Elasticity
According to the author, elasticity may be viewed in many ways. For some, it is a dusty, classical subject . . . to others it is the paradise of mathematics." But, he concludes, the subject of elasticity is really "an entity itself," a unified subject deserving comprehensive treatment. He gives elasticity that full treatment in this valuable and instructive text. In his preface, Soutas-Little offers a brief survey of the development of the theory of elasticity, the major mathematical formulation of which was developed in the 19th century after the first concept was proposed by Robert Hooke in 1678. The theory was further refined in the 20th century as a means of solving the equations presented earlier.The book is divided into three major sections. The first section presents a review of mathematical notation and continuum mechanics, covering vectors and tensors, kinematics, stress, basic equations of continuum mechanics, and linear elasticity. The second section, on two-dimensional elasticity, treats the general theory of plane elasticity, problems in Cartesian coordinates, problems in polar coordinates, complex variable solutions, finite difference and finite element methods, and energy theorems and variational techniques. Section three discusses three-dimensional problems, and is devoted to Saint Venant torsion and bending theory, the Navier equation and the Galerkin vector, and the Papkovich-Neuber solution.Numerous illustrative figures and tables appear throughout the book, and valuable reference material is provided in the appendices on eigenfunction analysis, trigonometric functions, Fourier transforms, inverse transforms, complex variable formulae, Hankel transforms, and Bessel and Legendre functions.Instructors will find this an ideal text for a two-course sequence in elasticity; they can also use it as a basic introduction to the subject by selecting appropriate sections of each part.
1003386031
Elasticity
According to the author, elasticity may be viewed in many ways. For some, it is a dusty, classical subject . . . to others it is the paradise of mathematics." But, he concludes, the subject of elasticity is really "an entity itself," a unified subject deserving comprehensive treatment. He gives elasticity that full treatment in this valuable and instructive text. In his preface, Soutas-Little offers a brief survey of the development of the theory of elasticity, the major mathematical formulation of which was developed in the 19th century after the first concept was proposed by Robert Hooke in 1678. The theory was further refined in the 20th century as a means of solving the equations presented earlier.The book is divided into three major sections. The first section presents a review of mathematical notation and continuum mechanics, covering vectors and tensors, kinematics, stress, basic equations of continuum mechanics, and linear elasticity. The second section, on two-dimensional elasticity, treats the general theory of plane elasticity, problems in Cartesian coordinates, problems in polar coordinates, complex variable solutions, finite difference and finite element methods, and energy theorems and variational techniques. Section three discusses three-dimensional problems, and is devoted to Saint Venant torsion and bending theory, the Navier equation and the Galerkin vector, and the Papkovich-Neuber solution.Numerous illustrative figures and tables appear throughout the book, and valuable reference material is provided in the appendices on eigenfunction analysis, trigonometric functions, Fourier transforms, inverse transforms, complex variable formulae, Hankel transforms, and Bessel and Legendre functions.Instructors will find this an ideal text for a two-course sequence in elasticity; they can also use it as a basic introduction to the subject by selecting appropriate sections of each part.
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Elasticity

Elasticity

by Robert William Soutas-Little
Elasticity
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Elasticity

Elasticity

by Robert William Soutas-Little

Overview

According to the author, elasticity may be viewed in many ways. For some, it is a dusty, classical subject . . . to others it is the paradise of mathematics." But, he concludes, the subject of elasticity is really "an entity itself," a unified subject deserving comprehensive treatment. He gives elasticity that full treatment in this valuable and instructive text. In his preface, Soutas-Little offers a brief survey of the development of the theory of elasticity, the major mathematical formulation of which was developed in the 19th century after the first concept was proposed by Robert Hooke in 1678. The theory was further refined in the 20th century as a means of solving the equations presented earlier.The book is divided into three major sections. The first section presents a review of mathematical notation and continuum mechanics, covering vectors and tensors, kinematics, stress, basic equations of continuum mechanics, and linear elasticity. The second section, on two-dimensional elasticity, treats the general theory of plane elasticity, problems in Cartesian coordinates, problems in polar coordinates, complex variable solutions, finite difference and finite element methods, and energy theorems and variational techniques. Section three discusses three-dimensional problems, and is devoted to Saint Venant torsion and bending theory, the Navier equation and the Galerkin vector, and the Papkovich-Neuber solution.Numerous illustrative figures and tables appear throughout the book, and valuable reference material is provided in the appendices on eigenfunction analysis, trigonometric functions, Fourier transforms, inverse transforms, complex variable formulae, Hankel transforms, and Bessel and Legendre functions.Instructors will find this an ideal text for a two-course sequence in elasticity; they can also use it as a basic introduction to the subject by selecting appropriate sections of each part.

