Modern Trends in Structural and Solid Mechanics 3 E-Book
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This book comprised of three separate volumes presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This third volume is devoted to non-deterministic mechanics. Modern Trends in Structural and Solid Mechanics 3 has broad scope, covering topics such: design optimization under uncertainty, interval field approaches, convex analysis, quantum inspired topology optimization and stochastic dynamics. The book is illustrated by many applications in the field of aerospace engineering, mechanical engineering, civil engineering, biomedical engineering and automotive engineering. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.
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Seitenzahl: 398
Veröffentlichungsjahr: 2021
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Table of Contents
Cover
Title Page
Copyright
Preface: Short Bibliographical Presentation of Prof. Isaac Elishakoff
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
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
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
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
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
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
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
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
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
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
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
List of Authors
Index
Summary of Volume 1
Summary of Volume 2
End User License Agreement
Guide
Cover
Table of Contents
Title Page
Copyright
Preface: Short Bibliographical Presentation of Prof. Isaac Elishakoff
Begin Reading
List of Authors
Index
Summary of Volume 1
Summary of Volume 2
Other titles from ISTE in Mechanical Engineering and Solid Mechanics
End User License Agreement
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Series Editor
Noël Challamel
Modern Trends in Structural and Solid Mechanics 3
Non-deterministic Mechanics
Edited by
Noël Challamel
Julius Kaplunov
Izuru Takewaki
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 Ltd27-37 St George’s RoadLondon SW19 4EUUK
www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2021The 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
PrefaceShort Bibliographical Presentation of Prof. Isaac Elishakoff
This book is dedicated to Prof. Isaac Elishakoff by his colleagues, friends and former students, on the occasion of his seventy-fifth birthday.
Figure P.1.Prof. Isaac Elishakoff
Prof. Isaac Elishakoff is an international leading authority across a broad area of structural mechanics, including dynamics and stability, optimization and antioptimization, probabilistic methods, analysis of structures with uncertainty, refined theories, functionally graded material structures, and nanostructures. He was born in Kutaisi, Republic of Georgia, on February 9, 1944.
Figure P.2.Elishakoff in middle school in the city of Sukhumi, Georgia
Elishakoff holds a PhD in Dynamics and Strength of Machines from the Power Engineering Institute and Technical University in Moscow, Russia (Figure P.4 depicts the PhD defense of Prof. Isaac Elishakoff).
Figure P.3.Elishakoff just before acceptance to university. Photo taken in Sukhumi, Georgia
Figure P.4.Public PhD defense, Moscow Power Engineering Institute and State University; topic “Vibrational and Acoustical Fields in the Circular Cylindrical Shells Excited by Random Loadings”, and dedicated to the evaluation of noise levels in TU-144 supersonic aircraft
His supervisor was Prof. V. V. Bolotin (1926–2008), a member of the Russian Academy of Sciences (Figure P.5 shows Elishakoff with Bolotin some years later).
Figure P.5.Elishakoff with Bolotin (middle), member of the Russian Academy of Sciences, and Prof. Yukweng (Mike) Lin (left), member of the US National Academy of Engineering. Photo taken at Florida Atlantic University during a visit from Bolotin
Currently, Elishakoff is a Distinguished Research Professor in the Department of Ocean and Mechanical Engineering at Florida Atlantic University. Before joining the university, he taught for one year at Abkhazian University, Sukhumi in the Republic of Georgia, and 18 years at the Technion – Israel Institute of Technology in Haifa, where he became the youngest full professor at the time of his promotion (Figure P.6 shows Elishakoff presenting a book to Prof. Josef Singer, Technion’s former president).
Figure P.6.Prof. Elishakoff presenting a book to Prof. J. Singer, Technion’s President; right: Prof. A. Libai, Aerospace Engineering Department, Technion
Elishakoff has lectured at about 200 meetings and seminars, including about 60 invited, plenary or keynote lectures, across Europe, North and South America, the Middle East and the Far East.
