Biomechanics : Optimization, Uncertainties and Reliability.

Cover -- Title Page -- Copyright -- Contents -- Preface -- Introduction -- List of Abbreviations -- 1. Introduction to Structural Optimization -- 1.1. Introduction -- 1.2. History of structural optimization -- 1.3. Sizing optimization -- 1.3.1. Definition -- 1.3.2. First works in sizing optimization -- 1.3.3. Numerical application -- 1.4. Shape optimization -- 1.4.1. Definition -- 1.4.2. First works in shape optimization -- 1.4.3. Numerical application -- 1.5. Topology optimization -- 1.5.1. Definition -- 1.5.2. First works in topology optimization -- 1.5.3. Numerical application -- 1.6. Conclusion -- 2. Integration of Structural Optimization into Biomechanics -- 2.1. Introduction -- 2.2. Integration of structural optimization into orthopedic prosthesis design -- 2.2.1. Structural optimization of the hip prosthesis -- 2.2.2. Sizing optimization of a 3D intervertebral disk prosthesis -- 2.3. Integration of structural optimization into orthodontic prosthesis design -- 2.3.1. Sizing optimization of a dental implant -- 2.3.2. Shape optimization of a mini-plate -- 2.4. Advanced integration of structural optimization into drilling surgery -- 2.4.1. Case of treatment of a crack with a single hole -- 2.4.2. Case of treatment of a crack with two holes -- 2.5. Conclusion -- 3. Integration of Reliability Into Structural Optimization -- 3.1. Introduction -- 3.2. Literature review of reliability-based optimization -- 3.3. Comparison between deterministic and reliability-based optimization -- 3.3.1. Deterministic optimization -- 3.3.2. Reliability-based optimization -- 3.4. Numerical application -- 3.4.1. Description and modeling of the studied problem -- 3.4.2. Numerical results -- 3.5. Approaches and strategies for reliability-based optimization -- 3.5.1. Mono-level approaches -- 3.5.2. Double-level approaches -- 3.5.3. Sequential decoupled approaches.

3.6. Two points of view for developments of reliability-based optimization -- 3.6.1. Point of view of "Reliability" -- 3.6.2. Point of view of "Optimization" -- 3.6.3. Method efficiency -- 3.7. Philosophy of integration of the concept of reliability into structural optimization groups -- 3.8. Conclusion -- 4. Reliability-based Design Optimization Model -- 4.1. Introduction -- 4.2. Classic method -- 4.2.1. Formulations -- 4.2.2. Optimality conditions -- 4.2.3. Algorithm -- 4.2.4. Advantages and disadvantages -- 4.3. Hybrid method -- 4.3.1. Formulation -- 4.3.2. Optimality conditions -- 4.3.3. Algorithm -- 4.3.4. Advantages and disadvantages -- 4.4. Improved hybrid method -- 4.4.1. Formulations -- 4.4.2. Optimality conditions -- 4.4.3. Algorithm -- 4.4.4. Advantages and disadvantages -- 4.5. Optimum safety factor method -- 4.5.1. Safety factor concept -- 4.5.2. Developments and optimality conditions -- 4.5.3. Algorithm -- 4.5.4. Advantages and disadvantages -- 4.6. Safest point method -- 4.6.1. Formulations -- 4.6.2. Algorithm -- 4.6.3. Advantages and disadvantages -- 4.7. Numerical applications -- 4.7.1. RBDO of a hook: CM and HM -- 4.7.2. RBDO of a triangular plate: HM &amp -- IHM -- 4.7.3. RBDO of a console beam (sandwich beam): HM and OSF -- 4.7.4. RBDO of an aircraft wing: HM &amp -- SP -- 4.8. Classification of the methods developed -- 4.8.1. Numerical methods -- 4.8.2. Semi-numerical methods -- 4.8.3. Comparison between the numerical and semi-numerical methods -- 4.9. Conclusion -- 5. Reliability-based Topology Optimization Model -- 5.1. Introduction -- 5.2. Formulation and algorithm for the RBTO model -- 5.2.1. Formulation -- 5.2.2. Algorithm -- 5.2.3. Validation of the RBTO code developed -- 5.3. Validation of the RBTO model -- 5.3.1. Analytical validation -- 5.3.2. Numerical validation -- 5.4. Variability of the reliability index.

5.4.1. Example 1: MBB beam -- 5.4.2. Example 2: Cantilever beam -- 5.4.3. Example 3: Cantilever beam with double loads -- 5.4.4. Example 4: Cantilever beam with a transversal hole -- 5.5. Numerical applications for the RBTO model -- 5.5.1. Static analysis -- 5.5.2. Modal analysis -- 5.5.3. Fatigue analysis -- 5.6. Two points of view for integration of reliability into topology optimization -- 5.6.1. Point of view of "topology" -- 5.6.2. Point of view of "reliability" -- 5.6.3. Numerical applications for the two points of view -- 5.7. Conclusion -- 6. Integration of Reliability and Structural Optimization into Prosthesis Design -- 6.1. Introduction -- 6.2. Prosthesis design -- 6.3. Integration of topology optimization into prosthesis design -- 6.3.1. Importance of topology optimization in prosthesis design -- 6.3.2. Place of topology optimization in the prosthesis design chain -- 6.4. Integration of reliability and structural optimization into hip prosthesis design -- 6.4.1. Numerical application of the deterministic approach -- 6.4.2. Numerical application of the reliability-based approach -- 6.5. Integration of reliability and structural optimization into the design of mini-plate systems used to treat fractured mandibles -- 6.5.1. Numerical application of the deterministic approach -- 6.5.2. Numerical application of the reliability-based approach -- 6.6. Integration of reliability and structural optimization into dental implant design -- 6.6.1. Description and modeling of the problem -- 6.6.2. Numerical results -- 6.7. Conclusion -- APPENDICES -- Appendix 1. ANSYS Code for Stem Geometry -- Appendix 2. ANSYS Code for Mini-Plate Geometry -- Appendix 3. ANSYS Code for Dental Implant Geometry -- Appendix 4. ANSYS Code for Geometry of Dental Implant with Bone -- Bibliography -- Index -- Other titles from iSTE in Mechanical Engineering and Solid Mechanics.

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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.