Elasticity - Theory, Applications, and Numerics (2nd Edition)
Elasticity is concerned with determining the strength and load carrying ability of engineering structures including buildings, bridges, cars, planes, and thousands of machine parts that most of us never see. It is especially important in the fields of mechanical, civil, aeronautical and materials en...
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| Hlavní autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier
2009
Elsevier, Academic Press Elsevier Science & Technology Academic Press |
| Vydání: | 2 |
| Témata: | |
| ISBN: | 0123744466, 9780123744463, 0124081363, 9780124081369 |
| On-line přístup: | Získat plný text |
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- Front Matter Preface Table of Contents Part I. Foundations and Elementary Applications 1. Mathematical Preliminaries 2. Deformation: Displacements and Strains 3. Stress and Equilibrium 4. Material Behavior - Linear Elastic Solids 5. Formulation and Solution Strategies 6. Strain Energy and Related Principles 7. Two-Dimensional Formulation 8. Two-Dimensional Problem Solution 9. Extension, Torsion, and Flexure of Elastic Cylinders Part II. Advanced Applications 10. Complex Variable Methods 11. Anisotropic Elasticity 12. Thermoelasticity 13. Displacement Potentials and Stress Functions 14. Nonhomogeneous Elasticity 15. Micromechanics Applications 16. Numerical Finite and Boundary Element Methods Appendices Index
- Index
- 11.6 Applications to Fracture Mechanics -- 11.7 Curvilinear Anisotropic Problems -- Chapter 12. Thermoelasticity -- 12.1 Heat Conduction and the Energy Equation -- 12.2 General Uncoupled Formulation -- 12.3 Two-Dimensional Formulation -- 12.4 Displacement Potential Solution -- 12.5 Stress Function Formulation -- 12.6 Polar Coordinate Formulation -- 12.7 Radially Symmetric Problems -- 12.8 Complex Variable Methods for Plane Problems -- Chapter 13. Displacement Potentials and Stress Functions -- 13.1 Helmholtz Displacement Vector Representation -- 13.2 Lamé's Strain Potential -- 13.3 Galerkin Vector Representation -- 13.4 Papkovich-Neuber Representation -- 13.5 Spherical Coordinate Formulations -- 13.6 Stress Functions -- Chapter 14. Nonhomogeneous Elasticity -- 14.1 Basic Concepts -- 14.2 Plane Problem of Hollow Cylindrical Domain under Uniform Pressure -- 14.3 Rotating Disk Problem -- 14.4 Point Force on the Free Surface of a Half-Space -- 14.5 Antiplane Strain Problems -- 14.6 Torsion Problem -- Chapter 15. Micromechanics Applications -- 15.1 Dislocation Modeling -- 15.2 Singular Stress States -- 15.3 Elasticity Theory with Distributed Cracks -- 15.4 Micropolar/Couple-Stress Elasticity -- 15.5 Elasticity Theory with Voids -- 15.6 Doublet Mechanics -- Chapter 16. Numerical Finite and Boundary Element Methods -- 16.1 Basics of the Finite Element Method -- 16.2 Approximating Functions for Two-Dimensional Linear Triangular Elements -- 16.3 Virtual Work Formulation for Plane Elasticity -- 16.4 FEM Problem Application -- 16.5 FEM Code Applications -- 16.6 Boundary Element Formulation -- Appendix A Basic Field Equations in Cartesian, Cylindrical, and Spherical Coordinates -- Appendix B Transformation of Field Variables Between Cartesian, Cylindrical, and Spherical Components -- Appendix C MATLAB Primer -- Appendix D Review of Mechanics of Materials
- 6.2 Uniqueness of the Elasticity Boundary-Value Problem -- 6.3 Bounds on the Elastic Constants -- 6.4 Related Integral Theorems -- 6.5 Principle of Virtual Work -- 6.6 Principles of Minimum Potential and Complementary Energy -- 6.7 Rayleigh-Ritz Method -- Chapter 7. Two-Dimensional Formulation -- 7.1 Plane Strain -- 7.2 Plane Stress -- 7.3 Generalized Plane Stress -- 7.4 Antiplane Strain -- 7.5 Airy Stress Function -- 7.6 Polar Coordinate Formulation -- Chapter 8. Two-Dimensional Problem Solution -- 8.1 Cartesian Coordinate Solutions Using Polynomials -- 8.2 Cartesian Coordinate Solutions Using Fourier Methods -- 8.3 General Solutions in Polar Coordinates -- 8.4 Example Polar Coordinate Solutions -- Chapter 9. Extension, Torsion, and Flexure of Elastic Cylinders -- 9.1 General Formulation -- 9.2 Extension Formulation -- 9.3 Torsion Formulation -- 9.4 Torsion Solutions Derived from Boundary Equation -- 9.5 Torsion Solutions Using Fourier Methods -- 9.6 Torsion of Cylinders with Hollow Sections -- 9.7 Torsion of Circular Shafts of Variable Diameter -- 9.8 Flexure Formulation -- 9.9 Flexure Problems without Twist -- PART II: ADVANCED