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.