Prof. Elishakoff has made vital and outstanding contributions in a number of areas in structural mechanics. In particular, he has analyzed random vibrations of homogeneous and composite beams, plates and shells, with special emphasis on the effects of refinements in structural theories and cross-correlations. Free structural vibrations have been tackled using a non-trivial generalization of Bolotin’s dynamic edge effect method. Nonlinear buckling has been investigated using a novel method, incorporating experimental analysis of imperfections. As a result, the fundamental concept of closing the gap – spanning the entire 20th century – between theory and practice in imperfection-sensitive structures has been proposed. Novel methods of evaluating structural reliability have been proposed, taking into account the error associated with various low-order approximations, as well as human error; innovative generalization of the stochastic linearization method has been advanced. A non-probabilistic theory for treating uncertainty in structural mechanics has been established. Dynamic stability of elastic and viscoelastic structures with imperfections has been studied. An improved, non-perturbative stochastic finite element method for structures has been developed. The list of Elishakoff’s remarkable research achievements goes on.
His research has been acknowledged by many awards and prizes. He is a member of the European Academy of Sciences and Arts, a Fellow of the American Academy of Mechanics and ASME, and a Foreign Member of the Georgian National Academy of Sciences. Elishakoff is also a recipient of the Bathsheva de Rothschild prize (1973) and the Worcester Reed Warner Medal of the American Society of Mechanical Engineers (2016).
Figure P.7.Elishakoff having received the William B. Johnson Inter- Professional Founders Award
Elishakoff is directly involved in numerous editorial activities. He serves as the book review editor of the “Journal of Shock and Vibration” and is currently, or has previously been an associate editor of the International Journal of Mechanics of Machines and Structures, Applied Mechanics Reviews, and Chaos, Solitons & Fractals. In addition, he is or has been on the editorial boards of numerous journals, for example Journal of Sound and Vibration, International Journal of Structural Stability and Dynamics, International Applied Mechanics and Computers & Structures. He also acts as a book series editor for Elsevier, Springer and Wiley.
Figure P.8.Inauguration as the Frank Freimann Visiting Professor of Aerospace and Mechanical Engineering; left: Rev. Theodore M. Hesburgh, President of the University of Notre Dame; right: Prof. Timothy O’Meara, Provost
Prof. Elishakoff has held prestigious visiting positions at top universities all over the world. Among them are Stanford University (S. P. Timoshenko Scholar); University of Notre Dame, USA (Frank M. Freimann Chair Professorship of Aerospace and Mechanical Engineering and Henry J. Massman, Jr. Chair Professorship of Civil Engineering); University of Palermo, Italy (Visiting Castigliano Distinguished Professor); Delft University of Technology, Netherlands (multiple appointments, including the W. T. Koiter Chair Professorship of the Mechanical Engineering Department – see Figure P.9); Universities of Tokyo and Kyoto, Japan (Fellow of the Japan Society for the Promotion of Science); Beijing University of Aeronautics and Astronautics, People’s Republic of China (Visiting Eminent Scholar); Technion, Haifa, Israel (Visiting Distinguished Professor); University of Southampton, UK (Distinguished Visiting Fellow of the Royal Academy of Engineering).
Figure P.9.Prof. Elishakoff with Prof. Warner Tjardus Koiter, Delft University of Technology (center), and Dr. V. Grishchak, of Ukraine (right)
Figure P.10.Elishakoff and his colleagues during the AIAA SDM Conference at Palm Springs, California in 2004; Standing, from right to left, are Prof. Elishakoff, the late Prof. Josef Singer and Dr. Giora Maymon of RAFAEL. Sitting is the late Prof. Avinoam Libai
Elishakoff has made a substantial contribution to conference organization. In particular, he participated in the organization of the Euro-Mech Colloquium on “Refined Dynamical Theories of Beams, Plates and Shells, and Their Applications” in Kassel, Germany (1986); the Second International Conference on Stochastic Structural Dynamics, in Boca Raton, USA (1990); “International Conference on Uncertain Structures” in Miami, USA and Western Caribbean (1996). He also coordinated four special courses at the International Centre for Mechanical Sciences (CISM), in Udine, Italy (1997, 2001, 2005, 2011).
