Elasticity in Engineering Mechanics / Edition 3

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Overview

Elasticity in Engineering Mechanics has been prized by many aspiring and practicing engineers as an easy-to-navigate guide to an area of engineering science that is fundamental to aeronautical, civil, and mechanical engineering, and to other branches of engineering. With its focus not only on elasticity theory, including nano- and biomechanics, but also on concrete applications in real engineering situations, this acclaimed work is a core text in a spectrum of courses at both the undergraduate and graduate levels, and a superior reference for engineering professionals.

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Editorial Reviews

From the Publisher
"Designers can utilize the contents of this book to understand the value as well as the limitations of the data." (Corrosion Review, August 2002)
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Product Details

  • ISBN-13: 9780470402559
  • Publisher: Wiley
  • Publication date: 12/21/2010
  • Edition description: New Edition
  • Edition number: 3
  • Pages: 656
  • Sales rank: 1,422,319
  • Product dimensions: 6.30 (w) x 9.40 (h) x 1.50 (d)

Meet the Author

Arthur P. Boresi, PhD, Fellow of AAM, ASME, ASCE, isProfessor Emeritus in the MechanicalScience and EngineeringDepartment at the University of Illinois at Urbana–Champaign,where he has taught for more than twenty years, and the Departmentof Civil and Architectural Engineering at the University of Wyomingin Laramie. He has published over 100 refereed papers and is thesenior author of a number of books, including ApproximateSolution Methods in Engineering Mechanics and AdvancedMechanics of Materials (Wiley).

Ken P. Chong, PhD, PE, Fellow of AAM, ASME, SEM,DistMASCE, is a Professor at The George Washington University andan associate at NIST. He has been an interim divisiondirector,engineering advisor, and director of the mechanics andmaterials for a total of twenty-one years at the U.S. NationalScience Foundation. He has published over 200 refereed papers, andis the author or coauthor of twelve books including IntelligentStructures, Modeling and Simulation-Based Life CycleEngineering, and Materials for the New Millennium. He hastaught at the Universities of Wyoming, Hong Kong, and Houston, inaddition to being a visiting professor at MIT and University ofWashington.

James D. Lee, PhD, PE, Fellow of ASME, is a Professor atThe George Washington University teaching in the areas of continuummechanics, nanomechanics, fracture mechanics, and finite elementmethods. He has been a researcher at General Tire and RubberCompany, NIST, and NASA, and has published over 100 journal papersand many conference papers. He also coauthored the book MeshlessMethods in Solid Mechanics. He received the School ofEngineering and Applied Science at GWU Distinguished ResearcherAward.

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Table of Contents

Preface.

CHAPTER 1 INTRODUCTORY CONCEPTS AND MATHEMATICS.

Part I Introduction.

1-1 Trends and Scopes.

1-2 Theory of Elasticity.

1-3 Numerical Stress Analysis.

1-4 General Solution of the Elasticity.

1-5 Experimental Stress Analysis.

1-6 Boundary Value Problems of Elasticity.

Part II Preliminary Concepts.

1-7 Brief Summary of Vector Algebra.

1-8 Scalar Point Functions.

1-9 Vector Fields.

1-10 Differentiation of Vectors.

1-11 Differentiation of a Scalar Field.

1-12 Differentiation of a Vector Field.

1-13 Curl of a Vector Field.

1-14 Eulerian Continuity Equation for Fluids.

1-15 Divergence Theorem.

1-16 Divergence Theorem in Two Dimensions.

1-17 Line and Surface Integrals (Application of ScalarProduct).

1-18 Stokes's Theorem.

1-19 Exact Differential.

1-20 Orthogonal Curvilinear Coordiantes in Three-DimensionalSpace.

1-21 Expression for Differential Length in OrthogonalCurvilinear Coordinates.

1-22 Gradient and Laplacian in Orthogonal CurvilinearCoordinates.

Part III Elements of Tensor Algebra.

1-23 Index Notation: Summation Convention.

1-24 Transformation of Tensors under Rotation of RectangularCartesian Coordinate System.

1-25 Symmetric and Antisymmetric Parts of a Tensor.

1-26 Symbols dij and ijk (the Kronecker Delta andthe Alternating Tensor).

