Studies of Postbuckled Shapes
The previous chapter considered the initiation of instabilities; we conclude this book with an introduction to postbuckled shapes. Postbuckling behavior is a large deformation problem initiated by a singularity and this singularity helps delineate between
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Spectral Analysis of Nonlinear Elastic Shapes
Spectral Analysis of Nonlinear Elastic Shapes
James F. Doyle
Spectral Analysis of Nonlinear Elastic Shapes
James F. Doyle School of Aeronautics & Astronautics Purdue University West Lafayette, IN, USA
ISBN 978-3-030-59493-0 ISBN 978-3-030-59494-7 (eBook) https://doi.org/10.1007/978-3-030-59494-7 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
For Linda thank you again and again. I could not have done this without you.
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 5
1
Overview of Shapes and Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Deformed Shapes of Simple Slender Members. . . . . . . . . . . . . . . . . . . . . . . . 1.2 Modeling Continuous Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Structural Stiffness and Its Spectral Properties . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Spectral Shapes of Slender Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 7 21 46 59 77
2
Shapes with Coupled Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Curved Beams and Arches. . . . . . . . . . . . . . . . . . . . .
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