Prof. Elishakoff has published over 540 original papers in leading journals and conference proceedings. He championed authoring, co-authoring or editing of 31 influential and extremely well-received books and edited volumes.
Here follows some praise of his work and books:
– “It was not until 1979, when Elishakoff published his reliability study … that a method has been proposed, which made it possible to introduce the results of imperfection surveys … into the analysis …” (Prof. Johann Arbocz, Delft University of Technology, The Netherlands,
Zeitschrift für Flugwissenschaften und Weltraumforschung
).
– “He has achieved world renown … His research is characterized by its originality and a combination of mathematical maturity and physical understanding which is reminiscent of von Kármán …” (Prof. Charles W. Bert, University of Oklahoma).
– “It is clear that Elishakoff is a world leader in his field … His outstanding reputation is very well deserved …” (Prof. Bernard Budiansky, Harvard University).
– “Professor Isaac Elishakoff … is subject-wise very much an all-round vibrationalist” (P. E. Doak, Editor in Chief,
Journal of Sound and Vibration
, University of Southampton, UK).
– “This is a beautiful book …” (Dr. Stephen H. Crandall, Ford Professor of Engineering, M.I.T.).
– “Das Buch ist in seiner Aufmachunghervorragendgestaltet und kannalsäusserstwertvolleErganzung … wäzmstensempfohlenwerden …” [The book’s appearance is perfectly designed and can be highly recommended as a valuable addition.] (Prof. Horst Försching, Institute of Aeroelasticity, Federal Republic of Germany,
Zeitschrift für Flugwissenschaften und Weltraumforschung
).
– “Because of you, Notre Dame is an even better place, a more distinguished University” (Prof. Rev. Theodore M. Hesburgh, President, University of Notre Dame).
– “It is an impressive volume …” (Prof. Warner T. Koiter, Delft University of Technology, The Netherlands).
– “This extremely well-written text, authored by one of the leaders in the field, incorporates many of these new applications … Professor Elishakoff’s techniques for developing the material are accomplished in a way that illustrates his deep insight into the topic as well as his expertise as an educator … Clearly, the second half of the text provides the basis for an excellent graduate course in random vibrations and buckling … Professor Elishakoff has presented us with an outstanding instrument for teaching” (Prof. Frank Kozin, Polytechnic Institute of New York,
American Institute of Aeronautics and Astronautics Journal
).
– “By far the best book on the market today …” (Prof. Niels C. Lind, University of Waterloo, Canada).
– “The book develops a novel idea … Elegant, exhaustive discussion … The study can be an inspiration for further research, and provides excellent applications in design …” (Prof. G. A. Nariboli,
Applied Mechanics Reviews
).
– “This volume is regarded as an advanced encyclopedia on random vibration and serves aeronautical, civil and mechanical engineers …” (Prof. Rauf Ibrahim, Wayne State University,
Shock and Vibration Digest
).
– “The book deals with a fundamental problem in Applied Mechanics and in Engineering Sciences: How the uncertainties of the data of a problem influence its solution. The authors follow a novel approach for the treatment of these problems … The book is written with clarity and contains original and important results for the engineering sciences …” (Prof. P. D. Panagiotopoulos, University of Thessaloniki, Greece and University of Aachen, Germany,
SIAM Review
).
– “The content should be of great interest to all engineers involved with vibration problems, placing the book well and truly in the category of an essential reference book …” (Prof. I. Pole,
Journal of the British Society for Strain Measurement
).
