Elasticity
This is a first year graduate textbook in Linear Elasticity. It is written with the practical engineering reader in mind, dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Emphasis is placed on engine
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SOLID MECHANICS AND ITS APPLICATIONS Volume 172 Series Editor:
G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3GI
Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity.
For other titles published in this series, go to www.springer.com/series/6557
J.R. Barber
Elasticity
3rd Revised Edition
J.R. Barber Department of Mechanical Engineering and Applied Mechanics University of Michigan Ann Arbor, MI 48109-2125 USA [email protected]
ISSN 0925-0042 ISBN 978-90-481-3808-1 e-ISBN 978-90-481-3809-8 DOI 10.1007/978-90-481-3809-8 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009940788 © Springer Science + Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose ofbeing entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
Part I GENERAL CONSIDERATIONS 1
2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Notation for stress and displacement . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Index and vector notation and the summation convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Vector operators in index notation . . . . . . . . . . . . . . . . . . . 1.1.4 Vectors, tensors and transformation rules . . . . . . . . . . . . . 1.1.5 Principal stresses and Von Mises stress . . . . . . . . . . . . . . . 1.1.6 Displacement . . . . . . . . . . . . . . . . . . . . . . . . . .
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