文档介绍：NONLINEAR CONTINUUM
MECHANICS FOR FINITE
ELEMENT ANALYSIS
Javier Richard D. Wood
University of Wales Swansea University of Wales Swansea
PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge CB2 1RP, United Kingdom
CAMBRIDGE UNIVERSITY PRESS
The Edinburgh Building, Cambridge CB2 2RU, United Kingdom
40 West 20th Street, New York, NY 10011-4211, USA
10 Stamford Road, Oakleigh, Melbourne 3166, Australia
c Cambridge University Press 1997
This book is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 1997
Printed in the United States of America
Typeset in Times and Univers
Library of Congress Cataloging-in-Publication Data
, Javier, 1961–
Nonlinear continuum mechanics for finite element analysis / Javier
, Richard D. Wood.
p. cm.
ISBN 0-521-57272-X
1. Materials – Mathematical models. 2. Continuum mechanics.
3. Nonlinear mechanics. 4. Finite element method. I. Wood.
Richard D. II. Title.
1997
1015118 – dc21 97-11366
CIP
A catalog record for this book is available from
the British Library.
ISBN 0 521 57272 X hardback
CONTENTS
Preface xiii
1 INTRODUCTION 1
PUTATIONAL MECHANICS 1
SIMPLE EXAMPLES OF NONLINEAR STRUCTURAL BEHAVIOR 2
Cantilever 2
Column 3
NONLINEAR STRAIN MEASURES 4
One-Dimensional Strain Measures 5
Nonlinear Truss Example 6
Continuum Strain Measures 10
DIRECTIONAL DERIVATIVE, LINEARIZATION AND
EQUATION SOLUTION 13
Directional Derivative 14
Linearization and Solution of Nonlinear
Algebraic Equations 16
2 MATHEMATICAL PRELIMINARIES 21
INTRODUCTION 21
VECTOR AND TENSOR ALGEBRA 21
Vectors 22
Second-Order Tensors 26
Vector and Tensor Invariants 33
viii