Modern Trends in Structural and Solid Mechanics 3

Nöel Challamel is Professor at the University of Southern Brittany, France. He is the co-author of several books and over a hundred journal papers in the field of mechanics and civil engineering and is on the editorial board of numerous international journals. He is also Editor and Head of the “Solid Mechanics and Mechanical Engineering” series published by ISTE-Wiley.Julius Kaplunov is Professor at Keele University, UK. He is the co-author of over a hundred publications in mechanics, including three books. He is a member of the European Academy of Sciences and sits on the editorial boards of more than ten journals.Izuru Takewaki is Professor of building structures at Kyoto University, Japan, and is the 56th President of the Architectural Institute of Japan. He is the Field Chief Editor of Frontiers in Built Environment and has published over 200 international journal papers.

• Preface xiNoël CHALLAMEL, Julius KAPLUNOV and Izuru TAKEWAKIChapter 1. Optimization in Mitochondrial Energetic Pathways 1Haym BENAROYA1.1. Optimization in neural and cell biology 11.2. Mitochondria 31.3. General morphology; fission and fusion 51.4. Mechanical aspects 91.5. Mitochondrial motility 131.6. Cristae, ultrastructure and supercomplexes 141.7. Mitochondrial diseases and neurodegenerative disorders 151.8. Modeling 161.9. Concluding summary 171.10. Acknowledgments 181.11. Appendix 181.12. References 19Chapter 2. The Concept of Local and Non-Local Randomness for Some Mechanical Problems 23Giovanni FALSONE and Rossella LAUDANI2.1. Introduction 232.2. Preliminary concepts 242.2.1. Statically determinate stochastic beams 242.2.2. Statically indeterminate stochastic beams 262.3. Local and non-local randomness 292.3.1. Statically determinate stochastic beams 312.3.2. Statically indeterminate stochastic beams 322.3.3. Comments on the results 362.4. Conclusion 362.5. References 37Chapter 3. On the Applicability of First-Order Approximations for Design Optimization under Uncertainty 39Benedikt KRIEGESMANN3.1. Introduction 393.2. Summary of first- and second-order Taylor series approximations for uncertainty quantification 413.2.1. Approximations of stochastic moments 423.2.2. Probabilistic lower bound approximation 433.2.3. Convex anti-optimization 443.2.4. Correlation of probabilistic approaches and convex anti-optimization 453.3. Design optimization under uncertainty 463.3.1. Robust design optimization 463.3.2. Reliability-based design optimization 473.3.3. Optimization with convex anti-optimization 483.4. Numerical examples 483.4.1. Imperfect von Mises truss analysis 483.4.2. Three-bar truss optimization 503.4.3. Topology optimization 523.5. Conclusion and outlook 563.6. References 57Chapter 4. Understanding Uncertainty 61Maurice LEMAIRE4.1. Introduction 614.2. Uncertainty and uncertainties 614.3. Design and uncertainty 634.3.1. Decision modules 634.3.2. Designing in uncertain 664.4. Knowledge entity 674.4.1. Structure of a knowledge entity 674.5. Robust and reliable engineering 704.5.1. Definitions 704.5.2. Robustness 714.5.3. Reliability 724.5.4. Optimization 724.5.5. Reliable and robust optimization 734.6. Conclusion 744.7. References 75Chapter 5. New Approach to the Reliability Verification of Aerospace Structures 77Giora MAYMON5.1. Introduction 775.2. Factor of safety and probability of failure 785.3. Reliability verification of aerospace structural systems 845.3.1. Reliability demonstration is integrated into the design process 865.3.2. Analysis of failure mechanism and failure modes 875.3.3. Modeling the structural behavior, verifying the model by tests 875.3.4. Design of structural development tests to surface failure modes 885.3.5. Design of development tests to find unpredicted failure modes 885.3.6. “Cleaning” failure mechanism and failure modes 885.3.7. Determination of required safety and confidence in models 895.3.8. Determination of the reliability by “orders of magnitude” 895.4. Summary 925.5. References 