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The Finite Element Method: Its
Basis and Fundamentals
Sixth edition
Professor O.C. Zienkiewicz, CBE, FRS, FREng is Professor Emeritus at the Civil and
Computational Engineering Centre, University of Wales Swansea and previously Director
of the Institute for Numerical Methods in Engineering at the University of Wales Swansea,
UK. He holds the UNESCO Chair of Numerical Methods in Engineering at the Technical
University of Catalunya, Barcelona, Spain. He was the head of the Civil Engineering
Department at the University of Wales Swansea between 1961 and 1989. He established
that department as one of the primary centres of finite element research. In 1968 he became
the Founder Editor of the International Journal for Numerical Methods in Engineering
which still remains today the major journal in this field. The recipient of 27 honorary
degrees and many medals, Professor Zienkiewicz is also a member of five academies – an
honour he has received for his many contributions to the fundamental developments of the
finite element method. In 1978, he became a Fellow of the Royal Society and the Royal
Academy of Engineering. 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 Chinese
Academy of Sciences (1998), and the National Academy of Science, Italy (Academia dei
Lincei) (1999). He published the first edition of this book in 1967 and it remained the only
book on the subject until 1971.
Professor R.L. Taylor has more than 40 years’ experience in the modelling and simulation
of structures and solid continua including two years in industry. He is Professor in the
Graduate School and the Emeritus T.Y. and Margaret Lin Professor of Engineering at the
University of California at Berkeley. In 1991 he was elected to membership in the US
National Academy of Engineering in recognition of his educational and research contri-
butions to the field of computational mechanics. Professor Taylor is a Fellow of the US
Association of Computational Mechanics – USACM (1996) and a Fellow of the Interna-
tionalAssociation of Computational Mechanics – IACM (1998). He has received numerous
awards including the Berkeley Citation, the highest honour awarded by the University of
California at Berkeley, the USACM John von Neumann Medal, the IACM Gauss–Newton
Congress Medal and a Dr.-Ingenieur ehrenhalber awarded by the Technical University of
Hannover, Germany. Professor Taylor has written several computer programs for finite
element analysis of structural and non-structural systems, one of which, FEAP, is used
world-wide in education and research environments. A personal version, FEAPpv, avail-
able from the publisher’s website, is incorporated into the book.
Dr J.Z. Zhu has more than 20 years’ experience in the development of finite element
methods. During the last 12 years he has worked in industry where he has been developing
commercial finite element software to solve multi-physics problems. Dr Zhu read for his
Bachelor of Science degree at Harbin Engineering University and his Master of Science
at Tianjin University, both in China. He was awarded his doctoral degree in 1987 from
the University of Wales Swansea, working under the supervision of Professor Zienkiewicz.
Dr Zhu is the author of more than 40 technical papers on finite element methods including
several on error estimation and adaptive automatic mesh generation. These have resulted
in his being named in 2000 as one of the highly cited researchers for engineering in the
world and in 2001 as one of the top 20 most highly cited researchers for engineering in the
United Kingdom.
The Finite Element
Method: Its Basis and
Fundamentals
Sixth edition
O.C. Zienkiewicz, CBE, FRS
UNESCO Professor of Numerical Methods in Engineering
International Centre for Numerical Methods in Engineering, Barcelona
Previously Director of the Institute for Numerical Methods in Engineering
University of Wales, Swansea
R.L. Taylor J.Z. Zhu
Professor in the Graduate School Senior Scientist
Department of Civil and Environmental Engineering ESI USR&DInc.
University of California at Berkeley 5850 Waterloo Road, Suite 140
Berkeley, California Columbia, Maryland
AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD
PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Elsevier Butterworth-Heinemann
Linacre House, Jordan Hill, Oxford OX2 8DP
30 Corporate Drive, Burlington, MA 01803
First published in 1967 by McGraw-Hill
Fifth edition published by Butterworth-Heinemann 2000
Reprinted 2002
Sixth edition 2005
Copyright
c
2000, 2005. O.C. Zienkiewicz, R.L. Taylor and J.Z. Zhu. All rights reserved
The rights of O.C. Zienkiewicz, R.L. Taylor and J.Z. Zhu to be identified as the authors of this work
have been asserted in accordance with the Copyright, Designs and Patents Act 1988
No part of this publication may be reproduced in any material form (including
photocopying or storing in any medium by electronic means and whether or not
transiently or incidentally to some other use of this publication) without the written
permission of the copyright holder except in accordance with the provisions of the
Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by
the Copyright Licensing Agency Ltd, 90, Tottenham Court Road, London,
England W1T 4LP. Applications for the copyright holder’s written permission
to reproduce any part of this publication should be addressed to the publisher.
Permissions may be sought directly from Elsevier’s Science & Technology
Rights Department in Oxford, UK: phone: (+44) 1865 843830,
fax: (+44) 1865 853333, e-mail: permissions @ elsevier.co.uk. You may also
complete your request on-line via the Elsevier homepage (http://www.elsevier.com),
by selecting ‘Customer Support’ and then ‘Obtaining Permissions’
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing in Publication Data
A catalogue record for this book is available from the Library of Congress
ISBN 0 7506 6320 0
Published with the cooperation of CIMNE,
the International Centre for Numerical Methods in Engineering,
Barcelona, Spain (www.cimne.upc.es)
For information on all Elsevier Butterworth-Heinemann publications
visit our website at http://books.elsevier.com
Typeset by Kolam Information Services P Ltd, Pondicherry, India
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