Preface
Part I Kinematics of Continuous Media (Displacement, Deformation, Strain)
Chapter 1 Introduction to the Kinematics of Continuous Media
1-1 Formulation of the Problem
1-2 Notation
Chapter 2 Review of Matrix Algebra
2-1 Introduction
2-2 Definition of a Matrix. Special Matrices
2-3 Index Notation and Summation Convention
2-4 Equality of Matrices. Addition and Subtraction
2-5 Multiplication of Matrices
2-6 Matrix Division. The Inverse Matrix
Problems
Chapter 3 Linear Transformation of Points
3-1 Introduction
3-2 Definitions and Elementary Operations
3-3 Conjugate and Principal Directions and Planes in a Linear Transformation
3-4 Orthogonal Transformations
3-5 Changes of Axes in a Linear Transformation
3-6 Characteristic Equations and Eigenvalues
3-7 Invariants of the Transformation Matrix in a Linear Transformation
3-8 Invariant Directions of a Linear Transformation
3-9 Antisymmetric Linear Transformations
3-10 Symmetric Transformations. Definitions and General Theorems
3-11 Principal Directions and Principal Unit Displacements of a Symmetric Transformation
3-12 Quadratic Forms
3-13 Normal and Tangential Displacements in a Symmetric Transformation. Mohr's Representation
3-14 Spherical Dilatation and Deviation in a Linear Symmetric Transformation
3-15 Geometrical Meaning of the aij'S in a Linear Symmetric Transformation
3-16 Linear Symmetric Transformation in Two Dimensions
Problems
Chapter 4 General Analysis of Strain in Cartesian Coordinates
4-1 Introduction
4-2 Changes in Length and Directions of Elements Initially Parallel to the Coordinate Axes
4-3 Components of the State of Strain at a Point
4-4 Geometrical Meaning of the Strain Components εij. Strain of a Line Element
4-5 Components of the State of Strain under a Change of Coordinate System
4-6 Principal Axes of Strain
4-7 Volumetric Strain
4-8 Small Strain
4-9 Linear Strain
4-10 Compatibility Relations for Linear Strains
Problems
Chapter 5 Cartesian Tensors
5-1 Introduction
5-2 Scalars and Vectors
5-3 Higher Rank Tensors
5-4 On Tensors and Matrices
5-5 The Kronecker Delta and the Alternating Symbol. Isotropic Tensors
5-6 Function of a Tensor. Invariants
5-7 Contraction
5-8 The Quotient Rule of Tensors
Problems
Chapter 6 Orthogonal Curvilinear Coordinates
6-1 Introduction
6-2 Curvilinear Coordinates
6-3 Metric Coefficients
6-4 Gradient, Divergence, Curl, and Laplacian in Orthogonal Curvilinear Coordinates
6-5 Rate of Change of the Vectors āi and of the Unit Vectors ēi in an Orthogonal Curvilinear Coordinate System
6-6 The Strain Tensor in Orthogonal Curvilinear Coordinates
6-7 Strain-Displacement Relations in Orthogonal Curvilinear Coordinates
6-8 Components of the Rotation in Orthogonal Curvilinear Coordinates
6-9 Equations of Compatibility for Linear Strains in Orthogonal Curvilinear Coordinates
Problems
Part II Theory of Stress
Chapter 7 Analysis of Stress
7-1 Introduction
7-2 Stress on a Plane at a Point. Notation and Sign Convention
7-3 State of Stress at a Point. The Stress Tensor
7-4 Equations of Equilibrium. Symmetry of the Stress Tensor. Boundary Conditions
7-5 Application of the Properties of Linear Symmetric Transformations to the Analysis of Stress
7-6 Stress Quadric
7-7 Further Graphical Representations of the State of Stress at a Point. Stress Ellipsoid. Stress Director Surface
7-8 The Octahedral Normal and Octahedral Shearing Stresses
7-9 The Haigh-Westergaard Stress Space
7-10 Components of the State of Stress at a Point in a Change of Coordinates
7-11 Stress Analysis in Two Dimensions
7-12 Equations of Equilibrium in Orthogonal Curvilinear Coordinates
Problems