Product Details

ISBN-13: 9780486150079
Publisher: Dover Publications
Publication date: 03/29/2012
Series: Dover Books on Physics
Sold by: Barnes & Noble
Format: eBook
Pages: 464
File size: 31 MB
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About the Author

A founding member of the American Society of Biomechanics, Robert William Soutas-Little is Professor Emeritus in the Department of Mechanical Engineering and the Department of Materials Science and Mechanics at Michigan State University.

Table of Contents

PrefacePart I Review of Mathematical Notation and Continuum MechanicsBasic Equations of the Linear Theory of Elasticity1 Vectors and Tensors 1. Notation 2. Vectors 3. Transformation Relations 3.1 Scalars 3.2 Vectors 3.3 Properties of the transformation matrix 4. Second Order Tensors 5. Higher Order Tensors 6. Dual Vector of an Antisymetric Tensor 7. Eigenvalue Problem 8. Isotropic Tensors 9. Tensor Fields 10. Integral Theorems 11. Classification of Vector Fields2. Kinematics 1. Introduction 2. Spatial and Material Coordinates 3. Velocity and Material Time Derivative 4. Volume Elements 5. Reynold's Transport Theorem 6. Displacement Vector 7. Compatibility Equation 8. Infinitesimal Strain Tensor in Curvilinear Coordinates 9. Spherical and Deviatroic Strain Tensors3. Stress 1. Introduction 2. Stress Tractions 3. Stress Tensor in the Material Sense 4. Properties of the Stress Tensor4. Basic Equations of Continuum Mechanics 1. Introduction 2. Conservation of Mass 3. Cauchy's Equations of Motion 4. Considerations of Angular Momentum 5. Energy Conservation Equation5. Linear Elasticity 1. Introduction 2. Geranlized Hooke's Law 3. Summary of the Equations of Isotropic Elasticity 4. Boundary Conditions 5. Uniqueness and Superposition 6. Saint-Venant's Principle 7. Displacement Formulation 8. ThermoelasticityPart II Two-Dimensional Elasticity6 General Theory of Plane Elasticity 1. Introduction 2. Plane Deformation or Plane Strain 3. Plane Stress 4. Biharmonic Solutions7 Problems in Cartesian Coordinates 1. Introduction 2. Mathematical Preliminaries 3. Polynomial Solutions 3.1 Uniaxial tension 3.2 Simply supported beam under pure moments 3.3 Beam bent by its own weight 4. Fourier Series Solutions 4.1 Beam subjected to sinusoidal load 5. Fourier Analysis 5.1 Fourier trigonometric series 6. General Fourier Solution of Elasticity Problem 6.1 Case 4-odd in x and even in y 6.2 Displacement solution using Marguerre function 7. Multiple Fourier Analysis 8. Problems Involving Infinite or Semi-Infinite Dimensions 8.1 Infinite strip loaded by uniform pressure 8.2 Fourier transform solutions 8.3 Solution of the infinite strip problem using integral transforms 8.4 Semi-infinite strip problems 8.5 Solution for the half-plane 9. Saint-Venant Boundary Region in Elastic Strips 10. Nonorthogonal Boundary Function Expansions 10.1 Point-matching 10.2 Least squares 10.3 Iterative improvements to point-matching techniques 11. Plane Elasticity Problems Using Nonorthogonal Functions 11.1 Examples requring functions nonorthogonal on the boundaries8 Problems in Polor Coordinates 1. Introduction 2. Axially Symmetric Problems 2.1 Lamé problem 2.2 Pure bending of a curved beam 2.3 Rotational dislocation 3. Solution of Axisymmetric Problems Using the Navier Equation 4. Michell Solution 5. Examples Using the Michell Solution 5.1 Interior problem-stresses distributed around the edge of a disk 5.2 Exterior problem-infinite plane with circular hole 5.3 Annulus problem 5.4 Symmetry conditions 6. General Solutions Not Involving Orthogonal Functions 7. Wedge Problem 7.1 Wedge under uniform side load 7.2 Stress singularities at the tip of a wedge (M.L. williams solution) 7.3 Truncated semi-infinite wedge 8. Special Problems Using the Flamant Solution 8.1 Concentrated load in hole in infinite plate9 Complex Variable Solutions 1. Introduction 2. Complex Variables 3. Complex Stress Formulation 4. Polar Coordinates 5. Interior Problem 6. Conformal Transformations10 Finite Difference and Finite Element Methods 1. Introduction 2. Finite Element Method 3. Displacement Functions 4. Stresses and Strains 5. Nodal Force-Displacement Relations 6. Analysis of a Structure 7. Facet Stiffness Matrix 8. Local and Global Coordinates 9. Finite Element Example 10.
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