1-27 Homogeneous Quadratic Forms.

1-28 Elementary Matrix Algebra.

1-29 Some Topics in the Calculus of Variations.

CHAPTER 2 THEORY OF DEFORMATION.

2-1 Deformable, Continuous Media.

2-2 Rigid-Body Displacements.

2-3 Deformation of a Continuous Region. Material Variables.Spatial Variables.

2-4 Restrictions on Continuous Deformation of a DeformableMedium.

2-5 Gradient of the Displacement Vector. Tensor Quantity.

2-6 Extension of an Infinitesimal Line Element.

2-7 Physical Significance of ii. Strain Definitions.

2-8 Final Direction of Line Element. Definition of ShearingStrain. Physical Significance of ij(i ? j).

2-9 Tensor Character of . Strain Tensor.

2-10 Reciprocal Ellipsoid. Principal Strains. StrainInvariants.

2-11 Determination of Principal Strains. Principal Axes.

2-12 Determination of Strain Invariants. Volumetric Strain.

2-13 Rotation of a Volume Element. Relation to DisplacementGradients.

2-14 Homogeneous Deformation.

2-15 Theory of Small Strains and Small Angles of Rotation.

2-16 Compatibility Conditions of the Classical Theory of SmallDisplacements.

2-17 Additional Conditions Imposed by Continuity.

2-18 Kinematics of Deformable Media.

Appendix 2A Strain–Displacement Relations in OrthogonalCurvilinear Coordinates.

Appendix 2B Derivation of Strain–Displacement Relationsfor Special Coordinates by Cartesian Methods.

Appendix 2C Strain–Displacement Relations in GeneralCoordinates.

CHAPTER 3 THEORY OF STRESS.

3-1 Definition of Stress.

3-2 Stress Notation.

3-3 Summation of Moments. Stress at a Point. Stress on anOblique Plane.

3-4 Tensor Character of Stress. Transformation of StressComponents under Rotation of Coordinate Axes.

3-5 Principal Stresses. Stress Invariants. Extreme Values.

3-6 Mean and Deviator Stress Tensors. Octahedral Stress.

3-7 Approximations of Plane Stress. Mohr's Circles in Two andThree Dimensions.

3-8 Differential Equations of Motion of a Deformable BodyRelative to Spatial Coordinates.

Appendix 3A Differential Equations of Equilibrium in CurvilinearSpatial Coordinates.

Appendix 3B Equations of Equilibrium Including Couple Stress andBody Couple.

Appendix 3C Reduction of Differential Equations of Motion forSmall-Displacement Theory.

CHAPTER 4 THREE-DIMENSIONAL EQUATIONS OF ELASTICITY.

4-1 Elastic and Nonelastic Response of a Solid.

4-2 Intrinsic Energy Density Function (Adiabatic Process).

4-3 Relation of Stress Components to Strain Energy DensityFunction.

4-4 Generalized Hooke's Law.

4-5 Isotropic Media. Homogeneous Media.

4-6 Strain Energy Density for Elastic Isotropic Medium.

4-7 Special States of Stress.

4-8 Equations of Thermoelasticity.

4-9 Differential Equation of Heat Conduction.

4-10 Elementary Approach to Thermal-Stress Problem in One andTwo Variables.

4-11 Stress–Strain–Temperature Relations.

4-12 Thermoelastic Equations in Terms of Displacement.

4-13 Spherically Symmetrical Stress Distribution (TheSphere).

4-14 Thermoelastic Compatibility Equations in Terms ofComponents of Stress and Temperature. Beltrami–MichellRelations.

4-15 Boundary Conditions.

4-16 Uniqueness Theorem for Equilibrium Problem ofElasticity.

4-17 Equations of Elasticity in Terms of DisplacementComponents.

4-18 Elementary Three-Dimensional Problems of Elasticity.Semi-Inverse Method.

4-19 Torsion of Shaft with Constant Circular Cross Section.

4-20 Energy Principles in Elasticity.

4-21 Principle of Virtual Work.

4-22 Principle of Virtual Stress (Castigliano's Theorem).

4-23 Mixed Virtual Stress–Virtual Strain Principles(Reissner’s Theorem).

