Finite Element Analysis for Design Engineers

Finite Element Analysis (FEA) has been widely implemented by the automotive industry as a productivity tool for design engineers to reduce both development time and cost. This essential work serves as a guide for FEA as a design tool and addresses the specific needs of design engineers to improve productivity. It provides a clear presentation that will help practitioners to avoid mistakes. Easy to use examples of FEA fundamentals are clearly presented that can be simply applied during the product development process. The FEA process is fully explored in this fundamental and practical approach that includes: Understanding FEA basics Commonly used modeling techniques Application of FEA in the design process Fundamental errors and their effect on the quality of results Hands-on simple and informative exercises This indispensable guide provides design engineers with proven methods to analyze their own work while it is still in the form of easily modifiable CAD models. Simple and informative exercises provide examples for improving the process to deliver quick turnaround times and prompt implementation. This is the latest version of Finite Element Analysis for Design Engineers.

Table of Contents:
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