Contact Problems The legacy of L.A. Galin
L.A. Galin's book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second
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SOLID MECHANICS AND ITS APPLICATIONS Volume 155 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.
www.springer.com/series/6557
L.A. Galin† Author
G.M.L. Gladwell Editor
Contact Problems The legacy of L.A. Galin
13
L.A. Galin† and Prof. G.M.L. Gladwell University Waterloo Faculty Civil Engineering Waterloo, On N2L 3GI Canada
ISBN-13: 978-1-4020-9042-4
e-ISBN-13: 978-1-4020-9043-1
Library of Congress Control Number: 2008940577 © 2008 Springer Science+Business Media, B.V. 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, micro l ming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied speci cal ly for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper 987654321 springer.com
Table of Contents
Editor’s Preface
ix
Biographical Sketch of L.A. Galin
xi
Chapter 1 A Review of Research before 1953
1
1.1 1.2 1.3 1.4 1.5 1.6
1 1 3 4 5 7
Introduction Frictionless Plane Problems Plane Adhesive Contact Problems Plane Frictional Contact Problems Plane Contact between Two Elastic Bodies Three-Dimensional Contact Problems
Chapter 2 Plane Elasticity Theory
11
2.1 The Fundamental Equations 2.2 Stresses and Displacements in a Semi-Infinite Elastic Plane
11 21
Chapter 3 Plane Static Isotropic Contact Problems
33
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
33 35 39 41 44 49 51 55 58
Boundary Conditions for Plane Contact Problems The Riemann–Hilbert Problem for the Half-Plane Frictionless Punch Problems – Introduction Frictionless Punch Problems – Theory Examples of Frictionless Problems Frictional Punch Problems – Theory Frictional Punch Problems – Examples Sliding Contact with Coulomb Friction A Two-Punch Prob
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