APPLICATIONS -- Chapter 10. Complex Variable Methods -- 10.1 Review of Complex Variable Theory -- 10.2 Complex Formulation of the Plane Elasticity Problem -- 10.3 Resultant Boundary Conditions -- 10.4 General Structure of the Complex Potentials -- 10.5 Circular Domain Examples -- 10.6 Plane and Half-Plane Problems -- 10.7 Applications Using the Method of Conformal Mapping -- 10.8 Applications to Fracture Mechanics -- 10.9 Westergaard Method for Crack Analysis -- Chapter 11. Anisotropic Elasticity -- 11.1 Basic Concepts -- 11.2 Material Symmetry -- 11.3 Restrictions on Elastic Moduli -- 11.4 Torsion of a Solid Possessing a Plane of Material Symmetry -- 11.5 Plane Deformation Problems
- Front Cover -- Elasticity: Theory, Applications, and Numerics -- Copyright Page -- Contents -- Preface -- About the Author -- PART I: FOUNDATIONS AND ELEMENTARY APPLICATIONS -- Chapter 1. Mathematical Preliminaries -- 1.1 Scalar, Vector, Matrix, and Tensor Definitions -- 1.2 Index Notation -- 1.3 Kronecker Delta and Alternating Symbol -- 1.4 Coordinate Transformations -- 1.5 Cartesian Tensors -- 1.6 Principal Values and Directions for Symmetric Second-Order Tensors -- 1.7 Vector, Matrix, and Tensor Algebra -- 1.8 Calculus of Cartesian Tensors -- 1.9 Orthogonal Curvilinear Coordinates -- Chapter 2. Deformation: Displacements and Strains -- 2.1 General Deformations -- 2.2 Geometric Construction of Small Deformation Theory -- 2.3 Strain Transformation -- 2.4 Principal Strains -- 2.5 Spherical and Deviatoric Strains -- 2.6 Strain Compatibility -- 2.7 Curvilinear Cylindrical and Spherical Coordinates -- Chapter 3. Stress and Equilibrium -- 3.1 Body and Surface Forces -- 3.2 Traction Vector and Stress Tensor -- 3.3 Stress Transformation -- 3.4 Principal Stresses -- 3.5 Spherical, Deviatoric, Octahedral, and von Mises Stresses -- 3.6 Equilibrium Equations -- 3.7 Relations in Curvilinear Cylindrical and Spherical Coordinates -- Chapter 4. Material Behavior-Linear Elastic Solids -- 4.1 Material Characterization -- 4.2 Linear Elastic Materials-Hooke's Law -- 4.3 Physical Meaning of Elastic Moduli -- 4.4 Thermoelastic Constitutive Relations -- Chapter 5. Formulation and Solution Strategies -- 5.1 Review of Field Equations -- 5.2 Boundary Conditions and Fundamental Problem Classifications -- 5.3 Stress Formulation -- 5.4 Displacement Formulation -- 5.5 Principle of Superposition -- 5.6 Saint-Venant's Principle -- 5.7 General Solution Strategies -- Chapter 6. Strain Energy and Related Principles -- 6.1 Strain Energy
- 5.7 General solution strategies -- References -- Chapter 6 - Strain Energy and Related Principles -- 6.1 Strain energy -- 6.2 Uniqueness of the elasticity boundary-value problem -- 6.3 Bounds on the elastic constants -- 6.4 Related integral theorems -- 6.5 Principle of virtual work -- 6.6 Principles of minimum potential and complementary energy -- 6.7 Rayleigh-Ritz method -- References -- Chapter 7 - Two-Dimensional Formulation -- 7.1 Plane strain -- 7.2 Plane stress -- 7.3 Generalized plane stress -- 7.4 Antiplane strain -- 7.5 Airy stress function -- 7.6 Polar coordinate formulation -- References -- Chapter 8 - Two-Dimensional Problem Solution -- 8.1 Cartesian coordinate solutions using polynomials -- 8.2 Cartesian coordinate solutions using Fourier methods -- 8.3 General solutions in polar coordinates -- 8.4 Example polar coordinate solutions -- 8.5 Simple plane contact problems -- References -- Chapter 9 - Extension, Torsion, and Flexure of Elastic Cylinders -- 9.1 General formulation -- 9.2 Extension formulation -- 9.3 Torsion formulation -- 9.4 Torsion solutions derived from boundary equation -- 9.5 Torsion solutions using Fourier methods -- 9.6 Torsion of cylinders with hollow sections -- 9.7 Torsion of circular shafts of variable diameter -- 9.8 Flexure formulation -- 9.9 Flexure problems without twist -- References -- Part 2 - ADVANCED APPLICATIONS -- Chapter 10 - Complex Variable Methods -- 10.1 Review of complex variable theory -- 10.2 Complex formulation of the plane elasticity problem -- 10.3 Resultant boundary conditions -- 10.4 General structure of the complex potentials -- 10.5 Circular domain examples -- 10.6 Plane and half-plane problems -- 10.7 Applications using the method of conformal mapping -- 10.8 Applications to fracture mechanics -- 10.9 Westergaard method for crack analysis -- References
