Biomechanics

Ghias KHARMANDA, Associate Professor (HDR Europ. Dr Eng).Prof. Dr.Abdelkhalak EL HAMI, Laboratoire d'Optimisation et Fiabilité en Mécanique des Structures, LOFIMS, INSA de Rouen, France.

• Preface xiIntroduction xiiiList of Abbreviations xviiChapter 1 Introduction to Structural Optimization 11.1 Introduction 11.2 History of structural optimization 21.3 Sizing optimization 41.3.1 Definition 41.3.2 First works in sizing optimization 41.3.3 Numerical application 51.4 Shape optimization 101.4.1 Definition 101.4.2 First works in shape optimization 111.4.3 Numerical application 121.5 Topology optimization 161.5.1 Definition 161.5.2 First works in topology optimization 171.5.3 Numerical application 181.6 Conclusion 21Chapter 2 Integration of Structural Optimization into Biomechanics 232.1 Introduction 232.2 Integration of structural optimization into orthopedic prosthesis design 232.2.1 Structural optimization of the hip prosthesis 242.2.2 Sizing optimization of a 3D intervertebral disk prosthesis 422.3 Integration of structural optimization into orthodontic prosthesis design 472.3.1 Sizing optimization of a dental implant 472.3.2 Shape optimization of a mini-plate 492.4 Advanced integration of structural optimization into drilling surgery 522.4.1 Case of treatment of a crack with a single hole 532.4.2 Case of treatment of a crack with two holes 542.5 Conclusion 56Chapter 3 Integration of Reliability into Structural Optimization 573.1 Introduction 573.2 Literature review of reliability-based optimization 583.3 Comparison between deterministic and reliability-based optimization 603.3.1 Deterministic optimization 613.3.2 Reliability-based optimization 633.4 Numerical application 643.4.1 Description and modeling of the studied problem 643.4.2 Numerical results 653.5 Approaches and strategies for reliability-based optimization 683.5.1 Mono-level approaches 683.5.2 Double-level approaches 683.5.3 Sequential decoupled approaches 683.6 Two points of view for developments of reliability-based optimization 693.6.1 Point of view of “Reliability” 693.6.2 Point of view of “Optimization” 703.6.3 Method efficiency 703.7 Philosophy of integration of the concept of reliability into structural optimization groups 723.8 Conclusion 73Chapter 4 Reliability-based Design Optimization Model 754.1 Introduction 754.2 Classic method 764.2.1 Formulations 764.2.2 Optimality conditions 774.2.3 Algorithm 774.2.4 Advantages and disadvantages 794.3 Hybrid method 794.3.1 Formulation 794.3.2 Optimality conditions 824.3.3 Algorithm 844.3.4 Advantages and disadvantages 854.4 Improved hybrid method 864.4.1 Formulations 864.4.2 Optimality conditions 864.4.3 Algorithm 894.4.4 Advantages and disadvantages 904.5 Optimum safety factor method 914.5.1 Safety factor concept 914.5.2 Developments and optimality conditions 924.5.3 Algorithm 974.5.4 Advantages and disadvantages 984.6 Safest point method 984.6.1 Formulations 984.6.2 Algorithm 1024.6.3 Advantages and disadvantages 1044.7 Numerical applications 1054.7.1 RBDO of a hook: CM and HM 1054.7.2 RBDO of a triangular plate: HM & IHM 1074.7.3 RBDO of a console beam (sandwich beam): HM and OSF 1104.7.4 RBDO of an aircraft wing: HM & SP 1134.8 Classification of the methods developed 1154.8.1 Numerical methods 1154.8.2 Semi-numerical methods 1164.8.3 Comparison between the numerical- and semi-numerical methods 1184.9 Conclusion 119Chapter 5 Reliability-based Topology Optimization Model 1215.1 Introduction 1215.2 Formulation and algorithm for the RBTO model 1225.2.1 Formulation 1225.2.2 Algorithm 1235.2.3 Validation of the RBTO code developed 1255.3 Validation of the RBTO model 1265.3.1 Analytical validation 1265.3.2 Numerical validation 1285.4 Variability of the reliability index 1345.4.1 Example 1: MBB beam 1365.4.2 Example 2: Cantilever beam 1365.4.3 Example 3: Cantilever beam with double loads 1365.4.4 Example 4: Cantilever beam with a transversal hole 1365.5 Numerical applications for the RBTO model 1375.5.1 Static analysis 1385.5.2 Modal analysis 1395.5.3 Fatigue analysis 1415.6 Two points of view for integration of reliability into topology optimization 1425.6.1 Point of view of “topology” 1445.6.2 Point of view of “reliability” 1445.6.3 Numerical applications for the two points of view 1465.7 Conclusion 152Chapter 6 Integration of Reliability and Structural Optimization into Prosthesis Design 1536.1 Introduction 1536.2 Prosthesis design 1546.3 Integration of topology optimization into prosthesis design 1546.3.1 Importance of topology optimization in prosthesis design 1556.3.2 Place of topology optimization in the prosthesis design chain 1566.4 Integration of reliability and structural optimization into hip prosthesis design 1576.4.1 Numerical application of the deterministic approach 1586.4.2 Numerical application of the reliability-based approach 1676.5 Integration of reliability and structural optimization into the design of mini-plate systems used to treat fractured mandibles 1746.5.1 Numerical application of the deterministic approach 1746.5.2 Numerical application of the reliability-based approach 1816.6 Integration of reliability and structural optimization into dental implant design 1846.6.1 Description and modeling of the problem 1846.6.2 Numerical results 1866.7 Conclusion 188Appendices 189Appendix 1 ANSYS Code for Stem Geometry 191Appendix 2 ANSYS Code for Mini-Plate Geometry 197Appendix 3 ANSYS Code for Dental Implant Geometry 201Appendix 4 ANSYS Code for Geometry of Dental Implant with Bone 207Bibliography 213Index 229