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Elasticity: theory and applications /
Elasticity: Theory and Applications reviews the theory and applications of elasticity. The book is divided into three parts. The first part is concerned with the kinematics of continuous media; the second part focuses on the analysis of stress; and the third part considers the theory of elasticity a...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Pergamon Press,
[1974]
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| Colección: | Pergamon unified engineering series ;
16. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Elasticity Theory and Applications; Copyright Page; Table of Contents; Preface; Part I: KINEMATICS OF CONTINUOUS MEDIA; 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 Operations3-3 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 Representation3-14 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 Element4-5 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 Coordinates6-1 Introduction; 6-2 Curvilinear Coordinates; 6-3 Metric Coefficients; 6-4 Gradient, Divergence, Curl, and Laplacian in Orthogonal Curvilinear Coordinates; 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.