The Finite Element Method
Fifth edition
Volume 2: Solid Mechanics
PR
O
FD
O
C
,Professor O.C. Zienkiewicz, CBE, FRS, FREng is Professor Emeritus and 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 ®nite
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 ®eld. The recipient of 24 honorary degrees and many medals, Professor
Zienkiewicz is also a member of ®ve academies ± an honour he has received for his
many contributions to the fundamental developments of the ®nite 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
PR
Academy of Sciences (1998), and the National Academy of Science, Italy (Academia
dei Lincei) (1999). He published the ®rst edition of this book in 1967 and it remained
the 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 was
O
elected to membership in the U.S. National Academy of Engineering in recognition of
his educational and research contributions to the ®eld of computational mechanics.
He was appointed as the T.Y. and Margaret Lin Professor of Engineering in 1992
and, in 1994, received the Berkeley Citation, the highest honour awarded by the
FD
University of California, Berkeley. In 1997, Professor Taylor was made a Fellow in
the U.S. Association for Computational Mechanics and recently he was elected
Fellow in the International Association of Computational Mechanics, and was
awarded the USACM John von Neumann Medal. Professor Taylor has written sev-
eral computer programs for ®nite element analysis of structural and non-structural
systems, one of which, FEAP, is used world-wide in education and research environ-
O
ments. FEAP is now incorporated more fully into the book to address non-linear and
®nite deformation problems.
C
Front cover image: A Finite Element Model of the world land speed record (765.035 mph) car THRUST
SSC. The analysis was done using the ®nite element method by K. Morgan, O. Hassan and N.P. Weatherill
at the Institute for Numerical Methods in Engineering, University of Wales Swansea, UK. (see K. Morgan,
O. Hassan and N.P. Weatherill, `Why didn't the supersonic car ¯y?', Mathematics Today, Bulletin of the
Institute of Mathematics and Its Applications, Vol. 35, No. 4, 110±114, Aug. 1999).
, The Finite Element
Method
PR
Fifth edition
Volume 2: Solid Mechanics
O
FD
O.C. Zienkiewicz, CBE, FRS, FREng
UNESCO Professor of Numerical Methods in Engineering
International Centre for Numerical Methods in Engineering, Barcelona
Emeritus Professor of Civil Engineering and Director of the Institute for
Numerical Methods in Engineering, University of Wales, Swansea
O
R.L. Taylor
C
Professor in the Graduate School
Department of Civil and Environmental Engineering
University of California at Berkeley
Berkeley, California
OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI
, Butterworth-Heinemann
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
A division of Reed Educational and Professional Publishing Ltd
First published in 1967 by McGraw-Hill
Fifth edition published by Butterworth-Heinemann 2000
# O.C. Zienkiewicz and R.L. Taylor 2000
PR
All rights reserved. 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
O
licence issued by the Copyright Licensing Agency Ltd,
90 Tottenham Court Road, London, England W1P 9HE.
Applications for the copyright holder's written permission
to reproduce any part of this publication should
be addressed to the publishers
FD
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
O
ISBN 0 7506 5055 9
Published with the cooperation of CIMNE,
the International Centre for Numerical Methods in Engineering,
C
Barcelona, Spain (www.cimne.upc.es)
Typeset by Academic & Technical Typesetting, Bristol
Printed and bound by MPG Books Ltd
Fifth edition
Volume 2: Solid Mechanics
PR
O
FD
O
C
,Professor O.C. Zienkiewicz, CBE, FRS, FREng is Professor Emeritus and 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 ®nite
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 ®eld. The recipient of 24 honorary degrees and many medals, Professor
Zienkiewicz is also a member of ®ve academies ± an honour he has received for his
many contributions to the fundamental developments of the ®nite 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
PR
Academy of Sciences (1998), and the National Academy of Science, Italy (Academia
dei Lincei) (1999). He published the ®rst edition of this book in 1967 and it remained
the 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 was
O
elected to membership in the U.S. National Academy of Engineering in recognition of
his educational and research contributions to the ®eld of computational mechanics.
He was appointed as the T.Y. and Margaret Lin Professor of Engineering in 1992
and, in 1994, received the Berkeley Citation, the highest honour awarded by the
FD
University of California, Berkeley. In 1997, Professor Taylor was made a Fellow in
the U.S. Association for Computational Mechanics and recently he was elected
Fellow in the International Association of Computational Mechanics, and was
awarded the USACM John von Neumann Medal. Professor Taylor has written sev-
eral computer programs for ®nite element analysis of structural and non-structural
systems, one of which, FEAP, is used world-wide in education and research environ-
O
ments. FEAP is now incorporated more fully into the book to address non-linear and
®nite deformation problems.
C
Front cover image: A Finite Element Model of the world land speed record (765.035 mph) car THRUST
SSC. The analysis was done using the ®nite element method by K. Morgan, O. Hassan and N.P. Weatherill
at the Institute for Numerical Methods in Engineering, University of Wales Swansea, UK. (see K. Morgan,
O. Hassan and N.P. Weatherill, `Why didn't the supersonic car ¯y?', Mathematics Today, Bulletin of the
Institute of Mathematics and Its Applications, Vol. 35, No. 4, 110±114, Aug. 1999).
, The Finite Element
Method
PR
Fifth edition
Volume 2: Solid Mechanics
O
FD
O.C. Zienkiewicz, CBE, FRS, FREng
UNESCO Professor of Numerical Methods in Engineering
International Centre for Numerical Methods in Engineering, Barcelona
Emeritus Professor of Civil Engineering and Director of the Institute for
Numerical Methods in Engineering, University of Wales, Swansea
O
R.L. Taylor
C
Professor in the Graduate School
Department of Civil and Environmental Engineering
University of California at Berkeley
Berkeley, California
OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI
, Butterworth-Heinemann
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
A division of Reed Educational and Professional Publishing Ltd
First published in 1967 by McGraw-Hill
Fifth edition published by Butterworth-Heinemann 2000
# O.C. Zienkiewicz and R.L. Taylor 2000
PR
All rights reserved. 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
O
licence issued by the Copyright Licensing Agency Ltd,
90 Tottenham Court Road, London, England W1P 9HE.
Applications for the copyright holder's written permission
to reproduce any part of this publication should
be addressed to the publishers
FD
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
O
ISBN 0 7506 5055 9
Published with the cooperation of CIMNE,
the International Centre for Numerical Methods in Engineering,
C
Barcelona, Spain (www.cimne.upc.es)
Typeset by Academic & Technical Typesetting, Bristol
Printed and bound by MPG Books Ltd