– “A good book; a different book … It is hoped that the success of this book will encourage the author to provide a sequel in due course …” (Prof. John D. Robson, University of Glasgow, Scotland, UK,
Journal of Sound and Vibration
).
– “The book certainly satisfies the need that now exists for a readable textbook and reference book …” (Prof. Masanobu Shinozuka, Columbia University).
– “[the] author ties together reliability, random vibration and random buckling … Well written … useful book …” (Dr. H. Saunders,
Shock and Vibration Digest
).
– “A very useful text that includes a broad spectrum of theory and application” (
Mechanical Vibration
, Prof. Haym Benaroya, Rutgers University).
– “A treatise on random vibration and buckling … The reviewer wishes to compliment the author for the completion of a difficult task in preparing this book on a subject matter, which is still developing on many fronts …” (Prof. James T. P. Yao, Texas A&M University,
Journal of Applied Mechanics
).
– “It seems to me a hard work with great result …” (Prof. Hans G. Natke, University of Hannover, Federal Republic of Germany).
– “The approach is novel and could dominate the future practice of engineering” (
The Structural Engineer
).
– “An excellent presentation … well written … all readers, students, and certainly reviewers should read this preface for its excellent presentation of the philosophy and raison d’être for this book. It is well written, with the material presented in an informational fashion as well as to raise questions related to unresolved … challenges; in the vernacular of film critics, ‘thumbs up’” (Dr. R. L. Sierakowski, U.S. Air Force Research Laboratory,
AIAA Journal
).
– “This substantial and attractive volume is a well-organized and superbly written one that should be warmly welcomed by both theorists and practitioners … Prof. Elishakoff, Li, and Starnes, Jr. have given us a jewel of a book, one done with care and understanding of a complex and essential subject and one that seems to have ably filled a gap existing in the present-day literature and practice” (
Current Engineering Practice
).
– “Most of the subjects covered in this outstanding book have never been discussed exclusively in the existing treatises … (
Ocean Engineering
).
– “The treatment is scholarly, having about 900 items in the bibliography and additional contributors in the writing of almost every chapter … This reviewer believes that
Non-Classical Problems in the Theory of Elastic Stability
should be a useful reference for researchers, engineers, and graduate students in aeronautical, mechanical, civil, nuclear, and marine engineering, and in applied mechanics” (
Applied Mechanics Reviews
).
– “What more can be said about this monumental work, other than to express admiration? … The study is of great academic interest, and is clearly a labor of love. The author is to be congratulated on this work …” (Prof. H. D. Conway, Department of Theoretical and Applied Mechanics, Cornell University).
– “This book … is prepared by Isaac Elishakoff, one of the eminent solid mechanics experts of the 20th century and the present one, and his distinguished coauthors, will be of enormous use to researchers, graduate students and professionals in the fields of ocean, naval, aerospace and mechanical engineers as well as other fields” (Prof. Patricio A. A. Laura, Prof. Carlos A. Rossit, Prof. Diana V. Bambill, Universidad Nacional del Sur, Argentina,
Ocean Engineering
).
– “This book is an outstanding research monograph … extremely well written, informative, highly original … great scholarly contribution …. There is no comparable book discussing the combination of optimization and anti-optimization … magnificent monograph …. This book, which certainly is written with love and passion, is the first of its kind in applied mechanics literature, and has the potential of having a revolutionary impact on both uncertainty analysis and optimization” (Prof. Izuru Takewaki, Kyoto University,
Engineering Structures
).
– “This book is a collection of a surprisingly large number of closed form solutions, by the author and by others, involving the buckling of columns and beams, and the vibration of rods, beams and circular plates. The structures are, in general, inhomogeneous. Many solutions are published here for the first time. The text starts with an instructive review of direct, semi-inverse, and inverse eigenvalue problems. Unusual closed form solutions of column buckling are presented first, followed by closed form solutions of the vibrations of rods. Unusual closed form solutions for vibrating beams follow. The influence of boundary conditions on eigenvalues is discussed. An entire chapter is devoted to boundary conditions involving guided ends. Effects of axial loads and of elastic foundations are presented in two separate chapters. The closed form solutions of circular plates concentrate on axisymmetric vibrations. The scholarly effort that produced this book is remarkable” (Prof. Werner Soedel, then Editor-in-Chief of
Journal Sound and Vibration
).
