About the Item
Elasticity: Theory and Applications, now in a revised and updated second edition, has long been used as a textbook by seniors and graduate students in civil, mechanical, and biomedical engineering, since the first edition was published in 1974. The kinematics of continuous media and the analysis of stress are introduced through the concept of linear transformation of points and brought together to study in great detail the linear theory of elasticity as well as its application to a variety of practical problems. Elastic stability, the theory of thin plates, and the theory of thin shells are covered. Complex variables are introduced and used to solve two dimensional and fracturerelated problems. Through theory, solved examples and problems, this authoritative book helps the student acquire the foundation needed to pursue advanced studies in all the branches of continuum mechanics. It also helps practitioners understand the source of many of the formulas they use in their designs. A solutions manual is available to instructors. 
Key Features
Unifies the study of finite and linear strain, and that of stress under the notion of linear transformation of points
Uses matrices with an emphasis on geometry as the reader is introduced to the concept of tensor and its associated notations
Supports the theories and applications with a large number of solved examples throughout the book
Includes additional solved numerical examples and detailed explanations of key topics in the addendum

About the Author(s)
Adel S. Saada (Ing., E.C.P., Ph.D., Princeton University) is presently Professor of Civil Engineering at Case Western Reserve University, Cleveland, Ohio. Dr. Saada received his Ingénieur des Arts et Manufactures degree from École Centrale des Arts et Manufactures de Paris, France, and the equivalent of a Master of Science degree from the University of Grenoble, France. Before coming to Princeton University the author was a practicing structural engineer in France. Dr. Saada’s teaching activities are in two major areas: the first is that of the mechanics of solids and in particular elasticity; the second is that of mechanics applied to soils and foundations. His research activities are primarily in the area of stressstrain relations and failure of transversely isotropic geomaterials. Much of his research work has been supported by personal grants from the National Science Foundation, the U.S. Army, and the U.S. Air Force. Dr. Saada is a member of several professional societies, a consulting engineer, and the author of numerous papers published in both national and international journals. 
Table of Contents
About the Author
Preface
Part I KINEMATICS OF CONTINUOUS MEDIA (Displacement, Deformation, Strain)
Chapter 1 Introduction to the Kinematics of Continuous Media
11 Formulation of the Problem
12 Notation
Chapter 2 Review of Matrix Algebra
21 Introduction
22 Definition of a Matrix. Special Matrices
23 Index Notation and Summation Convention
24 Equality of Matrices. Addition and Subtraction
25 Multiplication of Matrices
26 Matrix Division. The Inverse Matrix Problems
Chapter 3 Linear Transformation of Points
31 Introduction
32 Definitions and Elementary Operations
33 Conjugate and principal Directions and Planes in a Linear Transformation
34 Orthogonal Transformations
35 Changes of Axes in a Linear Transformation
36 Characteristic Equations and Eigenvalues
37 Invariants of the Transformation Matrix in a Linear Transformation
38 Invariant Directions of a Linear Transformation
39 Antisymmetric Linear Transformations
310 Symmetric Transformations. Definitions and General Theorems
311 Principal Directions and Principal Unit Displacements of a Symmetric
Transformation
312 Quadratic Forms
313 Normal and Tangential Displacements in a Symmetric Transformation. Mohr's
Representation
314 Spherical Dilatation and Deviation in a Linear Symmetric Transformation
