Elasticity : Theory, Applications, and Numerics.

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.

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.

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.

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