Part III The Theory of Elasticity Applications to Engineering Problems
Chapter 8 Elastic Stress-Strain Relations and Formulation of Elasticity Problems
8-1 Introduction
8-2 Work, Energy, and the Existence of a Strain Energy Function
8-3 The Generalized Hooke's Law
8-4 Elastic Symmetry
8-5 Elastic Stress-Strain Relations for Isotropic Media
8-6 Thermoelastic Stress-Strain Relations for Isotropic Media
8-7 Strain Energy Density
8-8 Formulation of Elasticity Problems. Boundary-Value Problems of Elasticity
8-9 Elasticity Equations in Terms of Displacements
8-10 Elasticity Equations in Terms of Stresses
8-11 The Principle of Superposition
8-12 Existence and Uniqueness of the Solution of an Elasticity Problem
8-13 Saint-Venant's Principle
8-14 One Dimensional Elasticity
8-15 Plane Elasticity
8-16 State of Plane Strain
8-17 State of Plane Stress
8-18 State of Generalized Plane Stress
8-19 State of Generalized Plane Strain
8-20 Solution of Elasticity Problems
Problems
Chapter 9 Solution of Elasticity Problems by Potentials
9-1 Introduction
9-2 Some Results of Field Theory
9-3 The Homogeneous Equations of Elasticity and the Search for Particular Solutions
9-4 Scalar and Vector Potentials. Lame's Strain Potential
9-5 The Galerkin Vector. Love's Strain Function. Kelvin's and Cerruti's Problems
9-6 The Neuber-Papkovich Representation. Boussinesq's Problem
9-7 Summary of Displacement Functions
9-8 Stress Functions
9-9 Airy's Stress Function for Plane Strain Problems
9-10 Airy's Stress Function for Plane Stress Problems
9-11 Forms of Airy's Stress Function
Problems
Chapter 10 The Torsion Problem
10-1 Introduction
10-2 Torsion of Circular Prismatic Bars
10-3 Torsion of Non-Circular Prismatic Bars
10-4 Torsion of an Elliptic Bar
10-5 Prandtl's Stress Function
10-6 Two Simple Solutions Using Prandtl's Stress Function
10-7 Torsion of Rectangular Bars
10-8 Prandtl's Membrane Analogy
10-9 Application of the Membrane Analogy to Solid Sections
10-10 Application of the Membrane Analogy to Thin Tubular Members
10-11 Application of the Membrane Analogy to Multicellular Thin Sections
10-12 Torsion of Circular Shafts of Varying Cross Section
10-13 Torsion of Thin-Walled Members of Open Section in which some Cross Section is Prevented from Warping
A-10-1 The Green-Riemann Formula
Problems
Chapter 11 Thick Cylinders, Disks, and Spheres
11-1 Introduction
11-2 Hollow Cylinder with Internal and External Pressures and Free Ends
11-3 Hollow Cylinder with Internal and External Pressures and Fixed Ends
11-4 Hollow Sphere Subjected to Internal and External Pressures
11-5 Rotating Disks of Uniform Thickness
11-6 Rotating Long Circular Cylinder
11-7 Disks of Variable Thickness
11-8 Thermal Stresses in Thin Disks
11-9 Thermal Stresses in Long Circular Cylinders
11-10 Thermal Stresses in Spheres
Problems
Chapter 12 Straight Simple Beams
12-1 Introduction
12-2 The Elementary Theory of Beams
12-3 Pure Bending of Prismatical Bars
12-4 Bending of a Narrow Rectangular Cantilever by an End Load
12-5 Bending of a Narrow Rectangular Beam by a Uniform Load
12-6 Cantilever Prismatic Bar of Irregular Cross Section Subjected to a Transverse End Force
12-7 Shear Center
Problems
Chapter 13 Curved Beams
13-1 Introduction
13-2 The Simplified Theory of Curved Beams
13-3 Pure Bending of Circular Arc Beams
13-4 Circular Arc Cantilever Beam Bent by a Force at the End
Problems
Chapter 14 The Semi-Infinite Elastic Medium and Related Problems
14-1 Introduction
14-2 Uniform Pressure Distributed over a Circular Area on the Surface of a Semi-Infinite Solid
14-3 Uniform Pressure Distributed over a Rectangular Area
