Biomechanics Optimization, Uncertainties and Reliability

Content: Preface  xi    Introduction xiii    List of Abbreviations xvii    Chapter 1. Introduction to Structural Optimization 1    1.1. Introduction  1    1.2. History of structural optimization  2    1.3. Sizing optimization  4    1.3.1. Definition 4    1.3.2. First works in sizing optimization  4    1.3.3. Numerical application  5    1.4. Shape optimization  10    1.4.1. Definition 10    1.4.2. First works in shape optimization  11    1.4.3. Numerical application  12    1.5. Topology optimization  16    1.5.1. Definition 16    1.5.2. First works in topology optimization  17    1.5.3. Numerical application  18    1.6. Conclusion 21    Chapter 2. Integration of Structural Optimization into Biomechanics 23    2.1. Introduction  23    2.2. Integration of structural optimization into orthopedic prosthesis design  23    2.2.1. Structural optimization of the hip prosthesis  24    2.2.2. Sizing optimization of a 3D intervertebral disk prosthesis  42    2.3. Integration of structural optimization into orthodontic prosthesis design 47    2.3.1. Sizing optimization of a dental implant 47    2.3.2. Shape optimization of a mini-plate 49    2.4. Advanced integration of structural optimization into drilling surgery 52    2.4.1. Case of treatment of a crack with a single hole 53    2.4.2. Case of treatment of a crack with two holes  54    2.5. Conclusion 56    Chapter 3. Integration of Reliability into Structural Optimization  57    3.1. Introduction  57    3.2. Literature review of reliability-based optimization 58    3.3. Comparison between deterministic and reliability-based optimization 60    3.3.1. Deterministic optimization  61    3.3.2. Reliability-based optimization 63    3.4. Numerical application 64    3.4.1. Description and modeling of the studied problem 64    3.4.2. Numerical results 65    3.5. Approaches and strategies for reliability-based optimization 68    3.5.1. Mono-level approaches  68    3.5.2. Double-level approaches 68    3.5.3. Sequential decoupled approaches  68    3.6. Two points of view for developments of reliability-based optimization 69    3.6.1. Point of view of    Reliability     69    3.6.2. Point of view of    Optimization    70    3.6.3. Method efficiency 70    3.7. Philosophy of integration of the concept of reliability into structural optimization groups  72    3.8. Conclusion 73    Chapter 4. Reliability-based Design Optimization Model  75    4.1. Introduction  75    4.2. Classic method 76    4.2.1. Formulations 76    4.2.2. Optimality conditions 77    4.2.3. Algorithm 77    4.2.4. Advantages and disadvantages  79    4.3. Hybrid method 79    4.3.1. Formulation  79    4.3.2. Optimality conditions 82    4.3.3. Algorithm 84    4.3.4. Advantages and disadvantages  85    4.4. Improved hybrid method 86    4.4.1. Formulations 86    4.4.2. Optimality conditions 86    4.4.3. Algorithm 89    4.4.4. Advantages and disadvantages  90    4.5. Optimum safety factor method  91    4.5.1. Safety factor concept 91    4.5.2. Developments and optimality conditions  92    4.5.3. Algorithm 97    4.5.4. Advantages and disadvantages  98    4.6. Safest point method  98    4.6.1. Formulations 98    4.6.2. Algorithm 102    4.6.3. Advantages and disadvantages  104    4.7. Numerical applications  105    4.7.1. RBDO of a hook: CM and HM 105    4.7.2. RBDO of a triangular plate: HM & IHM  107    4.7.3. RBDO of a console beam (sandwich beam): HM and OSF  110    4.7.4. RBDO of an aircraft wing: HM & SP  113    4.8. Classification of the methods developed 115    4.8.1. Numerical methods  115    4.8.2. Semi-numerical methods 116    4.8.3. Comparison between the numerical- and semi-numerical methods 118    4.9. Conclusion 119    Chapter 5. Reliability-based Topology Optimization Model  121    5.1. Introduction  121    5.2. Formulation and algorithm for the RBTO model  122    5.2.1. Formulation  122    5.2.2. Algorithm 123    5.2.3. Validation of the RBTO code developed  125    5.3. Validation of the RBTO model  126    5.3.1. Analytical validation 126    5.3.2. Numerical validation 128    5.4. Variability of the reliability index  134    5.4.1. Example 1: MBB beam  136    5.4.2. Example 2: Cantilever beam 136    5.4.3. Example 3: Cantilever beam with double loads  136    5.4.4. Example 4: Cantilever beam with a transversal hole  136    5.5. Numerical applications for the RBTO model  137    5.5.1. Static analysis 138    5.5.2. Modal analysis  139    5.5.3. Fatigue analysis  141    5.6. Two points of view for integration of reliability into topology optimization 142    5.6.1. Point of view of    topology    144    5.6.2. Point of view of    reliability    144    5.6.3. Numerical applications for the two points of view 146    5.7. Conclusion 152    Chapter 6. Integration of Reliability and Structural Optimization into Prosthesis Design  153    6.1. Introduction  153    6.2. Prosthesis design  154    6.3. Integration of topology optimization into prosthesis design  154    6.3.1. Importance of topology optimization in prosthesis design 155    6.3.2. Place of topology optimization in the prosthesis design chain 156    6.4. Integration of reliability and structural optimization into hip prosthesis design  157    6.4.1. Numerical application of the deterministic approach 158    6.4.2. Numerical application of the reliability-based approach 167    6.5. Integration of reliability and structural optimization into the design of mini-plate systems used to treat fractured mandibles 174    6.5.1. Numerical application of the deterministic approach  174    6.5.2. Numerical application of the reliability-based approach  181    6.6. Integration of reliability and structural optimization into dental implant design  184    6.6.1. Description and modeling of the problem 184    6.6.2. Numerical results 186    6.7. Conclusion 188    Appendices 189    Appendix 1. ANSYS Code for Stem Geometry 191    Appendix 2. ANSYS Code for Mini-Plate Geometry  197    Appendix 3. ANSYS Code for Dental Implant Geometry 201    Appendix 4. ANSYS Code for Geometry of Dental Implant with Bone 207    Bibliography 213    Index 229