93Chapter 6. A Review of Interval Field Approaches for Uncertainty Quantification in Numerical Models 95Matthias FAES, Maurice IMHOLZ, Dirk VANDEPITTE and David MOENS6.1. Introduction 956.2. Interval finite element analysis 976.3. Convex-set analysis 996.4. Interval field analysis 1006.4.1. Explicit interval field formulation 1016.4.2. Interval fields based on KL expansion 1036.4.3. Interval fields based on convex descriptors 1056.5. Conclusion 1056.6. Acknowledgments 1066.7. References 106Chapter 7. Convex Polytopic Models for the Static Response of Structures with Uncertain-but-bounded Parameters 111Zhiping QIU and Nan JIANG7.1. Introduction 1117.2. Problem statements 1147.3. Analysis and solution of the convex polytopic model for the static response of structures 1167.4. Vertex solution theorem of the convex polytopic model for the static response of structures 1197.5. Review of the vertex solution theorem of the interval model for the static response of structures 1227.6. Numerical examples 1277.6.1. Two-step bar 1277.6.2. Ten-bar truss 1307.6.3. Plane frame 1357.7. Conclusion 1417.8. Acknowledgments 1417.9. References 141Chapter 8. On the Interval Frequency Response of Cracked Beams with Uncertain Damage 145Roberta SANTORO8.1. Introduction 1468.2. Crack modeling for damaged beams 1488.2.1. Finite element crack model 1488.2.2. Continuous crack model 1498.3. Statement of the problem 1508.3.1. Interval model for the uncertain crack depth 1518.3.2. Governing equations of damaged beams 1528.3.3. Finite element model versus continuous model 1548.4. Interval frequency response of multi-cracked beams 1628.4.1. Interval deflection function in the FE model 1628.4.2. Interval deflection function in the continuous model 1658.5. Numerical applications 1678.6. Concluding remarks 1738.7. Acknowledgments 1738.8. References 173Chapter 9. Quantum-Inspired Topology Optimization 177Xiaojun WANG, Bowen NI and Lei WANG9.1. Introduction 1779.2. General statements 1809.2.1. Density-based continuum structural topology optimization formulation 1809.2.2. Characteristics of quantum computing 1819.3. Topology optimization design model based on quantum-inspired evolutionary algorithms 1839.3.1. Classic procedure of topology optimization based on the SIMP method and optimality criteria 1839.3.2. The fundamental theory of a quantum-inspired evolutionary algorithm – DCQGA 1869.3.3. Implementation of the integral topology optimization framework 1899.4. A quantum annealing operator to accelerate the calculation and jump out  of local extremum 1919.5. Numerical examples 1959.5.1. Example of a short cantilever 1959.5.2. Example of a wing rib 1969.6. Conclusion 1989.7. Acknowledgments 1989.8. References 199Chapter 10. Time Delay Vibrations and Almost Sure Stability in Vehicle Dynamics 203Walter V. WEDIG10.1. Introduction to road vehicle dynamics 20310.2. Delay resonances of half-car models on road 20510.3. Extensions to multi-body vehicles on a random road 20910.4. Non-stationary road excitations applying sinusoidal models 21210.5. Resonance reduction or induction by means of colored noise 21510.6. Lyapunov exponents and rotation numbers in vehicle dynamics 21810.7. Concluding remarks and main new results 22110.8. References 222Chapter 11. Order Statistics Approach to Structural Optimization Considering Robustness and Confidence of Responses 225Makoto YAMAKAWA and Makoto OHSAKI11.1. Introduction 22511.2. Overview of order statistics 22611.2.1. Definition of order statistics 22611.2.2. Tolerance intervals and confidence intervals of quantiles 22711.3. Robust design 22911.3.1. Overview of the robust design problem 22911.3.2. Worst-case-based method 23011.3.3. Order statistics-based method 23011.4. Numerical examples 23111.4.1. Design response spectrum 23111.4.2. Optimization of the building frame considering seismic responses 23211.4.3. Multi-objective optimization considering robustness 23611.5. Conclusion 23911.6. References 240List of Authors 243Index 245Summaries of Volumes 1 and 2 249