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The Finite lementMethodFifth edition

Volume 3: Fluid DynamicsO .C . Z i e n k i e w i c z C B E FRS F R E n g

UNESCO Professor of Numerical Methods in EngineeringInternational Centre fo r Num erical Methods in Engineering BarcelonaEmeritus Professor of Civil Engineering and Director of the Institute forNumerical Methods in Engineering Un ivers ity of Wales Swansea

R L TaylorProfessor in the Graduate SchoolDepartm ent of C ivil and Environmental Engineering

University of California a t BerkeleyBerkeley California

OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI

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Butterworth-HeinemannLinacre House, Jord an Hill , Oxford OX 2 8D P225 Wildwood Avenue, Woburn, MA 01801-2041A division of Reed Educational and Professional Publishing Ltd@ e m b e r of the Reed Elsevier p l c g r o u pFirst published in 1967 by McG raw-H illFifth edition published by Butterworth-Heinemann 2000

.C. Zienkiewicz and R.L . Taylor 2000All rights reserved. No par t of this publicationma y be reproduced in any material form includingphotocopying or storing in any medium by electronicmeans and whether or not transiently o r incidentallyto some othe r use of this publication) without thewritten permission of the copyright holder exceptin accordance with th e provisions of the Cop yright,Designs and Patents Act 1988 or under the terms of alicence issued by the Copyright Licensing Agency Ltd,90 Tottenham Court Road, L ondon, England W I P 9HE.Applications for the copyright holders written permissionto reproduce any part of this publication shouldbe addressed to th e publishers

British Library Cataloguing in Publication Da taA catalogue record f or this boo k is available from the B ritish LibraryLibrary of Congress Cataloguing in Publication DataA catalogue record for this book is available from the Library of Congress

ISBN 0 7506 5050 8Published with the cooperation of CIMNE,the International Centre for Numerical Methods in Engineering,

Barcelona, Spain www.cimne.upc.es)

Typeset by Academ ic Technical Typesetting, BristolPrinted and bo und by M PG Books Ltd

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Dedication

This book is dedicated to our wives Helen and MaryLou and our families for their support and patience

during the preparation of this book, and also to all ofour students and colleagues who over the years havecontributed to our knowledge of the finite element

method. In particular we would like to mentionProfessor Eugenio Oiiate and his group at CIMNE for

their help, encouragement and support during thepreparation process.

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Professor O C Zienkiewicz, CBE, FR S, FREng is Professor Emeritus and Directorof the Institute for Numerical Methods in Engineering at the University of Wales,Swansea, UK. He holds the UNESCO Chair of Numerical Methods in Engineeringat the Technical University of Catalunya, Barcelona, Spain. He was the head of theCivil Engineering Department at the University of Wales Swansea between 1961and 1989. He established that department as one of the primary centres of finiteelement research. In 1968 he became the Founder Editor of the International Journalor Numerical Methods in Engineering which still remains today the major journalin this field. The recipient of 24 honorary degrees and many medals, ProfessorZienkiewicz is also a member of five academies an honour he has received for hismany contributions to the fundamental developments of the finite element method.In 1978, he became a Fellow of the Royal Society and the Royal Academy ofEngineering. This was followed by his election as a foreign member to the U.S.Academy of Engineering 1981), the Polish Academy of Science 1985), the ChineseAcademy of Sciences 1998), and the National Academy of Science, Italy Academiadei Lincei) 1999). He published the first edition of this book in 1967 and it remainedthe only book on the subject until 1971.Professor R.L. Taylor has more than 35 years experience in the modelling and simu-lation of structures and solid continua including two years in industry. In 1991 he waselected to membership in the U.S. National Academy of Engineering in recognition ofhis educational and research contributions to the field of computational mechanics.He was appointed as the T.Y. and Margaret Lin Professor of Engineering in 1992and, in 1994, received the Berkeley Citation, the highest honour awarded by theUniversity of California, Berkeley. In 1997, Professor Taylor was made a Fellow inthe U.S. Association for Computational Mechanics and recently he was electedFellow in the International Association of Computational Mechanics, and wasawarded the USACM John von Neumann Medal. Professor Taylor has writtenseveral computer programs for finite element analysis of structural and non-structuralsystems, one of which, FEAP, is used world-wide in education and research environ-ments. FEAP is now incorporated more fully into the book to address non-linear andfinite deformation problems.

Front cover image: Finite Element Model of the world land speed record 765.035mph) car THRUSTSSC. The analysis was done using the finite element method by K. Morgan, 0 Hassan and N.P. Weatherillat the Institute for Numerical Methods in Engineering, University of Wales Swansea, UK. see K. Morgan,0 Hassan and N.P. Weatherill, Why didnt the supersonic car fly?, Mathemat ics Today Bde t in of theInstitute o Mathematics and Its Applications. Vol. 35, No. 4, 110 1 14, Aug. 1999).