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;

• Preface ixIntroduction  xiChapter 1. Basic Tools for Reliability Analysis 11.1. Introduction  11.2. Advantages of numerical simulation and optimization 21.3. Numerical simulation by finite elements 31.3.1. Use 31.3.2. Principle  41.3.3. General approach  51.4. Optimization process 61.4.1. Basic concepts  71.4.2. Problem classification  101.4.3. Optimization methods  221.4.4. Unconstrained methods 231.4.5. Constrained methods  431.5. Sensitivity analysis  561.5.1. Importance of sensitivity  561.5.2. Sensitivity methods 571.6. Conclusion 61Chapter 2. Reliability Concept 632.1. Introduction  632.1.1. Preamble 632.1.2. Reliability history  632.1.3. Reliability definition  652.1.4. Importance of reliability  662.2. Basic functions and concepts for reliability analysis  662.2.1. Failure concept 672.2.2. Uncertainty concept  672.2.3. Random variables  682.2.4. Probability density function  692.2.5. Cumulative distribution function 692.2.6. Reliability function 702.3. System reliability  712.3.1. Series conjunction 712.3.2. Parallel conjunction 722.3.3. Mixed conjunction 732.3.4. Delta-star conjunction 742.4. Statistical measures 772.5. Probability distributions  812.5.1. Uniform distribution  822.5.2. Normal distribution 862.5.3. Lognormal distribution 912.6. Reliability analysis 972.6.1. Definitions  972.6.2. Algorithms  1052.6.3. Reliability analysis methods 1062.6.4. Optimality criteria 1102.7. Conclusion 112Chapter 3. Integration of Reliability Concept into Biomechanics  1133.1. Introduction  1133.2. Origin and categories of uncertainties  1153.3. Uncertainties in biomechanics 1163.3.1. Uncertainty in loading 1173.3.2. Uncertainty in geometry  1183.3.3. Uncertainty in materials  1183.4. Bone-related uncertainty  1193.4.1. Bone behavior law 1203.4.2. Contribution to the characterization of the bone’s mechanical properties 1253.5. Bone developments and formulations  1263.5.1. Current formulation 1263.5.2. Generalized formulation  1273.5.3. Optimized formulation 1283.5.4. Extension to orthotropic behavior formulation 1303.6. Characterization by experimentation of the bone’s mechanical properties  1333.6.1. Characterization by bending test 1343.6.2. Characterization by compression test 1353.7. Conclusion 136Chapter 4. Reliability Analysis of Orthopedic Prostheses  1374.1. Introduction to orthopedic prostheses 1374.1.1. History of prostheses 1394.1.2. Evolution of prostheses 1394.1.3. Examples of orthopedic prostheses  1404.2. Reliability analysis of the intervertebral disk 1404.2.1. Functional anatomy 1404.2.2. The lumbar functional spinal unit 1414.2.3. Intervertebral disk prosthesis  1454.2.4. Numerical application on the intervertebral disk  1474.3. Reliability analysis of the hip prosthesis 1544.3.1. Anatomy  1544.3.2. Presentation of the total hip prosthesis  1584.3.3. Numerical application of the hip prosthesis 1614.3.4. Boundary conditions  1644.3.5. Direct simulation 1644.3.6. Probabilistic sensitivity analysis  1664.3.7. Integration of reliability analysis 1674.4. Conclusion 173Chapter 5. Reliability Analysis of Orthodontic Prostheses 1755.1. Introduction to orthodontic prostheses  1755.2. Anatomy of the temporomandibular joint  1765.2.1. Articular bone regions and meniscus 1775.2.2. Ligaments 1795.2.3. Myology, elevator muscles and depressor muscles 1795.3. Numerical simulation of a non-fractured mandible 1835.3.1. Description of the studied mandible 1835.3.2. Numerical results  1855.4. Reliability analysis of the fixation system of the fractured mandible  1885.4.1. Description of a fractured mandible 1885.4.2. Fixation strategy using mini-plates  1895.4.3. Study of a homogeneous and isotropic structure  1905.4.4. Study of a composite and orthotropic structure  1985.4.5. Result discussion  2075.5. Conclusion  208Appendices 209Appendix 1: Matrix Calculation  211Appendix 2: ANSYS Code for the Disk Implant 217Appendix 3: ANSYS Code for the Stem Implant  221Appendix 4: Probability of Failure/Reliability Index  235Bibliography 237Index  245