The Finite Element Method in Thin Shell Theory: Application to Arch Dam Simulations
~his Monograph has two objectives : to analyze a f inite e l e m en t m e th o d useful for solving a large class of t hi n shell prob l e ms, and to show in practice how to use this method to simulate an arch dam prob lem. The first objective is develope
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M. Bernardou · J. M. Boisserie
The Finite Element Method in Thin Shell Theory: Application to Arch Dam Simulation
Progress in Scientific Computing Vol. 1 Edited by S. Abarbanel R. Glowinski G. Golub H.-O. Kreiss
Springer Science+Business Media, LLC
M. Bernadou J. M. Boisserie
The Finite Element Method in Thin Shell Theory:
Application to Arch Dam Simulations
1982
Springer Science+Business Media, LLC
Authors: Hichel Bernadou INRIA Domaine de Voluceau-Rocquencourt B.P. 105 F-78153 Le Chesnay Cedex FRANCE Jean-Harie Boisserie E.D.F.-D.E.R. 6, Quai Watier F-78400 Chatou FRANCE
CIP-Kurztitelaufnahme der Deutschen Bibliothek Bernadou, Hichel: The finite element method in thin shell theory application to arch dam stimulations / H. Bernadou ; J. H. Boisserie . 11 Boston; Basel; Stuttgart : Birkhauser, 1982. (Progress in scientific computing ; Vol.1) ISBN 978-0-8176-3070-6 ISBN 978-1-4684-9143-2 (eBook) DOI 10.1007/978-1-4684-9143-2 NE: Boisserie, Jean-Harie.; GT Library of Congress Cataloging in Publication Data Bernadou, H. (Michel), 1943The Finite element method in thin shell theory. (Progress in scientific computing ; v. ) Bibliography: p. Includes index. 1. Finite element method. 2. Shells (Engineering) 3. Arch dams--~mthematical models. I. Boisserie, J.-M. (Jean-Harie), 193211. Title. 111. Series. TA347.F5B47 627' .82 82-4293 AACR2 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission of the copyright owner. ©Springer Science+Business Media New York, 1982 Originally published by Birkhäuser Boston in 1982.
TABLE OF CONTENTS
Preface
ix
PART I : NUMERICAL ANALYSIS OF A LINEAR THIN SHELL MODEL Introduction 1 - The Continuous Problem
5
1.1 - Definition of the middle surface 1.2 - Geometrical definition of the undeformed shell
e
5 9
1.3 - The linear model of W.T. KOlTER
10
1.4 - Two equivalent formulations of the shell problem
16
1.5 - Other expressions for the bilinear form and the linear form
18
1.6 - Existence and uniqueness of a solution 2 - The Discrete Problem
......,.
2.1 - The finite element space V h
21 27 29
2.2 - The discrete problem
33
2.3 - Examples of error estimates
37
2 .4 - Uathematical studies of the convergence and of the error estimates 3 - Implementation 3. I - Interpolation modules
39 65 65
3.2 - Energy functional and second member modules when the spaces X and X are constructed using hl h2 ARGYRIS triangles
80
3.3 - Energy functional and second member modules when the spaces X and X are constructed using hl h2 the complete HSIEH-CLOUGH-TOCHER triangle
82
vi
3.4 - Energy functional and second member modules when the spaces
~I
and
~2
are constructed using triangles of
type (2) and complete HSIEH-CLOUGH-TOCHER triangles, respectively
84
3.5 - Energy functional and second member modules when the and X are constructed using reduced h2 HSIEH-CLOUGH-TOCHER triangles spaces
~I
85
3.
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