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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.