Table of Contents

Preface ix

Introduction  xi

Chapter 1. Basic Tools for Reliability Analysis 1

1.1. Introduction  1

1.2. Advantages of numerical simulation and optimization 2

1.3. Numerical simulation by finite elements 3

1.3.1. Use 3

1.3.2. Principle  4

1.3.3. General approach  5

1.4. Optimization process 6

1.4.1. Basic concepts  7

1.4.2. Problem classification  10

1.4.3. Optimization methods  22

1.4.4. Unconstrained methods 23

1.4.5. Constrained methods  43

1.5. Sensitivity analysis  56

1.5.1. Importance of sensitivity  56

1.5.2. Sensitivity methods 57

1.6. Conclusion 61

Chapter 2. Reliability Concept 63

2.1. Introduction  63

2.1.1. Preamble 63

2.1.2. Reliability history  63

2.1.3. Reliability definition  65

2.1.4. Importance of reliability  66

2.2. Basic functions and concepts for reliability analysis  66

2.2.1. Failure concept 67

2.2.2. Uncertainty concept  67

2.2.3. Random variables  68

2.2.4. Probability density function  69

2.2.5. Cumulative distribution function 69

2.2.6. Reliability function 70

2.3. System reliability  71

2.3.1. Series conjunction 71

2.3.2. Parallel conjunction 72

2.3.3. Mixed conjunction 73

2.3.4. Delta-star conjunction 74

2.4. Statistical measures 77

2.5. Probability distributions  81

2.5.1. Uniform distribution  82

2.5.2. Normal distribution 86

2.5.3. Lognormal distribution 91

2.6. Reliability analysis 97

2.6.1. Definitions  97

2.6.2. Algorithms  105

2.6.3. Reliability analysis methods 106

2.6.4. Optimality criteria 110

2.7. Conclusion 112

Chapter 3. Integration of Reliability Concept into Biomechanics  113

3.1. Introduction  113

3.2. Origin and categories of uncertainties  115

3.3. Uncertainties in biomechanics 116

3.3.1. Uncertainty in loading 117

3.3.2. Uncertainty in geometry  118

3.3.3. Uncertainty in materials  118

3.4. Bone-related uncertainty  119

3.4.1. Bone behavior law 120

3.4.2. Contribution to the characterization of the bone’s mechanical properties 125

3.5. Bone developments and formulations  126

3.5.1. Current formulation 126

3.5.2. Generalized formulation  127

3.5.3. Optimized formulation 128

3.5.4. Extension to orthotropic behavior formulation 130

3.6. Characterization by experimentation of the bone’s mechanical properties  133

3.6.1. Characterization by bending test 134

3.6.2. Characterization by compression test 135

3.7. Conclusion 136

Chapter 4. Reliability Analysis of Orthopedic Prostheses  137

4.1. Introduction to orthopedic prostheses 137

4.1.1. History of prostheses 139

4.1.2. Evolution of prostheses 139

4.1.3. Examples of orthopedic prostheses  140

4.2. Reliability analysis of the intervertebral disk 140

4.2.1. Functional anatomy 140

4.2.2. The lumbar functional spinal unit 141

4.2.3. Intervertebral disk prosthesis  145

4.2.4. Numerical application on the intervertebral disk  147

4.3. Reliability analysis of the hip prosthesis 154

4.3.1. Anatomy  154

4.3.2. Presentation of the total hip prosthesis  158

4.3.3. Numerical application of the hip prosthesis 161

4.3.4. Boundary conditions  164

4.3.5. Direct simulation 164

4.3.6. Probabilistic sensitivity analysis  166

4.3.7. Integration of reliability analysis 167

4.4. Conclusion 173

Chapter 5. Reliability Analysis of Orthodontic Prostheses 175

5.1. Introduction to orthodontic prostheses  175

5.2. Anatomy of the temporomandibular joint  176

5.2.1. Articular bone regions and meniscus 177

5.2.2. Ligaments 179

5.2.3. Myology, elevator muscles and depressor muscles 179

5.3. Numerical simulation of a non-fractured mandible 183

5.3.1. Description of the studied mandible 183

5.3.2. Numerical results  185

5.4. Reliability analysis of the fixation system of the fractured mandible  188

5.4.1. Description of a fractured mandible 188

5.4.2. Fixation strategy using mini-plates  189

5.4.3. Study of a homogeneous and isotropic structure  190

5.4.4. Study of a composite and orthotropic structure  198

5.4.5. Result discussion  207

5.5. Conclusion  208

Appendices 209

Appendix 1: Matrix Calculation  211

Appendix 2: ANSYS Code for the Disk Implant 217

Appendix 3: ANSYS Code for the Stem Implant  221

Appendix 4: Probability of Failure/Reliability Index  235

Bibliography 237

Index  245

About the Author

Ghias KHARMANDA, Associate Professor (HDR Europ. Dr Eng).

Dr. Abdelkhalak EL HAMI, Laboratoire d'Optimisation et Fiabilité en Mécanique des Structures, LOFIMS, INSA de Rouen, France;