315 Geometrical Meaning of the aij's in a Linear Symmetric Transformation
316 Linear Symmetric Transformation in Two Dimensions Problems
Chapter 4 General Analysis of Strain in Cartesian Coordinates
41 Introduction
42 Changes in Length and Directions of Elements Initially Parallel to the
Coordinate Axes
43 Components of the State of Strain at a Point
44 Geometrical Meaning of the Strain Components e.Strain of a Line Element
45 Components of the State of Strain under a Change of Coordinate System
46 Principal Axes of Strain
47 Volumetric Strain
48 Small Strain
49 Linear Strain
410 Compatibility Relations for Linear Strains Problems
Chapter 5 Cartesian Tensors
51 Introduction
52 Scalars and Vectors
53 Higher Rank Tensors
54 On Tensors and Matrices
55 The Kronecker Delta and the Alternating Symbol. Isotropic Tensors
56 Function of a Tensor. Invariants
57 Contraction
58 The Quotient Rule of Tensors Problems
Chapter 6 Orthogonal Curvilinear Coordinates
61 Introduction
62 Curvilinear Coordinates
63 Metric Coefficients
64 Gradient, Divergence, Curl, and Laplacian in Orthogonal Curvilinear Coordinates
65 Rate of Change of the Vectors a, and of the Unit Vectors Z, in an Orthogonal Curvilinear Coordinate System
66 The Strain Tensor in Orthogonal Curvilinear Coordinates
67 StrainDisplacement Relations in Orthogonal Curvilinear Coordinates
68 Components of the Rotation in Orthogonal Curvilinear Coordinates
69 Equations of Compatibility for Linear Strains in Orthogonal Curvilinear Coordinates Problems
Part II THEORY OF STRESS
Chapter 7 Analysis of Stress
71 Introduction
72 Stress on a Plane at a Point. Notation and Sign Convention
73 State of Stress at a Point. The Stress Tensor
74 Equations of Equilibrium. Symmetry of the Stress Tensor. Boundary Conditions
75 Application of the Properties of Linear Symmetric Transformations to the Analysis of Stress
76 Stress Quadric
77 Further Graphical Representations of the State of Stress at a Point. Stress Ellipsoid. Stress Director Surface
78 The Octahedral Normal and Octahedral Shearing Stresses
79 The HaighWestergaard Stress Space
710 Components of the State of Stress at a Point in a Change of Coordinates
711 Stress Analysis in Two Dimensions
712 Equations of Equilibrium in Orthogonal Curvilinear Coordinates Problems
Part III THE THEORY OF ELASTICITY  APPLICATIONS TO ENGINEERING PROBLEMS
Chapter 8 Elastic StressStrain Relations and Formulation of Elasticity Problems
81 Introduction
82 Work, Energy, and the Existence of a Strain Energy Function
83 The Generalized Hooke's Law
84 Elastic Symmetry
85 Elastic StressStrain Relations for Isotropic Media
86 Thermoelastic StressStrain Relations for Isotropic Media
87 Strain Energy Density
88 Formulation of Elasticity Problems. BoundaryValue Problems of Elasticity
89 Elasticity Equations in Terms of Displacements
810 Elasticity Equations in Terms of Stresses
811 The Principle of Superposition
812 Existence and Uniqueness of the Solution of an Elasticity Problem
813 SaintVenant's Principle
814 One Dimensional Elasticity
815 Plane Elasticity
816 State of Plane Strain
817 State of Plane Stress
818 State of Generalized Plane Stress
819 State of Generalized Plane Strain
820 Solution of Elasticity Problems
Problems
Chapter 9 Solution of Elasticity Problems by Potentials
91 Introduction
92 Some Results of Field Theory
93 The Homogeneous Equations of Elasticity and the Search for Particular Solutions
94 Scalar and Vector Potentials. Lame's Strain Potential
95 The Galerkin Vector. Love's Strain Function. Kelvin's and Cerruti's Problems
96 The NeuberPapkovich Representation. Boussinesq's Problem
97 Summary of Displacement Functions
98 Stress Functions
99 Airy's Stress Function for Plane Strain Problems
910 Airy's Stress Function for Plane Stress Problems
911 Forms of Airy's Stress Function Problems
Chapter 10 The Torsion Problem
101 Introduction
102 Torsion of Circular Prismatic Bars
103 Torsion of NonCircular Prismatic Bars
104 Torsion of an Elliptic Bar