– “The field has been brilliantly presented in book form …” (Prof. Luis A. Godoy
et al
., Institute of Advanced Studies in Engineering and Technology, Science Research Council of Argentina and National University of Cordoba, Argentina,
Thin-Walled Structures
).
– “Elishakoff is one of the pioneers in the use of the probabilistic approach for studying imperfection-sensitive structures” (Prof. Chiara Bisagni and Dr. Michela Alfano, Delft University of Technology;
AIAA Journal
).
– “Recently, Elishakoff
et al
. presented an excellent literature review on the historical development of Timoshenko’s beam theory” (Prof. Zhenlei Chen
et al
.,
Journal of Building Engineering
).
Professor Isaac Elishakoff is the author or co-author of an impressive list of seminal books in the field of deterministic and non-deterministic mechanics, presented below.
Books by Elishakoff
Ben-Haim, Y. and Elishakoff, I. (1990). Convex Models of Uncertainty in Applied Mechanics. Elsevier, Amsterdam.
Cederbaum, G., Elishakoff, I., Aboudi, J., Librescu, L. (n.d.). Random Vibration and Reliability of Composite Structures. Technomic, Lancaster.
Elishakoff, I. (1983). Probabilistic Methods in the Theory of Structures. Wiley, New York.
Elishakoff, I. (1999). Probabilistic Theory of Structures. Dover Publications, New York.
Elishakoff, I. (2004). Safety Factors and Reliability: Friends or Foes? Kluwer Academic Publishers, Dordrecht.
Elishakoff, I. (2005). Eigenvalues of Inhomogeneous Structures: Unusual Closed-Form Solutions of Semi-Inverse Problems. CRC Press, Boca Raton.
Elishakoff, I. (2014). Resolution of the Twentieth Century Conundrum in Elastic Stability. World Scientific/Imperial College Press, Singapore.
Elishakoff, I. (2017). Probabilistic Methods in the Theory of Structures: Random Strength of Materials, Random Vibration, and Buckling. World Scientific, Singapore.
Elishakoff, I. (2018). Probabilistic Methods in the Theory of Structures: Solution Manual to Accompany Probabilistic Methods in the Theory of Structures: Problems with Complete, Worked Through Solutions. World Scientific, Singapore.
Elishakoff, I. (2020). Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells. Springer Nature, Switzerland.
Elishakoff, I. (2020). Handbook on Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories. World Scientific, Singapore.
Elishakoff, I. and Ohsaki, M. (2010). Optimization and Anti-Optimization of Structures under Uncertainty. Imperial College Press, London.
Elishakoff, I. and Ren, Y. (2003). Finite Element Methods for Structures with Large Stochastic Variations. Oxford University Press, Oxford.
Elishakoff, I., Lin, Y.K., Zhu, L.P. (1994). Probabilistic and Convex Modeling of Acoustically Excited Structures. Elsevier, Amsterdam.
Elishakoff, I., Li, Y., Starnes Jr., J.H. (2001). Non-Classical Problems in the Theory of Elastic Stability. Cambridge University Press, Cambridge.
Elishakoff, I., Pentaras, D., Dujat, K., Versaci, C., Muscolino, G., Storch, J., Bucas, S., Challamel, N., Natsuki, T., Zhang, Y., Ming Wang, C., Ghyselinck, G. (2012). Carbon Nanotubes and Nano Sensors: Vibrations, Buckling, and Ballistic Impact. ISTE Ltd, London, and John Wiley & Sons, New York.
