Geometric Continuum Mechanics and Induced Beam Theories
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theori
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Simon R. Eugster
Geometric Continuum Mechanics and Induced Beam Theories
Lecture Notes in Applied and Computational Mechanics Volume 75
Series editors Friedrich Pfeiffer, Technische Universität München, Garching, Germany e-mail: [email protected] Peter Wriggers, Universität Hannover, Hannover, Germany e-mail: [email protected]
About this Series This series aims to report new developments in applied and computational mechanics—quickly, informally and at a high level. This includes the fields of fluid, solid and structural mechanics, dynamics and control, and related disciplines. The applied methods can be of analytical, numerical and computational nature.
More information about this series at http://www.springer.com/series/4623
Simon R. Eugster
Geometric Continuum Mechanics and Induced Beam Theories
123
Simon R. Eugster Institute for Nonlinear Mechanics University of Stuttgart Stuttgart Germany
ISSN 1613-7736 ISSN 1860-0816 (electronic) Lecture Notes in Applied and Computational Mechanics ISBN 978-3-319-16494-6 ISBN 978-3-319-16495-3 (eBook) DOI 10.1007/978-3-319-16495-3 Library of Congress Control Number: 2015933617 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
In the last centuries continuum mechanics developed from a theory treating very specific problems to a general theory suitable for many applications. Continuum mechanics started with the description of one-dimensional continua where Euler’s elastica is maybe its most famous problem. With the seminal work of Cauchy on the existence of the stress tensor in a three-dimensional continuum, the foundations of modern continuum mechanics have been laid down. After a century with the paradigm of infinitesimal deformations and linear elastic material
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