105 Prandtl's Stress Function
106 Two Simple Solutions Using Prandtl's Stress Function
107 Torsion of Rectangular Bars
108 Prandtl's Membrane Analogy
109 Application of the Membrane Analogy to Solid Sections
1010 Application of the Membrane Analogy to Thin Tubular Members
1011 Application of the Membrane Analogy to Multicellular Thin Sections
1012 Torsion of Circular Shafts of Varying Cross Section
1013 Torsion of ThinWalled Members of Open Section in which some Cross
Section is Prevented from Warping A101 The GreenRiemann Formula
Problems
Chapter 11 Thick Cylinders, Disks, and Spheres
111 Introduction
112 Hollow Cylinder with Internal and External Pressures and Free Ends
113 Hollow Cylinder with Internal and External Pressures and Fixed Ends
114 Hollow Sphere Subjected to Internal and External Pressures
115 Rotating Disks of Uniform Thickness
116 Rotating Long Circular Cylinder
117 Disks of Variable Thickness
118 Thermal Stresses in Thin Disks
119 Thermal Stresses in Long Circular Cylinders
1110 Thermal Stresses in Spheres Problems
Chapter 12 Straight Simple Beams
121 Introduction
122 The Elementary Theory of Beams
123 Pure Bending of Prismatical Bars
124 Bending of a Narrow Rectangular Cantilever by an End Load
125 Bending of a Narrow Rectangular Beam by a Uniform Load
126 Cantilever Prismatic Bar of Irregular Cross Section Subjected to a Transverse End Force
127 Shear Center
Problems
Chapter 13 Curved Beams
131 Introduction
132 The Simplified Theory of Curved Beams
133 Pure Bending of Circular Arc Beams
134 Circular Arc Cantilever Beam Bent by a Force at the End
Problems
Chapter 14 The SemiInfinite Elastic Medium and Related Problems
141 Introduction
142 Uniform Pressure Distributed over a Circular Area on the Surface of a SemiInfinite Solid
143 Uniform Pressure Distributed over a Rectangular Area
144 Rigid Die in the Form of a Circular Cylinder
145 Vertical Line Load on a SemiInfinite Elastic Medium
146 Vertical Line Load on a SemiInfinite Elastic Plate
147 Tangential Line Load at the Surface of a SemiInfinite Elastic Medium
148 Tangential Line Load on a SemiInfinite Elastic Plate
149 Uniformly Distributed Vertical Pressure on Part of the Boundary of a SemiInfinite Elastic Medium
1410 Uniformly Distributed Vertical Pressure on Part of the Boundary of a SemiInfinite Elastic Plate
1411 Rigid Strip at the Surface of a Semi Infinite Elastic Medium
1412 Rigid Die at the Surface of a SemiInfinite Elastic Plate
1413 Radial Stresses in Wedges
1414 M. Levy's Problems of the Triangular and Rectangular Retaining Walls
Chapter 15 Energy Principles and Introduction To Variational Methods
151 Introduction
152 Work, Strain and Complementary Energies. Clapeyron's Law
153 Principle of Virtual Work
154 Variational Problems and Euler's Equations
155 The Reciprocal Laws of Betti and Maxwell
156 Principle of Minimum Potential Energy
157 Castigliano's First Theorem
158 Principle of Virtual Complementary Work
159 Principle of Minimum Complementary Energy
1510 Castigliano's Second Theorem
1511 Theorem of Least Work
1512 Summary of Energy Theorems
1513 Working Form of the Strain Energy for Linearly Elastic Slender Members
1514 Strain Energy of a Linearly Elastic Slender Member in Terms of the Unit Displacements of the Centroid G and of the Unit Rotations
1515 A Working Form of the Principles of Virtual Work and of Virtual Complementary Work for a Linearly Elastic Slender Member
1516 Examples of Application of the Theorems of Virtual Work and Virtual Complementary Work
1517 Examples of Application of Castigliano's First and Second Theorems
1518 Examples of Application of the Principles of Minimum Potential Energy and Minimum Complementary Energy
1519 Example of Application of the Theorem of Least Work
1520 The RayleighRitz Method
Problems
Chapter 16 Elastic Stability: Columns and BeamColumns
161 Introduction
162 Differential Equations of Columns and BeamColumns
163 Simple Columns
