT01 99
Description 99
Objective 99
Procedure 99
6.3.5. PRESSURE TANK 100
Description 100
Objective 100
Procedure 100
6.3.6. RING 101
Description 101
Objective 101
Procedure 101
6.3.7. LINK01 102
Description 102
Objective 102
Procedure 103
Chapter 7
Nonlinear Geometry Analysis 105
7.1. Classification of Different Types of Nonlinearities 105
7.2. Geometric Nonlinearity 106
Contents xi
7.3. Membrane Stress Stiffening 112
7.4. Contact 117
7.5. Hands-On Exercises 122
7.5.1. CANTILEVER BEAM 122
Description 122
Objective 123
Procedure 123
7.5.2. SHAFT02 123
Description 123
Objective 123
Procedure 123
7.5.3. ROUND PLATE01 123
Description 123
Objective 124
Procedure 124
7.5.4. LINK02 124
Description 124
Objective 124
Procedure 124
7.5.5. SLIDING SUPPORT 125
Description 125
Objective 125
Procedure 125
7.5.6. CLAMP01 125
Description 125
Objective 125
Procedure 125
7.5.7. CLAMP02 126
Description 126
Objective 126
Procedure 126
Chapter 8
Nonlinear Material Analysis 129
8.1. Review of Nonlinear Material Models 129
8.2. Use of Nonlinear Material to Control Stress Singularity 132
8.3. Other Types of Nonlinearities 134
8.4. Hands-On Exercises 134
8.4.1. BRACKET NL 134
Objective 135
Contentsxii
Procedure 135
8.4.2. L BRACKET02 135
Description 135
Objective 135
Procedure 135
Chapter 9
Modal Analysis 139
9.1. Differences between Modal and
Static Analysis 139
9.2. Interpretation of Displacement and Stress Results in
Modal Analysis 140
9.3. Modal Analysis with Rigid Body Motions 141
9.4. Importance of Supports in Modal Analysis 143
9.5. Applications of Modal Analysis 144
9.5.1. Finding Modal Frequencies and Associated Shapes of Vibration 144
9.5.2. Locating "Weak Spots" in Structure 145
9.5.3. Modal Analysis Provides Input to Vibration Analysis 146
9.6. Pre-stress Modal Analysis 146
9.7. Symmetry and Anti-symmetry Boundary Conditions in
Modal Analysis 148
9.8. Convergence of Modal Frequencies 149
9.9. Meshing Consideration for Modal Analysis 150
9.10. Hands-On Exercises 150
9.10.1. TUNING FORK 150
Description 150
Objective 150
Procedure 150
Comments 150
9.10.2. BOX 151
Description 151
Objective 151
Procedure 151
Comments 151
9.10.3. AIRPLANE 151
Description 151
Objective 151
Procedure 151
Comments 152
Contents xiii
9.10.4. BALL 152
Description 152
Objective 152
Procedure 152
Comments 152
9.10.5. LINK03 152
Description 152
Objective 152
Procedure 152
Comments 153
9.10.6. HELICOPTER BLADE 153
Description 153
Objective 153
Procedure 153
Comments 153
9.10.7. COLUMN 154
Description 154
Objective 154
Procedure 154
Comments 155
9.10.8. BRACKET03 155
Description 155
Objective 155
Procedure 155
Comments 156
Chapter 1 0
Buckling Analysis 159
10.1. Linear Buckling Analysis 160
10.2. Convergence of Results in Linear Buckling Analysis 163
10.3. Nonlinear Buckling Analysis 163
10.4. Controlling an Onset of Buckling in Nonlinear Buckling
Analysis 174
10.5. Summary 175
10.6. Hands-On Exercises 176
10.6.1. NOTCHED COLUMN - Free End 176
Description 176
Objective 176
Procedure 176
Comments 177
Contentsxiv
10.6.2. NOTCHED COLUMN - Sliding End 177
Procedure 177
10.6.3. ROUND PLATE02 177
Description 177
Objective 177
Procedure 177
Comments 178
10.6.4. CURVED COLUMN 178
Objective 178
10.6.5. STAND 178
Description 178
Objective 178
Procedure 178
Comments 179
10.6.6. CURVED SHEET 179
Description 179
Objective 179
Procedure 179
Chapter 1 1
Vibration Analysis 181
11.1. Modal Superposition Method 181
11.2. Time Response Analysis 183
11.3. Frequency Response Analysis 186
11.4. Nonlinear Vibration Analysis 190
11.5. Hands-On Exercises 192
11.5.1. HAMMER - Impulse Load 192
Description 192
Objective 192
Procedure 192
Comments 193
11.5.2. HAMMER - Beating 193
Description 193
Objective 193
Procedure 193
Comments 194
11.5.3. ELBOW PIPE 194
Description 194
Objective 194
Procedure 194
Comments 194
Contents xv
11.5.4. CENTRIFUGE 194
Description 194
Objective 195
Procedure 195
Comments 195
11.5.5. PLANK 195
Description 195
Objective 195
Procedure 195
Comments 196
Chapter 1 2
Thermal Analysis 199
12.1. Heat Flow by Conduction 200
12.2. Heat Flow by Convection 201
12.3. Heat Transfer by Radiation 203
12.4. Modeling Considerations in Thermal Analysis 204
12.5. Challenges in Thermal Analysis 206
12.6. Hands-On Exercises 207
12.6.1. BRACKET04 207
Description 207
Objective 207
Procedure 207
Comments 207
12.6.2. HEAT SINK 207
Description 207
Objective 207
Procedure 207
Comments 208
12.6.3. CHANNEL 208
Description 208
Objective 208
Procedure 208
Comments 208
12.6.4. SPACE HEATER 209
Description 209
Objective 209
Procedure 209
Comments 209
Contentsxvi
Chapter 1 3
Implementation of Finite Element Analysis in
the Design Process 211
13.1. Differences between CAD and FEA Geometry 211
13.1.1. Defeaturing 212
13.1.2. Idealization 213
13.1.3. Cleanup 214
13.2. Common Meshing Problems 216
13.3. Mesh Adequacy 218
13.4. Integration of CAD and FEA Programs 219
13.4.1. Stand-Alone FEA Programs 219
13.4.2. FEA Programs Integrated with CAD 219
13.4.3. Computer Aided Engineering (CAE) Programs 219
13.5. FEA Implementation 220
13.5.1. Positioning of CAD and FEA Activities 220
13.5.2. Personnel Training 221
13.5.3. FEA Program Selection 223
13.5.4. Hardware Selection 225
13.5.5. Building Confidence in FEA 225
13.5.6. Return on Investment 226
13.6. FEA Project 226
13.6.1. Before FEA Project Starts 227
13.6.2. Establish the Scope of Analysis 227
13.6.3. Create the Mathematical Model 227
13.6.4. Create the Finite Element Model and Solve It 228
13.6.5. Review the Results 228
13.6.6. Presentation of the Results 229
13.6.7. FEA Report 230
13.6.8. Project Documentation and Backups 231
13.6.9. Contracting Out FEA Services 231
13.6.10. Common Errors in Management of FEA Projects 232
Chapter 1 4
Summary 235
14.1. FEA Quiz 235
14.2. Frequently Asked Questions 238
Contents xvii
Chapter 1 5
FEA Resources 249
Chapter 1 6
Glossary 253
Chapter 1 7
List of Exercises 259
Index 261
About the Author 265
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