E-Book Overview
This book presents a modern continuum mechanics and mathematical framework to study shell physical behaviors, and to formulate and evaluate finite element procedures. With a view towards the synergy that results from physical and mathematical understanding, the book focuses on the fundamentals of shell theories, their mathematical bases and finite element discretizations. The complexity of the physical behaviors of shells is analysed, and the difficulties to obtain uniformly optimal finite element procedures are identified and studied. Some modern finite element methods are presented for linear and nonlinear analyses.
In this Second Edition the authors give new developments in the field and - to make the book more complete - more explanations throughout the text, an enlarged section on general variational formulations and new sections on 3D-shell models, dynamic analyses, and triangular elements.
The analysis of shells represents one of the most challenging fields in all of mechanics, and encompasses various fundamental and generally applicable components. Specifically, the material presented in this book regarding geometric descriptions, tensors and mixed variational formulations is fundamental and widely applicable also in other areas of mechanics.
E-Book Content
Computational Fluid and Solid Mechanics
Series Editor K.J. Bathe Massachusetts Institute of Technology, Cambridge, MA, USA
For other titles published in this series, go to http://www.springer.com/series/4449
Dominique Chapelle · Klaus-J¨urgen Bathe
The Finite Element Analysis of Shells – Fundamentals Second Edition
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Dominique Chapelle INRIA Paris-Rocquencourt France
Klaus-J¨urgen Bathe Massachusetts Institute of Technology USA
ISSN 1860-482X e-ISSN 1860-4838 ISBN 978-3-642-16407-1 e-ISBN 978-3-642-16408-8 DOI 10.1007/978-3-642-16408-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010937756 c Springer-Verlag Berlin Heidelberg 2003, 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To our fruitful collaboration and long-lasting friendship
Preface – Second Edition
Since our writing of the first edition of this book, some important advances in finite element methods for shell analyses have been achieved. In this new edition, we present some of these new developments. In addition, we have endeavored to strengthen the presentation throughout the text. The major changes and additions in the book pertain to the section on the presentation of general variational formulations and finite element approximations, the new sections on 3D-shell models and finite element discretizations, on dynamic analyses, and on triangular elements. We also added more explanations in the text, and many new examples and figures in order to render the book more complete. We endeavored to achieve more completeness also be