164 Energy Solution of the Buckling Problem
165 Examples of Calculation of Buckling Loads by the Energy Method
166 Combined Compression and Bending
167 Lateral Buckling of Thin Rectangular Beams
Problems
Chapter 17 Bending of Thin Flat Plates
171 Introduction and Basic Assumptions. Strains and Stresses
172 Geometry of Surfaces with Small Curvatures
173 Stress Resultants and Stress Couples
174 Equations of Equilibrium of Laterally Loaded Thin Plates
175 Boundary Conditions
176 Some Simple Solutions of Lagrange's Equation
177 Simply Supported Rectangular Plate. Navier's Solution
178 Elliptic Plate with Clamped Edges under Uniform Load
179 Bending of Circular Plates
1710 Strain Energy and Potential Energy of a Thin Plate in Bending
1711 Application of the Principle of Minimum Potential Energy to Simply Supported Rectangular Plates
Problems
Chapter 18 Introduction to the Theory of Thin Shells
181 Introduction
182 Space Curves
183 Elements of the Theory of Surfaces 1) Gaussian surface coordinates. First fundamental form. 2) Second fundamental form. 3) Curvature of a normal section. Meunier's theorem. 4) Principal directions and lines of curvature. 5) Principal curvatures, first and second curvatures. 6) Euler's theorem. 7) Rate of change of the vectors a, and the corresponding unit vectors along the parametric lines. 8) The GaussCodaizi conditions. 9) Application to surfaces of revolution. 10) Important remarks.
184 Basic Assumptions and Reference System of Coordinates
185 StrainDisplacement Relations
186 Stress Resultants and Stress Couples
187 Equations of Equilibrium of Loaded Thin Shells
188 Boundary Conditions
189 Membrane Theory of Shells
1810 Membrane Shells of Revolution
1811 Membrane Theory of Cylindrical Shells
1812 General Theory of Circular Cylindrical Shells
1813 Circular Cylindrical Shell Loaded Symmetrically with Respect to its Axis Problems
Chapter 19 Solutions of Elasticity Problems by Means of Complex Variables
191 Introduction
192 Complex Variables and Complex Functions: A Short Review
193 Line Integrals of Complex Functions. Cauchy's Integral Theorem
194 Cauchy's Integral Formula
195 Taylor Series
196 Laurent Series, Residues and Cauchy 's Residue Theorem
197 Singular Points of an Analytic Function
198 Evaluation of Residues
199 Conformal Representation or Conformal Mapping
1910 Examples of Mapping by Elementary Functions
1911 The Theorem of Harnack and the Formulas of Schwarz and Poisson
1912 Torsion of Prismatic Bars Using Complex Variables
1913 Torsion of Prismatic Bars with Various Shapes
1914 The Plane Stress and Strain Problems and the Solution to the Biharmonic Equation 1) Displacements and stresses. 2) Boundary conditions. 3) The structure of the functions +(i)and ~(7.) in simply connected regions. 4) The structure of the functions +(z) and ~(z)in finite, multiply connected regions. 5) The structure of the functions +(z) and ~(z)in infinite, multiply connected regions. 6) The first and second boundary value problems in plane elasticity. 7) Displacements and stresses in curvilinear coordinates. 8) Conformal mapping for plane problems. 9) Solution by means of power series for simply connected regions. 10) Mapping of infinite regions.
1915 Solutions Using Timoshenko's Equations. Westergaard's Stress Function
1916 Simple Examples Using Complex Potentials
1917 The Infinite Plate with a Circular Hole
1918 The Infinite Plate under the Action of a Concentrated Force and Moment
1919 The Infinite Plate with an Elliptic Hole Subjected to a Tensile Stress Normal to the Major Principal Axis of the Ellipse
1920 Infinite Plate with an Elliptic Hole Subjected to a Uniform all around Tension S
1921 Conformal Mapping Applied to the Problem of the Elliptic Hole
1922 Infinite Plate with an Elliptic Hole Subjected to a Uniform Pressure P
1923 Application to Fracture Mechanics
References
Appendices
Addendum: Comments and Detailed Explanations. Additional Solved Examples. Additional Problems.
Index