Appendix 4A Application of the Principle of Virtual Work to aDeformable Medium (Navier–Stokes Equations).

Appendix 4B Nonlinear Constitutive Relationships.

Appendix 4C Micromorphic Theory.

Appendix 4D Atomistic Field Theory.

CHAPTER 5 PLANE THEORY OF ELASTICITY IN RECTANGULAR CARTESIANCOORDINATES.

5-1 Plane Strain.

5-2 Generalized Plane Stress.

5-3 Compatibility Equation in Terms of Stress Components.

5-4 Airy Stress Function.

5-5 Airy Stress Function in Terms of Harmonic Functions.

5-6 Displacement Components for Plane Elasticity.

5-7 Polynomial Solutions of Two-Dimensional Problems inRectangular Cartesian Coordinates.

5-8 Plane Elasticity in Terms of Displacement Components.

5-9 Plane Elasticity Relative to Oblique Coordinate Axes.

Appendix 5A Plane Elasticity with Couple Stresses.

Appendix 5B Plane Theory of Elasticity in Terms of ComplexVariables.

CHAPTER 6 PLANE ELASTICITY IN POLAR COORDINATES.

6-1 Equilibrium Equations in Polar Coordinates.

6-2 Stress Components in Terms of Airy Stress Function F= F(r,0 ).

6-3 Strain–Displacement Relations in PolarCoordinates.

6-4 Stress–Strain–Temperature Relations.

6-5 Compatibility Equation for Plane Elasticity in Terms ofPolar Coordinates.

6-6 Axially Symmetric Problems.

6-7 Plane Elasticity Equations in Terms of DisplacementComponents.

6-8 Plane Theory of Thermoelasticity.

6-9 Disk of Variable Thickness and Nonhomogeneous AnisotropicMaterial.

6-10 Stress Concentration Problem of Circular Hole in Plate.

6-11 Examples.

Appendix 6A Stress–Couple Theory of Stress ConcentrationResulting from Circular Hole in Plate.

Appendix 6B Stress Distribution of a Diametrically CompressedPlane Disk.

CHAPTER 7 PRISMATIC BAR SUBJECTED TO END LOAD.

7-1 General Problem of Three-Dimensional Elastic Bars Subjectedto Transverse End Loads.

7-2 Torsion of Prismatic Bars. Saint-Venant's Solution. WarpingFunction.

7-3 Prandtl Torsion Function.

7-4 A Method of Solution of the Torsion Problem: Elliptic CrossSection.

7-5 Remarks on Solutions of the Laplace Equation, v2F =0.

7-6 Torsion of Bars with Tubular Cavities.

7-7 Transfer of Axis of Twist.

7-8 Shearing–Stress Component in Any Direction.

7-9 Solution of Torsion Problem by the Prandtl MembraneAnalogy.

7-10 Solution by Method of Series. Rectangular Section.

7-11 Bending of a Bar Subjected to Transverse End Force.

7-12 Displacement of a Cantilever Beam Subjected to TransverseEnd Force.

7-13 Center of Shear.

7-14 Bending of a Bar with Elliptic Cross Section.

7-15 Bending of a Bar with Rectangular Cross Section.

Appendix 7A Analysis of Tapered Beams.

CHAPTER 8 GENERAL SOLUTIONS OF ELASTICITY.

8-1 Introduction.

8-2 Equilibrium Equations.

8-3 The Helmholtz Transformation.

8-4 The Galerkin (Papkovich) Vector.

8-5 Stress in Terms of the Galerkin Vector F.

8-6 The Galerkin Vector: A Solution of the Equilibrium Equationsof Elasticity.

8-7 The Galerkin Vector kZ and Love's StrainFunction for Solids of Revolution.

8-8 Kelvin's Problem: Single Force Applied in the Interior of anInfinitely Extended Solid.

8-9 The Twinned Gradient and Its Application to Determine theEffects of a Change of Poisson's Ratio.

8-10 Solutions of the Boussinesq and Cerruti Problems by theTwinned Gradient Method.

8-11 Additional Remarks on Three-Dimensional StressFunctions.

References.

Bibliography.

INDEX.

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