Elishakoff, I., Pentaras, D., Gentilini, C., Cristina, G. (2015). Mechanics of Functionally Graded Material Structures. World Scientific/Imperial College Press, Singapore.
Books edited or co-edited by Elishakoff
Ariaratnam, S.T., Schuëller, G.I., Elishakoff, I. (1988). Stochastic Structural Dynamics – Progress in Theory and Applications. Elsevier, London.
Casciati, F., Elishakoff, I., Roberts, J.B. (1990). Nonlinear Structural Systems under Random Conditions. Elsevier, Amsterdam.
Chuh, M., Wolfe, H.F., Elishakoff, I. (1989). Vibration and Behavior of Composite Structures. ASME Press, New York.
David, H. and Elishakoff, I. (1990). Impact and Buckling of Structures. ASME Press, New York.
Elishakoff, I. (1999). Whys and Hows in Uncertainty Modeling. Springer, Vienna.
Elishakoff, I. (2007). Mechanical Vibration: Where Do We Stand? Springer, Vienna.
Elishakoff, I. and Horst, I. (1987). Refined Dynamical Theories of Beams, Plates and Shells and Their Applications. Springer Verlag, Berlin.
Elishakoff, I. and Lin, Y.K. (1991). Stochastic Structural Dynamics 2 – New Applications. Springer, Berlin.
Elishakoff, I. and Lyon, R.H. (1986), Random Vibration-Status and Recent Developments. Elsevier, Amsterdam.
Elishakoff, I. and Seyranian, A.P. (2002). Modern Problems of Structural Stability. Springer, Vienna.
Elishakoff, I. and Soize, C. (2012). Non-Deterministic Mechanics. Springer, Vienna.
Elishakoff, I., Arbocz, J., Babcock Jr., C.D., Libai, A. (1988). Buckling of Structures: Theory and Experiment. Elsevier, Amsterdam.
Lin, Y.K. and Elishakoff, I. (1991). Stochastic Structural Dynamics 1 – New Theoretical Developments. Springer, Berlin.
Noor, A.K., Elishakoff, I., Hulbert, G. (1990). Symbolic Computations and Their Impact on Mechanics. ASME Press, New York.
Figure P.11.Elishakoff with his wife, Esther Elisha, M.D., during an ASME awards ceremony
On behalf of all the authors of this book, including those friends who were unable to contribute, we wish Prof. Isaac Elishakoff many more decades of fruitful works and collaborations for the benefit of world mechanics, in particular.
Modern Trends in Structural and Solid Mechanics 1 – the first of three separate volumes that comprise this book – presents recent developments and research discoveries in structural and solid mechanics, with a focus on the statics and stability of solid and structural members.
The book is centered around theoretical analysis and numerical phenomena and has broad scope, covering topics such as: buckling of discrete systems (elastic chains, lattices with short and long range interactions, and discrete arches), buckling of continuous structural elements including beams, arches and plates, static investigation of composite plates, exact solutions of plate problems, elastic and inelastic buckling, dynamic buckling under impulsive loading, buckling and post-buckling investigations, buckling of conservative and non-conservative systems, buckling of micro and macro-systems. The engineering applications concern both small-scale phenomena with micro and nano-buckling up to large-scale structures, including the buckling of drillstring systems.
Each of the three volumes is intended for graduate students and researchers in the field of theoretical and applied mechanics.
Prof. Noël CHALLAMEL
Lorient, France
Prof. Julius KAPLUNOV
Keele, UK
Prof. Izuru TAKEWAKI
Kyoto, Japan
February 2021
For a color version of all the figures in this chapter, see
www.iste.co.uk/challamel/mechanics3.zip
.
