Elasticity

PrefacePart 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 eij. 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 ai and of the Unit Vectors ei 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 ProblemsPart 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.