ANALYSIS OF MECHANICAL STRUCTURES USING

FINITE ELEMENT METHOD

- Lecture notes -

Contents

1. INTRODUCTION 7

1.1. PREFACE 7

1.2. ABOUT PLM, CAD / CAE / CAM 8

1.3. ABOUT FEM AND FEA 13

1.3.1. A Brief History of the FEM and FEA 13

1.3.2. FEM in Engineering 14

1.3.3. Available Commercial FEM Software Packages 18

1.4. COURSE DESCRIPTION 23

1.4.1. Course Overview 24

1.4.2. Course Objectives 24

1.4.3. Recommended Background 25

2. GENERAL PROBLEM DEFINITION 27

2.1. GENERAL CONSIDERATIONS ON THE METHOD 27

2.2. FEM TERMINOLOGY 33

2.3. IDEALIZATION 35

2.3.1. Models 35

2.3.2. Mathematical Models 36

2.3.3. Implicit vs. Explicit Modeling 37

2.4. THE THEORETICAL QUASI-GENERAL MODEL FOR FINITE ELEMENT ANALYSIS OF A MECHANICAL SUBASSEMBLY ELEMENT 39

2.5. TYPES OF SOLVABLE PROBLEMS USING FINITE ELEMENTS ANALYSIS 42

2.6. THE MODEL FOR ANALYSIS 45

2.7. SAMPLES OF ANALYSIS MODELS 52

2.8. THE GENERAL PROCEDURE OF FEA 54

3. PRE-PROCESSING PHASE 55

3.1. GEOMETRY MODELING 58

3.1.1. General considerations about geometry modeling 58

3.1.2. Basic concepts about 3D modeling 62

3.1.3. Samples of the various 3D modeling software 67

3.2. ASSIGN MATERIAL PROPERTIES 82

3.2.1. Modeling the mechanical behavior of materials 82

3.2.2. Modeling thermal behavior of materials 85

3.3. MESHING (DISCRETIZATION) – TYPES OF FINITE ELEMENTS 3D, 2D, 1D 87

3.3.1. Discretization 87

3.3.2. The Finite Elements 89

3.3.3. The meshing procedure 89

3.3.4. Types of Finite Elements 91

3.3.5. Classification of Mechanical Elements 96

3.3.6. Assembly 99

3.3.7. Modeling methods with elements 99

3.3.8. Choosing finite elements and meshing parameters 102

3.3.9. Meshing example (1D, 2D, 3D) 106

3.4. BOUNDARY CONDITIONS. INTRODUCING SUPPORTS 117

3.4.1. Boundary Conditions 117

3.4.2. Introducing supports 118

3.4.3. Restraints in CATIA 120

3.4.4. Restraints in ANSYS 122

3.5. LOAD MODELING 127

3.5.1. Loads in CATIA 128

3.5.2. Loads in ANSYS 130

4. SOLVING PHASE 135

4.1. GENERAL CONSIDERATIONS ABOUT SOLVING PHASE 136

4.2. MODERN DESIGN PROBLEM 138

4.3. SOLVING METHODS 138

4.3.1. Numerical Methods 138

4.3.2. Fundamental concepts 140

4.3.3. FEM formulation for a linear differential equation 144

4.3.4. From Strong Form to Weak form (1D) 145

4.4. TYPES OF ANALYSIS 151

4.4.1. Linear Static Analysis 152

4.4.2. Vibration Analysis 158

4.4.3. Buckling Analysis 163

4.4.4. Thermal Analysis 167

4.5. EXAMPLES FOR SOLVING COMMANDS 176

4.5.1. Solving the Model in CATIA 176

4.5.2. Solving the Model in ANSYS 176

5. POST-PROCESSING PHASE 179

5.1. ABOUT PRE- AND POST-PROCESSOR 179

5.2. GENERAL CONSIDERATIONS ABOUT THE POST-PROCESSING PHASE 181

5.3. RESULTS 183

5.3.1. Displacements 183

5.3.2. Stresses 184

5.3.3. Strains 187

5.4. SAMPLES OF POST-PROCESSING 188

5.4.1. Post-processing in CATIA 188

5.4.2. Post-processing in ANSYS 192

6. REFERENCES 196

These lecture notes represent an educational material for students of Automotive specialization (AE) and Virtual Automotive Design (VAD), Faculty of Mechanical Engineering from Transilvania University of Brasov. Use of these lecture notes will be reduced to this University.

In order to complete these lecture notes, I have used data from various sources: books, lecture notes, laboratory guidance of some colleagues by our country or abroad and tutorials of specialized programs in MEF (CATIA, ANSYS, Z88 Aurora). References were marked precisely in the chapters that I use. For full texts used from various sources, I have requested and I received written permission from the authors.