Modern Trends in Structural and Solid Mechanics 3

1 Cover

2 Title Page Series Editor Noël Challamel

3 Copyright First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2021 The rights of Noël Challamel, Julius Kaplunov and Izuru Takewaki to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2020952868 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-718-7

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 Problems2.1. 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 Uncertainty3.1. 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 Uncertainty4.1. 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 Structures5.1. 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 Models6.1. 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 Parameters7.1. 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

13 9 Quantum-Inspired Topology Optimization 9.1. Introduction 9.2. General statements 9.3. Topology optimization design model based on quantum-inspired evolutionary algorithms 9.4. A quantum annealing operator to accelerate the calculation and jump out of local extremum 9.5. Numerical examples 9.6. Conclusion 9.7. Acknowledgments 9.8. References

14 10 Time Delay Vibrations and Almost Sure Stability in Vehicle Dynamics 10.1. Introduction to road vehicle dynamics 10.2. Delay resonances of half-car models on road 10.3. Extensions to multi-body vehicles on a random road 10.4. Non-stationary road excitations applying sinusoidal models 10.5. Resonance reduction or induction by means of colored noise 10.6. Lyapunov exponents and rotation numbers in vehicle dynamics 10.7. Concluding remarks and main new results 10.8. References

15 11 Order Statistics Approach to Structural Optimization Considering Robustness and Confidence of Responses 11.1. Introduction 11.2. Overview of order statistics 11.3. Robust design 11.4. Numerical examples 11.5. Conclusion 11.6. References

16 List of Authors

17 Index

18 Summary of Volume 1

19 Summary of Volume 2

20 End User License Agreement

1 Preface: Short Bibliographical Presentation of Prof. Isaac ElishakoffFigure P.1. Prof. Isaac Elishakoff Figure P.2. Elishakoff in middle school in the city of Sukhumi, Georgia Figure P.3. Elishakoff just before acceptance to university. Photo taken in Sukh...Figure P.4. Public PhD defense, Moscow Power Engineering Institute and State Uni...Figure P.5. Elishakoff with Bolotin (middle), member of the Russian Academy of S...Figure P.6. Prof. Elishakoff presenting a book to Prof. J. Singer, Technion’s Pr...Figure P.7. Elishakoff having received the William B. Johnson Inter- Professiona...Figure P.8. Inauguration as the Frank Freimann Visiting Professor of Aerospace a...Figure P.9. Prof. Elishakoff with Prof. Warner Tjardus Koiter, Delft University ...Figure P.10. Elishakoff and his colleagues during the AIAA SDM Conference at Pal...Figure P.11. Elishakoff with his wife, Esther Elisha, M.D., during an ASME award...

2 Chapter 1Figure 1.1. Mitochondria shown undergoing fission/fusion. The respiratory comple...Figure 1.2. Derivation of mitochondrial performance phenomenologically (Chauhan ...Figure 1.3. The schematic diagram of the components and fluxes included in the c...Figure 1.4. Schematic representation of how mitochondria modulate [Ca 2+] Cyt. Ide...Figure 1.5. Mitochondria serve as Ca2+ reservoirs. The minimal values of [Ca2+]E...

3 Chapter 2Figure 2.1. Example 1: statically indeterminate stochastic beam Figure 2.2. Some parametric classes of correlation functions for a Gaussian proc...Figure 2.3. Statically determinate stochastic beams Figure 2.4. Example 1: PDF of the redundant force X: (a) L = 10; (b) L = 20. For...Figure 2.5. Example 1: PDF of the transversal displacement u(|) = L/2: (a) L = 1...Figure 2.6. Example 1: PDF of the transversal displacement for L = 10: (a) | = 0...Figure 2.7. Example 1: PDF of the transversal displacement for L = 20: (a) | = 0...

4 Chapter 3Figure 3.1. Principle of first-order reliability method, original space (left) a...Figure 3.2. Two-dimensional example of a set of data points, their mean vector µ...Figure 3.3. von Mises truss (left) and associated load–displacement curve (right...Figure 3.4. Three-bar truss example Figure 3.5. Compliance over horizontal load Ph for the optimized design using th...Figure 3.6. Design space and load of the tension bar example Figure 3.7. Result of deterministic (left) and robust (right) topology optimizat...Figure 3.8. Design space and load of the cantilever beam example Figure 3.9. Result of deterministic (left) and robust (right) topology optimizat...

5 Chapter 4Figure 4.1. Exploration of the uncertain domain at a place and time. For a color...Figure 4.2. Decision-making modules for creating an object and its life. For a c...Figure 4.3. Designing with uncertainty: using all resources to make the decision...Figure 4.4. An illustration of the concepts – robustness and reliability. For a ...Figure 4.5. Illustration of data robustness (left) and model robustness (right) ...Figure 4.6. Illustration of data reliability (left) and model reliability (right...Figure 4.7. Robust and reliable optimization