14-4 Rigid Die in the Form of a Circular Cylinder
14-5 Vertical Line Load on a Semi-Infinite Elastic Medium
14-6 Vertical Line Load on a Semi-Infinite Elastic Plate
14-7 Tangential Line Load at the Surface of a Semi-Infinite Elastic Medium
14-8 Tangential Line Load on a Semi-Infinite Elastic Plate
14-9 Uniformly Distributed Vertical Pressure on Part of the Boundary of a Semi-Infinite Elastic Medium
14-10 Uniformly Distributed Vertical Pressure on Part of the Boundary of a Semi-Infinite Elastic Plate
14-11 Rigid Strip at the Surface of a Semi-Infinite Elastic Medium
14-12 Rigid Die at the Surface of a Semi-Infinite Elastic Plate
14-13 Radial Stresses in Wedges
14-14 M. Levy's Problems of the Triangular and Rectangular Retaining Walls
Chapter 15 Energy Principles and Introduction To Variational Methods
15-1 Introduction
15-2 Work, Strain and Complementary Energies. Clapeyron's Law
15-3 Principle of Virtual Work
15-4 Variational Problems and Euler's Equations
15-5 The Reciprocal Laws of Betti and Maxwell
15-6 Principle of Minimum Potential Energy
15-7 Castigliano's First Theorem
15-8 Principle of Virtual Complementary Work
15-9 Principle of Minimum Complementary Energy
15-10 Castigliano's Second Theorem
15-11 Theorem of Least Work
15-12 Summary of Energy Theorems
15-13 Working Form of the Strain Energy for Linearly Elastic Slender Members
15-14 Strain Energy of a Linearly Elastic Slender Member in Terms of the Unit Displacements of the Centroid G and of the Unit Rotations
15-15 A Working Form of the Principles of Virtual Work and of Virtual Complementary Work for a Linearly Elastic Slender Member
15-16 Examples of Application of the Theorems of Virtual Work and Virtual Complementary Work
15-17 Examples of Application of Castigliano's First and Second Theorems
15-18 Examples of Application of the Principles of Minimum Potential Energy and Minimum Complementary Energy
15-19 Example of Application of the Theorem of Least Work
15-20 The Rayleigh-Ritz Method
Problems
Chapter 16 Elastic Stability: Columns and Beam-Columns
16-1 Introduction
16-2 Differential Equations of Columns and Beam-Columns
16-3 Simple Columns
16-4 Energy Solution of the Buckling Problem
16-5 Examples of Calculation of Buckling Loads by the Energy Method
16-6 Combined Compression and Bending
16-7 Lateral Buckling of Thin Rectangular Beams
Problems
Chapter 17 Bending of Thin Flat Plates
17-1 Introduction and Basic Assumptions. Strains and Stresses
17-2 Geometry of Surfaces with Small Curvatures
17-3 Stress Resultants and Stress Couples
17-4 Equations of Equilibrium of Laterally Loaded Thin Plates
17-5 Boundary Conditions
17-6 Some Simple Solutions of Lagrange's Equation
17-7 Simply Supported Rectangular Plate. Navier's Solution
17-8 Elliptic Plate with Clamped Edges under Uniform Load
17-9 Bending of Circular Plates
17-10 Strain Energy and Potential Energy of a Thin Plate in Bending
17-11 Application of the Principle of Minimum Potential Energy to Simply Supported Rectangular Plates
Problems
Chapter 18 Introduction to the Theory of Thin Shells
18-1 Introduction
18-2 Space Curves
18-3 Elements of the Theory of Surfaces
18-4 Basic Assumptions and Reference System of Coordinates
18-5 Strain-Displacement Relations
18-6 Stress Resultants and Stress Couples
18-7 Equations of Equilibrium of Loaded Thin Shells
18-8 Boundary Conditions
18-9 Membrane Theory of Shells
18-10 Membrane Shells of Revolution
18-11 Membrane Theory of Cylindrical Shells
18-12 General Theory of Circular Cylindrical Shells
18-13 Circular Cylindrical Shell Loaded Symmetrically with Respect to Its Axis
Problems
Index