- Chapter 11 - Anisotropic Elasticity -- 11.1 Basic concepts -- 11.2 Material symmetry -- 11.3 Restrictions on elastic moduli -- 11.4 Torsion of a solid possessing a plane of material symmetry -- 11.5 Plane deformation problems -- 11.6 Applications to fracture mechanics -- 11.7 Curvilinear anisotropic problems -- References -- Chapter 12 - Thermoelasticity -- 12.1 Heat conduction and the energy equation -- 12.2 General uncoupled formulation -- 12.3 Two-dimensional formulation -- 12.4 Displacement potential solution -- 12.5 Stress function formulation -- 12.6 Polar coordinate formulation -- 12.7 Radially symmetric problems -- 12.8 Complex variable methods for plane problems -- References -- Chapter 13 - Displacement Potentials and Stress Functions: Applications to Three-Dimensional Problems -- 13.1 Helmholtz displacement vector representation -- 13.2 Lamé's strain potential -- 13.3 Galerkin vector representation -- 13.4 Papkovich-Neuber representation -- 13.5 Spherical coordinate formulations -- 13.6 Stress functions -- References -- Chapter 14 - Nonhomogeneous Elasticity -- 14.1 Basic concepts -- 14.2 Plane problem of a hollow cylindrical domain under uniform pressure -- 14.3 Rotating disk problem -- 14.4 Point force on the free surface of a half-space -- 14.5 Antiplane strain problems -- 14.6 Torsion problem -- References -- Chapter 15 - Micromechanics Applications -- 15.1 Dislocation modeling -- 15.2 Singular stress states -- 15.3 Elasticity theory with distributed cracks -- 15.4 Micropolar/couple-stress elasticity -- 15.5 Elasticity theory with voids -- 15.6 Doublet mechanics -- References -- Chapter 16 - Numerical Finite and Boundary Element Methods -- 16.1 Basics of the finite element method -- 16.2 Approximating functions for two-dimensional linear triangular elements -- 16.3 Virtual work formulation for plane elasticity
- Front Cover -- Elasticity: Theory, Applications, and Numerics -- Copyright -- Contents -- Preface -- Acknowledgments -- About the Author -- Part 1 - FOUNDATIONS AND ELEMENTARY APPLICATIONS -- Chapter 1 - Mathematical Preliminaries -- 1.1 Scalar, vector, matrix, and tensor definitions -- 1.2 Index notation -- 1.3 Kronecker delta and alternating symbol -- 1.4 Coordinate transformations -- 1.5 Cartesian tensors -- 1.6 Principal values and directions for symmetric second-order tensors -- 1.7 Vector, matrix, and tensor algebra -- 1.8 Calculus of Cartesian tensors -- 1.9 Orthogonal curvilinear coordinates -- References -- Chapter 2 - Deformation: Displacements and Strains -- 2.1 General deformations -- 2.2 Geometric construction of small deformation theory -- 2.3 Strain transformation -- 2.4 Principal strains -- 2.5 Spherical and deviatoric strains -- 2.6 Strain compatibility -- 2.7 Curvilinear cylindrical and spherical coordinates -- References -- Chapter 3 - Stress and Equilibrium -- 3.1 Body and surface forces -- 3.2 Traction vector and stress tensor -- 3.3 Stress transformation -- 3.4 Principal stresses -- 3.5 Spherical, deviatoric, octahedral, and von mises stresses -- 3.6 Stress distributions and contour lines -- 3.7 Equilibrium equations -- 3.8 Relations in curvilinear cylindrical and spherical coordinates -- References -- Chapter 4 - Material Behavior-Linear Elastic Solids -- 4.1 Material characterization -- 4.2 Linear elastic materials-Hooke's law -- 4.3 Physical meaning of elastic moduli -- 4.4 Thermoelastic constitutive relations -- References -- Chapter 5 - Formulation and Solution Strategies -- 5.1 Review of field equations -- 5.2 Boundary conditions and fundamental problem classifications -- 5.3 Stress formulation -- 5.4 Displacement formulation -- 5.5 Principle of superposition -- 5.6 Saint-Venant's principle
- 16.4 FEM problem application -- 16.5 FEM code applications -- 16.6 Boundary element formulation -- References -- Appendix A - Basic Field Equations in Cartesian, Cylindrical, and Spherical Coordinates -- Strain-displacement relations -- Equilibrium equations -- Hooke's law -- Equilibrium equations in terms of displacements (Navier's equations) -- Appendix B - Transformation of Field Variables between Cartesian, Cylindrical, and Spherical Components -- Cylindrical components from Cartesian -- Spherical components from cylindrical -- Spherical components from Cartesian -- APPENDIX C - MATLAB® Primer -- C.1 Getting started -- C.2 Examples -- Reference -- Appendix D - Review of Mechanics of Materials -- D.1 Extensional deformation of rods and beams -- D.2 Torsion of circular rods -- D.3 Bending deformation of beams under moments and shear forces -- D.4 Curved beams -- D.5 Thin-walled cylindrical pressure vessels -- Index