Modern Trends in Structural and Solid Mechanics 1

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: 2020952688 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-714-9

4 Preface: Short Bibliographical Presentation of Prof. Isaac Elishakoff

5 1 Static Deformations of Fiber-Reinforced Composite Laminates by the Least-Squares Method 1.1. Introduction 1.2. Formulation of the problem 1.3. Results and discussion 1.4. Remarks 1.5. Conclusion 1.6. Acknowledgments 1.7. References

6 2 Stability of Laterally Compressed Elastic Chains2.1. Introduction 2.2. Compression of stacked elastic sheets 2.3. Stability of an elastically coupled cyclic chain 2.4. Elastic stability of two coupled rods with disorder 2.5. Spatial localization of lateral buckling in a disordered chain of elastically coupled rigid rods 2.6. Conclusion 2.7. References

7 3 Analysis of a Beck’s Column over Fractional-Order Restraints via Extended Routh–Hurwitz Theorem3.1. Introduction 3.2. Material hereditariness 3.3. Dynamic equilibrium of an elastic cantilever over a fractional-order foundation 3.4. Stability analysis of Beck’s column over fractional-order hereditary foundation 3.5. Numerical application 3.6. Conclusion 3.7. References

8 4 Localization in the Static Response of Higher-Order Lattices with Long-Range Interactions 4.1. Introduction 4.2. Two-neighbor interaction – general formulation – homogeneous solution 4.3. Two-neighbor interaction – localization in a weakened problem 4.4. Conclusion 4.5. References

9 5 New Analytic Solutions for Elastic Buckling of Isotropic Plates5.1. Introduction 5.2. Equilibrium equation 5.3. Solution 5.4. Boundary condition 5.5. Numerical results 5.6. Conclusion 5.7. Appendix A: Deflection, slopes, bending moments and shears 5.8. Appendix B: Function transformation 5.9. References

10 6 Buckling and Post-Buckling of Parabolic Arches with Local Damage6.1. Introduction 6.2. A one-dimensional model for arches 6.3. Parabolic arches 6.4. Crack models for one-dimensional elements 6.5. An application 6.6. Final remarks 6.7. Acknowledgments 6.8. References

11 7 Inelastic Microbuckling of Composites by Wave-Buckling Analogy7.1. Introduction 7.2. Buckling-wave propagation analogy 7.3. Microbuckling in elastic orthotropic composites 7.4. Inelastic microbuckling 7.5. Results and discussion 7.6. References

12 8 Quasi-Bifurcation of Discrete Systems with Unstable Post-Critical Behavior under Impulsive Loads 8.1. Introduction 8.2. Case study of a two DOF system with unstable static behavior 8.3. Exploring the static and dynamic behavior of the two DOF system 8.4. The dynamic stability criterion due to Lee 8.5. New stability bounds following Lee’s approach 8.6. Conclusion 8.7. Acknowledgments 8.8. References

13 9 Singularly Perturbed Problems of Drill String Buckling in Deep Curvilinear Borehole Channels9.1. Introduction 9.2. Singular perturbation theory: elements and history 9.3. Posing the problem of a drill string buckling in the curvilinear borehole 9.4. Modeling the drill string buckling in lowering operation 9.5. References

14 10 Shape-optimized Cantilevered Columns under a Rocket-based Follower Force 10.1. Background 10.2. Aims 10.3. Numerical analysis 10.4. Experiment 10.5. Flutter test 10.6. Concluding remarks 10.7. Acknowledgments 10.8. Appendix 10.9. References

15 11 Hencky Bar-Chain Model for Buckling Analysis and Optimal Design of Trapezoidal Arches 11.1. Introduction 11.2. Buckling analysis of trapezoidal arches based on the HBM 11.3. Optimal design of symmetric trapezoidal arches 11.4. Concluding remarks 11.5. References

16 List of Authors

17 Index

18 Summary of Volume 2

19 Summary of Volume 3

20 End User License Agreement

1 Preface: Short Bibliographical Presentation of Prof. Isaac Elishakoff Figure 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 1 Figure 1.1. Geometry and coordinate-axes of a laminated plate

3 Chapter 2Figure 2.1. A schematic diagram of a structure consisting of identical layers st...Figure 2.2. The schematic view of the sample showing gripping area (purple), glu...Figure 2.3. Photographs of the experimentally observed modes. (a) The top and th...Figure 2.4. A chain of N identical rigid rods. Each rod has length L and is atta...Figure 2.5. The plot of versus general mode number ( n − 1)/N (blue line) for a...Figure 2.6. The angular displacement θm of the m-th rod plotted versus its numbe...Figure 2.7. A model of two rigid rods on hinge supports with torsional springs k...Figure 2.8. Plots of the first and the second critical buckling loads of two cou...Figure 2.9. Plots of λ 1factors as functions of loading parameter | for various ...Figure 2.10. The localization factor λ plotted as a function of | for disorder m...Figure 2.11. Four lowest extended buckling modes of a chain with N = 100 rigid r...Figure 2.12. Plots of the selected buckling modes of the disordered chain in a n...

4 Chapter 3Figure 3.1. Creep test Figure 3.2. Relaxation test Figure 3.3. Classic viscoelastic model Figure 3.4. a) Zener model: a spring in series to a Voigt model and b) Zener mod...Figure 3.5. Springpot element Figure 3.6. Fractional models Figure 3.7. Onset of the column bifurcations and its generic section Figure 3.8. Onset of the column bifurcation Figure 3.9. Stability region on the complex plane Figure 3.10. Stability region and complex map Figure 3.11. Plot of the critical load for β = 0.0001Figure 3.12. Plot of the critical load for β = 0.14Figure 3.13. Plot of the critical load for β = 1

5 Chapter 4Figure 4.1. Extension of a generalized lattice with direct and indirect interact...Figure 4.2. Extension of a generalized lattice with direct and indirect interact...Figure 4.3. Displacement field in the generalized lattice under uniform loading ...Figure 4.4. Displacement field in the generalized lattice under uniform loading ...Figure 4.5. Displacement field in the generalized lattice under uniform loading ...Figure 4.6. Equivalent stiffness versus n; uniform loading – truncated higher-or...Figure 4.7. Displacement field in the generalized lattice under uniform loading ...