Reliability in Biomechanics.

Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- Introduction -- 1. Basic Tools for Reliability Analysis -- 1.1. Introduction -- 1.2. Advantages of numerical simulation and optimization -- 1.3. Numerical simulation by finite elements -- 1.3.1. Use -- 1.3.2. Principle -- 1.3.3. General approach -- 1.4. Optimization process -- 1.4.1. Basic concepts -- 1.4.1.1. Optimization parameters -- 1.4.1.2. Local or global optimal solutions -- 1.4.1.3. Simplified algorithm -- 1.4.2. Problem classification -- 1.4.2.1. Constraint classification -- 1.4.2.2. Linearity classification -- 1.4.2.3. Objective classification -- 1.4.3. Optimization methods -- 1.4.4. Unconstrained methods -- 1.4.4.1. Zero-order methods -- 1.4.4.2. First-order methods -- 1.4.4.3. Second-order methods -- 1.4.5. Constrained methods -- 1.4.5.1. Direct methods -- 1.4.5.2. Transformation methods -- 1.5. Sensitivity analysis -- 1.5.1. Importance of sensitivity -- 1.5.2. Sensitivity methods -- 1.6. Conclusion -- 2. Reliability Concept -- 2.1. Introduction -- 2.1.1. Preamble -- 2.1.2. Reliability history -- 2.1.3. Reliability definition -- 2.1.4. Importance of reliability -- 2.2. Basic functions and concepts for reliability analysis -- 2.2.1. Failure concept -- 2.2.2. Uncertainty concept -- 2.2.2.1. Intrinsic risks -- 2.2.2.2. Extrinsic risks -- 2.2.3. Random variables -- 2.2.4. Probability density function -- 2.2.5. Cumulative distribution function -- 2.2.6. Reliability function -- 2.3. System reliability -- 2.3.1. Series conjunction -- 2.3.2. Parallel conjunction -- 2.3.3. Mixed conjunction -- 2.3.4. Delta-star conjunction -- 2.4. Statistical measures -- 2.5. Probability distributions -- 2.5.1. Uniform distribution -- 2.5.1.1. Probability density function -- 2.5.1.2. Cumulative distribution function -- 2.5.1.3. Reliability function -- 2.5.2. Normal distribution.

2.5.2.1. Probability density function -- 2.5.2.2. Cumulative distribution function -- 2.5.2.3. Reliability function -- 2.5.3. Lognormal distribution -- 2.5.3.1. Probability density function -- 2.5.3.2. Cumulative distribution function -- 2.5.3.3. Reliability function -- 2.6. Reliability analysis -- 2.6.1. Definitions -- 2.6.1.1. Random variables versus deterministic variables -- 2.6.1.2. Probability of failure -- 2.6.1.3. Limit state function -- 2.6.1.4. Design point -- 2.6.1.5. Reliability index -- 2.6.2. Algorithms -- 2.6.3. Reliability analysis methods -- 2.6.3.1. Monte-Carlo simulation method -- 2.6.3.2. Approximation methods -- 2.6.3.3. Response surface methods -- 2.6.4. Optimality criteria -- 2.7. Conclusion -- 3. Integration of Reliability Concept into Biomechanics -- 3.1. Introduction -- 3.2. Origin and categories of uncertainties -- 3.3. Uncertainties in biomechanics -- 3.3.1. Uncertainty in loading -- 3.3.2. Uncertainty in geometry -- 3.3.3. Uncertainty in materials -- 3.4. Bone-related uncertainty -- 3.4.1. Bone behavior law -- 3.4.2. Contribution to the characterization of the bone's mechanical properties -- 3.5. Bone developments and formulations -- 3.5.1. Current formulation -- 3.5.2. Generalized formulation -- 3.5.3. Optimized formulation -- 3.5.4. Extension to orthotropic behavior formulation -- 3.6. Characterization by experimentation of the bone's mechanical properties -- 3.6.1. Characterization by bending test -- 3.6.2. Characterization by compression test -- 3.7. Conclusion -- 4. Reliability Analysis of Orthopedic Prostheses -- 4.1. Introduction to orthopedic prostheses -- 4.1.1. History of prostheses -- 4.1.2. Evolution of prostheses -- 4.1.3. Examples of orthopedic prostheses -- 4.2. Reliability analysis of the intervertebral disk -- 4.2.1. Functional anatomy -- 4.2.2. The lumbar functional spinal unit -- 4.2.2.1. Description.

4.2.2.2. The intervertebral disk -- 4.2.2.3. The ligaments -- 4.2.3. Intervertebral disk prosthesis -- 4.2.4. Numerical application on the intervertebral disk -- 4.2.4.1. Numerical simulation using finite elements -- 4.2.4.2. Optimization for the optimal solution -- 4.2.4.3. Calculation of reliability -- 4.3. Reliability analysis of the hip prosthesis -- 4.3.1. Anatomy -- 4.3.1.1. Different views -- 4.3.1.2. Articular surfaces of the coxofemoral joint -- 4.3.1.3. Means of union -- 4.3.1.4. Muscles enabling hip mobility -- 4.3.2. Presentation of the total hip prosthesis -- 4.3.3. Numerical application of the hip prosthesis -- 4.3.4. Boundary conditions -- 4.3.5. Direct simulation -- 4.3.6. Probabilistic sensitivity analysis -- 4.3.7. Integration of reliability analysis -- 4.3.7.1. Case 1: Two parameters -- 4.3.7.2. Case 2: six parameters -- 4.4. Conclusion -- 5. Reliability Analysis of Orthodontic Prostheses -- 5.1. Introduction to orthodontic prostheses -- 5.2. Anatomy of the temporomandibular joint -- 5.2.1. Articular bone regions and meniscus -- 5.2.1.1. Bone structure -- 5.2.1.2. Meniscus and the articular capsules -- 5.2.2. Ligaments -- 5.2.3. Myology, elevator muscles and depressor muscles -- 5.2.3.1. Elevator muscles -- 5.2.3.2. Depressor muscles -- 5.2.3.3. Lateral pterygoid, unclassified -- 5.3. Numerical simulation of a non-fractured mandible -- 5.3.1. Description of the studied mandible -- 5.3.2. Numerical results -- 5.3.2.1. Case of muscle force exclusion -- 5.3.2.2. Case of muscle force inclusion -- 5.4. Reliability analysis of the fixation system of the fractured mandible -- 5.4.1. Description of a fractured mandible -- 5.4.2. Fixation strategy using mini-plates -- 5.4.3. Study of a homogeneous and isotropic structure -- 5.4.3.1. Model construction -- 5.4.3.2. Developed algorithm -- 5.4.3.3. Numerical results.

5.4.4. Study of a composite and orthotropic structure -- 5.4.4.1. Construction of the model -- 5.4.4.2. Developed algorithm -- 5.4.4.3. Numerical result -- 5.4.5. Result discussion -- 5.5. Conclusion -- Appendices -- Appendix 1. Matrix Calculation -- A1.1. Linear equations system -- A1.2. Addition and subtraction of matrices -- A1.3. Scalar multiplication -- A1.4. Product of matrices -- A1.5. Transpose of a matrix -- A1.6. Symmetric matrix -- A1.7. Unit matrix -- A1.8. Determinant of a matrix -- A1.9. Singular matrix -- A1.10. Inverse matrix -- Appendix 2. ANSYS Code for the Disk Implant -- Appendix 3. ANSYS Code for the Stem Implant -- Appendix 4. Probability of Failure/Reliability Index -- Bibliography -- Index -- Other titles from in iSTE Mechanical Engineering and Solid Mechanics -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.