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This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provided, for each problem considered, a description of the deformation; the equilibrium in terms of stresses; the constitutive equation; the equilibrium equation in terms of displacements; formulation of boundary value problems; and, variational principles, generalized solutions and conditions for solvability. "Introduction to Mathematical Elasticity" will also be of essential reference to engineers specializing in elasticity, and to mathematicians working on abstract formulations of the related boundary value problems.
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Introduction to Mathematical Elasticity 7313.tp.indd 1 7/23/09 4:29:37 PM This page intentionally left blank Introduction to Mathematical Elasticity Leonid P. Lebedev National University of Colombia Michael J. Cloud Lawrence Technological University, USA World Scientific NEW JERSEY 7313.tp.indd 2 • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TA I P E I • CHENNAI 7/23/09 4:29:38 PM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. INTRODUCTION TO MATHEMATICAL ELASTICITY Copyright © 2009 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-4273-72-5 ISBN-10 981-4273-72-4 Desk Editor: Tjan Kwang Wei Printed in Singapore. KwangWei - Intro to Math Elasticity.pmd 1 12/26/2008, 11:35 AM December 24, 2008 10:59 World Scientific Book - 9in x 6in Foreword In the twenty first century much of Applied Science is concerned with problems of great subtlety and complexity, and the greater the difficulty the more sophisticated are the mathematical and computational techniques needed in order to make significant progress. It is therefore particularly unfortunate that the gap between applied scientists and mathematicians is growing, indeed one is tempted to say has grown, so large that these groups are usually unable to understand each other and so to communicate. The training of undergraduate applied scientists frequently fails to cover even the basic level of the powerful mathematical tools available. On the other hand, mathematical students often learn little about the problems which originally motivated the very mathematics they are studying. Thus communication between the various groups at research level is often exceedingly difficult, and as a consequence joint research, essential now in many areas, faces major obstacles. It is thus timely that the present volume, which is aimed at bridging the gap, should appear. The book i