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Elasticityby Robert Williams SoutasLittle
Synopses & ReviewsPlease note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Publisher Comments: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, SoutasLittle 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 twodimensional 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 threedimensional problems, and is devoted to Saint Venant torsion and bending theory, the Navier equation and the Galerkin vector, and the PapkovichNeuber 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 twocourse sequence in elasticity; they can also use it as a basic introduction to the subject by selecting appropriate sections of each part. Book News Annotation:A text for a twocourse sequence. Reviews continuum mechanics briefly, but assumes students to have completed a full course beforehand. Then covers the mathematical notation, the basic equations of the linear theory of elasticity, and elasticity in two and three dimensions. The 1973 edition was published by PrenticeHall.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:A comprehensive survey of the methods and theories of linear elasticity, this threepart introductory treatment covers general theory, twodimensional elasticity, and threedimensional elasticity. Ideal text for a twocourse sequence on elasticity. 1984 edition. Synopsis:This instructive volume offers a comprehensive survey of the methods and theories of linear elasticity. Three major sections cover general theory, twodimensional elasticity, and threedimensional elasticity. An ideal text for a twocourse sequence on elasticity, this volume can also introduce the subject in a more general math course. About the AuthorA founding member of the American Society of Biomechanics, Robert William SoutasLittle is Professor Emeritus in the Department of Mechanical Engineering and the Department of Materials Science and Mechanics at Michigan State University. Table of ContentsPreface
Part I Review of Mathematical Notation and Continuum Mechanics Basic Equations of the Linear Theory of Elasticity 1 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 Fields 2. 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 Tensors 3. Stress 1. Introduction 2. Stress Tractions 3. Stress Tensor in the Material Sense 4. Properties of the Stress Tensor 4. 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 Equation 5. 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. SaintVenant's Principle 7. Displacement Formulation 8. Thermoelasticity Part II TwoDimensional Elasticity 6 General Theory of Plane Elasticity 1. Introduction 2. Plane Deformation or Plane Strain 3. Plane Stress 4. Biharmonic Solutions 7 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 4odd in x and even in y 6.2 Displacement solution using Marguerre function 7. Multiple Fourier Analysis 8. Problems Involving Infinite or SemiInfinite 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 Semiinfinite strip problems 8.5 Solution for the halfplane 9. SaintVenant Boundary Region in Elastic Strips 10. Nonorthogonal Boundary Function Expansions 10.1 Pointmatching 10.2 Least squares 10.3 Iterative improvements to pointmatching techniques 11. Plane Elasticity Problems Using Nonorthogonal Functions 11.1 Examples requring functions nonorthogonal on the boundaries 8 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 problemstresses distributed around the edge of a disk 5.2 Exterior probleminfinite 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 semiinfinite wedge 8. Special Problems Using the Flamant Solution 8.1 Concentrated load in hole in infinite plate 9 Complex Variable Solutions 1. Introduction 2. Complex Variables 3. Complex Stress Formulation 4. Polar Coordinates 5. Interior Problem 6. Conformal Transformations 10 Finite Difference and Finite Element Methods 1. Introduction 2. Finite Element Method 3. Displacement Functions 4. Stresses and Strains 5. Nodal ForceDisplacement Relations 6. Analysis of a Structure 7. Facet Stiffness Matrix 8. Local and Global Coordinates 9. Finite Element Example 10. Finite Difference Methods 11 Energy Theorems and Variational Techniques 1. Introduction 2. Calculus of Variations 3. Strain Energy Methods 4. Theorem of Stationary Potential Energy 5. RayleighRitz Method 6. Energy Method for Problems Involving Multiply Connected Domains Part III ThreeDimensional Elasticity 12 SaintVenant Tension and Bending Theory 1. Torsion of Circular Cylinder 2. NonCircular Section 3. Uniqueness of SaintVenant Torsion Problem 4. SemiInverse ApproachProblems of SaintVenant 5. Torsion of Rectangular Bars Using Fourier Anaylsis 6. Prandtl Stress Functions 7. Solution of a Hollow Cylinder 8. Solution by Use of Orthogonal Series 9. Polar Coordinates 10. Nonorthogonal Functions on Boundary 11. Complex Variable Solutions of Torsion Problems 12. Membrane Anaogy for Torsion 13. Torsion of Circular Shafts of Variable Diameter 14. SaintVenant Approximation for Circular Cylinders 15. Flexure of Beams by Transverse End Loads 16. Flexure of a Circular Beam Under a Load Py Through the Centroid 13 Navier Equation and the Galerkin Vector 1. Solution of the Navier Equation in ThreeDimensional Elastostatics 2. Stress Functions 3. The Galerkin Vector 4. Equivalent Galerkin Vector 5. Mathematical Notes on the Galerkin Vector 6. Love's Strain Function 7. Long Solid Cylinders Axisymmetrically Loaded 8. Infinite Cylinder or Hole in an Elastic Body 9. Thick Axisymmetrically Loaded Plate 10. Axisymmetrically Loaded Plate with a Hole 11. Hankel Transform Methods 12. Axisymmetric Problem of a Half Space 13. Boussinesq Problem 14. Contact Problems 15. Short CylindersMultiple FourierBessel Series Analysis 16. EndLoading on a SemiInfinite Cylinder 17. Axisymmetric Torsion 18. Asymmetric Loadings 14 PapkovichNeuber Solution 1. Introduction 2. Concentrated Force in the Infinite Solid 3. Concentrated Load Not at the Origin 4. Other Special Singular Solutions 5. Concentrated Load Tangential to the Surface of the Half SpaceCerruti's Problem 6. Concentrated Loads at the Tip of an Elastic Cone 7. Symmetrically Loaded Spheres 8. Spherical Harmonics 9. The Internal Problem 10. Interior Problem with Body Forces 11. Gravitating Sphere 12. Rotating Sphere 13. The External Problem 14. Stress Concentration Due to a Spherical Cavity 15. Hollow Sphere 16. End Effects in a Truncated SemiInfinited Cone 17. General Solution of NonAxismmetric Problems by 6. Complex Variable Formulae 7. Bessel Functions 8. Hankel Transform 9. Legendre Functions What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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