1Optimization in Mitochondrial Energetic Pathways
1.1. Optimization in neural and cell biology
Neuronal networks and their countless pathways, as well as their companion cells, the glia, are the foundation of our functioning brain. These neurons and glia send signals to each other and process information in tremendously complex ways, which we are only beginning to have some understanding of. How pathway choices in neurons lead to physiological or pathological responses are of critical interest. What causes one progression path to be followed rather than another? Are there underlying principles, for example, an optimization of energy or time, a minimization of materials or some other underlying rules and characteristics?
Each neuron cell is composed of numerous organelles and other components, each with their own function, all of which communicate intracellularly and respond as a team to the needs of the cell, as well as to extracellular signals. One of those organelles is the mitochondria. It is well established that the connections between energetics and mitochondria – the organelle responsible for almost all of the energy production in the cell – determine whether physiological or pathological pathways are taken at all levels: subcellular, cellular, tissue and organism. Dysfunction in the mechanisms of energy production appears to be at the center of neurological and neuropsychiatric pathologies. Thus, the profound interest is in understanding how these organelles function and govern their operations. One example of dysfunction is how secondary pathologies in traumatic brain injuries result from energetic dysfunction.
Neurons and glia are the components of brain function, but energy homeostasis must be maintained in order to assure proper functioning, and begins within the subcellular organelle, the mitochondria. This homeostasis is the product of metabolic reactions that are coupled to energy demands in space and time throughout the brain, and are regulated by feedforward and feedback mechanisms. Any mismatch between supply and demand over significant time intervals invariably initiates cascades of dysfunction leading to well-known neurodegenerative and neuropsychiatric pathologies.
These mechanisms, at all scales, “choose” from numerous progression paths, some of which lead to dysfunction due, in large part, to ineffective energy production. Understanding how these “choices” are made requires us to formulate models of the mechanisms alluded to above. If there are governing optimal “choices” or mechanisms, then dysfunction and defects may also sometimes be optimal choices for the organism, and perhaps the optimizations are energy-dependent given the criticality of energy production and usage. Perhaps, optimal choices can lead to negative outcomes. Given the multiple constraints for a successful living organism, there may only be local sub-optimizations. Thus, when we refer to optimization, we are having the above discussion, about how we frame the multitude of progression paths within the cell and external to it. Evolution governed which organisms survived, and which did not, based on their fitness for the environment. At the cellular level, this may entail a minimization of energy use, or perhaps the quickest transfer of information between two neurons.
Understanding these optimality decisions can provide clues for clinical interventions and eventually, cures for some of humanity’s most serious neurodegenerative diseases. Optimal pathways may be identified via the multitude of techniques that have been developed for the physical sciences and engineering, taking the morphological (and mechanical), biochemical and metabolic constraints into account. Constraints such as signaling mechanisms at all scales, cell and organelle morphology, feedback mechanisms, and imbalances of energetics and other intermediate products of mitochondrial functioning are part of a possible formulation. The community is at the beginning of formulating such models. This overview aims to pull together a very brief summary of current thoughts and evidence that, at least for the mitochondrial organelle at the subcellular level, the responses are evolutionarily conserved local and global optimizations.
In the following sections, we discuss some of the key functions of the mitochondria and identify, or suggest how these appear to be evolutionarily conserved properties that are based on an optimization. While optimization in biology has been discussed for decades, the application of optimization methodologies to such systems has been slow to develop, in part due to an incomplete understanding of significant aspects of functioning and an incomplete dataset.
We also refer to the work of Elishakoff (e.g. 1994, 2003, and with Qiu 2001). Elishakoff developed the concept of anti-optimization, where system uncertainties are studied by combining conventional optimization methods with interval analysis. In this approach, the optimal solution is a domain, rather than a point and is a two-level process. At one level, the optimal values of system parameters are obtained, and at the other level, uncertainties are anti-optimized. The anti-optimization yields the least favorable and most favorable system response and relies on knowledge of the bounds of uncertainty, rather than probability density functions. Such an approach can be potentially useful in biological systems where data can be sparse, with uncertainties only known via the upper and lower bounds.
