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Table of Contents
1 Cover
4 Preface: Short Bibliographical Presentation of Prof. Isaac Elishakoff
5 1 Optimization in Mitochondrial Energetic Pathways 1.1. Optimization in neural and cell biology 1.2. Mitochondria 1.3. General morphology; fission and fusion 1.4. Mechanical aspects 1.5. Mitochondrial motility 1.6. Cristae, ultrastructure and supercomplexes 1.7. Mitochondrial diseases and neurodegenerative disorders 1.8. Modeling 1.9. Concluding summary 1.10. Acknowledgments 1.11. Appendix 1.12. References
6 2 The Concept of Local and Non-Local Randomness for Some Mechanical Problems 2.1. Introduction 2.2. Preliminary concepts 2.3. Local and non-local randomness 2.4. Conclusion 2.5. References
7 3 On the Applicability of First-Order Approximations for Design Optimization under Uncertainty 3.1. Introduction 3.2. Summary of first- and second-order Taylor series approximations for uncertainty quantification 3.3. Design optimization under uncertainty 3.4. Numerical examples 3.5. Conclusion and outlook 3.6. References
8 4 Understanding Uncertainty 4.1. Introduction 4.2. Uncertainty and uncertainties 4.3. Design and uncertainty 4.4. Knowledge entity 4.5. Robust and reliable engineering 4.6. Conclusion 4.7. References
9 5 New Approach to the Reliability Verification of Aerospace Structures 5.1. Introduction 5.2. Factor of safety and probability of failure 5.3. Reliability verification of aerospace structural systems 5.4. Summary 5.5. References
10 6 A Review of Interval Field Approaches for Uncertainty Quantification in Numerical Models 6.1. Introduction 6.2. Interval finite element analysis 6.3. Convex-set analysis 6.4. Interval field analysis 6.5. Conclusion 6.6. Acknowledgments 6.7. References
11 7 Convex Polytopic Models for the Static Response of Structures with Uncertain-but-bounded Parameters 7.1. Introduction 7.2. Problem statements 7.3. Analysis and solution of the convex polytopic model for the static response of structures 7.4. Vertex solution theorem of the convex polytopic model for the static response of structures 7.5. Review of the vertex solution theorem of the interval model for the static response of structures 7.6. Numerical examples 7.7. Conclusion 7.8. Acknowledgments 7.9. References
12 8 On the Interval Frequency Response of Cracked Beams with Uncertain Damage 8.1. Introduction 8.2. Crack modeling for damaged beams 8.3. Statement of the problem 8.4. Interval frequency response of multi-cracked beams 8.5. Numerical applications 8.6. Concluding remarks 8.7. Acknowledgments 8.8. References