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ELASTICITY IN ENGINEERING MECHANICS
Elasticity in Engineering Mechanics, Third Edition Arthur P. Boresi, Ken P. Chong and James D. Lee Copyright © 2011 John Wiley & Sons, Inc.
ELASTICITY IN ENGINEERING MECHANICS
Third Edition
ARTHUR P. BORESI Professor Emeritus
University of Illinois, Urbana, Illinois
and
University of Wyoming, Laramie, Wyoming
KEN P. CHONG Associate
National Institute of Standards and Technology, Gaithersburg, Maryland
and
Professor
Department of Mechanical and Aerospace Engineering George Washington University, Washington, D.C.
JAMES D. LEE Professor
Department of Mechanical and Aerospace Engineering George Washington University, Washington, D.C.
JOHN WILEY & SONS, INC.
This book is printed on acid-free paper.
Copyright 2011 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Boresi, Arthur P. (Arthur Peter), 1924-
Elasticity in engineering mechanics / Arthur P. Boresi, Ken P. Chong and James D. Lee. – 3rd ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-40255-9 (hardback : acid-free paper); ISBN 978-0-470-88036-4 (ebk);
ISBN 978-0-470-88037-1 (ebk); ISBN 978-0-470-88038-8 (ebk); ISBN 978-0-470-95000-5 (ebk); ISBN 978-0-470-95156-9 (ebk); ISBN 978-0-470-95173-6 (ebk)
1. Elasticity. 2. Strength of materials. I. Chong, K. P. (Ken Pin), 1942- II. Lee, J. D. (James D.) III. Title.
TA418.B667 2011 620.101232–dc22
2010030995
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
CONTENTS
Preface xvii
CHAPTER 1
Part I
INTRODUCTORY CONCEPTS AND MATHEMATICS 1
Introduction 1
1-1 Trends and Scopes 1 1-2 Theory of Elasticity 7 1-3 Numerical Stress Analysis 8 1-4 General Solution of the Elasticity
Problem 9 1-5 Experimental Stress Analysis 9 1-6 Boundary Value Problems of Elasticity 10
Part II Preliminary Concepts 11
1-7 Brief Summary of Vector Algebra 12 1-8 Scalar Point Functions 16 1-9 Vector Fields 18 1-10 Differentiation of Vectors 19 1-11 Differentiation of a Scalar Field 21 1-12 Differentiation of a Vector Field 21 1-13 Curl of a Vector Field 22 1-14 Eulerian Continuity Equation for Fluids 22
v
vi CONTENTS
1-15 Divergence Theorem 25 1-16 Divergence Theorem in Two
Dimensions 27 1-17 Line and Surface Integrals (Application of
Scalar Product) 28 1-18 Stokes’s Theorem 29 1-19 Exact Differential 30 1-20 Orthogonal Curvilinear Coordiantes in
Three-Dimensional Space 31 1-21 Expression for Differential Length in
Orthogonal Curvilinear Coordinates 32 1-22 Gradient and Laplacian in Orthogonal
Curvilinear Coordinates 33
Part III
CHAPTER 2
Elements of Tensor Algebra 36
1-23 Index Notation: Summation Convention 36 1-24 Transformation of Tensors under Rotation
of Rectangular Cartesian Coordinate
System 40 1-25 Symmetric and Antisymmetric Parts of a
Tensor 46 1-26 Symbols δ and ² (the Kronecker Delta
and the Alternating Tensor) 47 1-27 Homogeneous Quadratic Forms 49 1-28 Elementary Matrix Algebra 52 1-29 Some Topics in the Calculus of
Variations 56 References 60 Bibliography 63
THEORY OF DEFORMATION 65
2-1 Deformable, Continuous Media 65 2-2 Rigid-Body Displacements 66 2-3 Deformation of a Continuous Region.
Material Variables. Spatial Variables 68 2-4 Restrictions on Continuous Deformation
of a Deformable Medium 71 Problem Set 2-4 75
2-5 Gradient of the Displacement Vector.
Tensor Quantity 76
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