1.2. Mitochondria
Our brief overview is about the very exciting area of the intense biological research of the mitochondria, an intracellular organelle. The mitochondria’s primary functions include the maintenance of energy homeostasis, cell integrity and survival (Simcox and Reeve 2016). The mitochondria variably comprise between about 20% of the cell, up to most of the cell volume, dynamically depending on the energetic needs of the cell. In the aggregate, mitochondria account for about 10% of body weight, attesting to their importance. These organelles produce up to 95% of a eukaryotic cell’s energy through oxidative phosphorylation (Tzameli 2012), driven by an electrochemical proton gradient created by the respiratory chain housed within the mitochondria’s inner membrane. Oxidative phosphorylation is the metabolic pathway in the mitochondrial matrix containing the cristae, where enzymes oxidize nutrients. Energy is released, producing adenosine triphosphate (ATP), a complex organic chemical that provides energy for many cellular processes. The human body consumes, on average, a quantity of ATP per day that approximates its body weight (Zick and Reichert 2011).
Eukaryotes are organisms with cells that have a nucleus enclosed within membranes, unlike prokaryotes (bacteria and archaea). Eukaryotes may also be multicellular and consist of many cell types.
The cristae are tight folds of the inner membrane studded with proteins, with the folds providing a significant increase in surface area (much in the same way as the folded cerebral cortex), over which the above energy-producing processes can occur. Cristae biogenesis, regulated through the large enzyme ATP synthase, closely links mitochondrial morphology to energy demand (Simcox and Reeve 2016).
Mitochondrial functions also include quality control through fission (division) and fusion (merging), iron–sulfur cluster formation, calcium handling, cell signaling, cell repair and maintenance, and reactive oxygen species (ROS) production (Simcox and Reeve 2016). ROS emission is harmful to the mitochondrial DNA, which is a byproduct of energy production (Kembro et al. 2013) and is at least partially eliminated. As part of their metabolic functions, mitochondria also perform critical programmed cell death functions called apoptosis (Vakifahmetoglu-Norberg et al. 2017), which are related to the function of fission. Figure 1.1 summarizes some of these functions.
Figure 1.1.Mitochondria shown undergoing fission/fusion. The respiratory complexes are shown, identified using roman numerals. Various mechanisms are also shown, including signaling, Ca2+ transport across the membrane, and others outside of our current scope (Vakifahmetoglu-Norberg et al. 2017, with permission). For a color version of this figure, see www.iste.co.uk/challamel/mechanics3.zip
Mitochondria are believed to be the reason why complex cellular beings evolved from single celled entities. They originated as individual cell bacteria, but eventually integrated with our ancestral cells, leading to the current eukaryotic cells with nuclei. This ancestry partially explains why mitochondria, to this day, contain mtDNA, remnants of their own DNA.
The goal of this chapter is to refer to aspects of mitochondrial behavior that appear to be governed by optimization principles, which are constrained by biological limitations. It is reasonable to assume that the mathematical machinery of optimization can be useful in modeling some of these processes. Also, given that there are numerous mechanistic determinants of cell and intracellular functioning, we believe that these can be modeled using some of the principles of mechanics that govern engineered systems, as well as the frequently observed feedback and feedforward mechanisms that coordinate the multitude of processes within cells. Of course, biological systems are significantly more complex and require considerably more experimentation in order to ascertain behavior. We suggest the ideas herein with humility. A more detailed review of some of these ideas is available (Benaroya 2020), where the links between mitochondria, cellular energy production and the coupling of these to diseases and the body’s response to injury are discussed.
1.3. General morphology; fission and fusion
Mitochondria exist in varying numbers, dependent on cell type, and sometimes form intracellular networks of interconnecting organelles called a reticulum, extending throughout the cytosol and in close contact with the nucleus, the endoplasmic reticulum, the Golgi network and the cytoskeleton (Benard et al
