Elsevier S & T

Elasticity: Theory, Applications, and Numerics

Sadd, Martin H.

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Table of contents
  • Cover
  • PrefaceCover
  • ContentsCover
  • About the AuthorCover
  • Part I: Foundations and Elementary ApplicationsCover
  • 1. Mathematical Preliminaries3
  • 1.1 Scalar, Vector, Matrix, and Tensor DefinitionsCover
  • 1.2 Index NotationCover
  • 1.3 Kronecker Delta and Alternating SymbolCover
  • 1.4 Coordinate TransformationsCover
  • 1.5 Cartesian TensorsCover
  • 1.6 Principal Values and Directions for Symmetric Second-Order TensorsCover
  • 1.7 Vector, Matrix, and Tensor AlgebraCover
  • 1.8 Calculus of Cartesian TensorsCover
  • 1.9 Orthogonal Curvilinear CoordinatesCover
  • ReferencesCover
  • ExercisesCover
  • 2. Deformation: Displacements and Strains27
  • 2.1 General DeformationsCover
  • 2.2 Geometric Construction of Small Deformation TheoryCover
  • 2.3 Strain TransformationCover
  • 2.4 Principal StrainsCover
  • 2.5 Spherical and Deviatoric StrainsCover
  • 2.6 Strain CompatibilityCover
  • 2.7 Curvilinear Cylindrical and Spherical CoordinatesCover
  • ReferencesCover
  • ExercisesCover
  • 3. Stress and Equilibrium49
  • 3.1 Body and Surface ForcesCover
  • 3.2 Traction Vector and Stress TensorCover
  • 3.3 Stress TransformationCover
  • 3.4 Principal StressesCover
  • 3.5 Spherical and Deviatoric StressesCover
  • 3.6 Equilibrium EquationsCover
  • 3.7 Relations in Curvilinear Cylindrical and Spherical CoordinatesCover
  • ReferencesCover
  • ExercisesCover
  • 4. Material Behavior„Linear Elastic Solids69
  • 4.1 Material CharacterizationCover
  • 4.2 Linear Elastic Materials„Hookes LawCover
  • 4.3 Physical Meaning of Elastic ModuliCover
  • 4.4 Thermoelastic Constitutive RelationsCover
  • ReferencesCover
  • ExercisesCover
  • 5. Formulation and Solution Strategies83
  • 5.1 Review of Field EquationsCover
  • 5.2 Boundary Conditions and Fundamental Problem ClasificationsCover
  • 5.3 Stress FormulationCover
  • 5.4 Displacement FormulationCover
  • 5.5 Principle of SuperpositionCover
  • 5.6 Saint-Venant’s PrincipleCover
  • 5.7 General Solution StrategiesCover
  • ReferencesCover
  • ExercisesCover
  • 6. Strain Energy and Related Principles103
  • 6.1 Strain EnergyCover
  • 6.2 Uniqueness of the Elasticity Boundary-Value ProblemCover
  • 6.3 Bounds on the Elastic ConstantsCover
  • 6.4 Related Integral TheoremsCover
  • 6.5 Principle of Virtual WorkCover
  • 6.6 Principles of Minimum Potential and Complementary EnergyCover
  • 6.7 Rayleigh-Ritz MethodCover
  • ReferencesCover
  • ExercisesCover
  • 7. Two-Dimensional Formulation123
  • 7.1 Plane StrainCover
  • 7.2 Plane StressCover
  • 7.3 Generalized Plane StressCover
  • 7.4 Antiplane StrainCover
  • 7.5 Airy Stress FunctionCover
  • 7.6 Polar Coordinate FormulationCover
  • ReferencesCover
  • ExercisesCover
  • 8. Two-Dimensional Problem Solution139
  • 8.1 Cartesian Coordinate Solutions Using PolynomialsCover
  • 8.2 Cartesian Coordinate Solutions Using Fourier MethodsCover
  • 8.3 General Solutions in Polar CoordinatesCover
  • 8.4 Polar Coordinate SolutionsCover
  • ReferencesCover
  • ExercisesCover
  • 9. Extension, Torsion, and Flexure of Elastic Cylinders201
  • 9.1 General FormulationCover
  • 9.2 Extension FormulationCover
  • 9.3 Torsion FormulationCover
  • 9.4 Torsion Solutions Derived from Boundary EquationCover
  • 9.5 Torsion Solutions Using Fourier MethodsCover
  • 9.6 Torsion of Cylinders With Hollow SectionsCover
  • 9.7 Torsion of Circular Shafts of Variable DiameterCover
  • 9.8 Flexure FormulationCover
  • 9.9 Flexure Problems Without TwistCover
  • ReferencesCover
  • ExercisesCover
  • Part II: Advanced ApplicationsCover
  • 10. Complex Variable Methods245
  • 10.1 Review of Complex Variable TheoryCover
  • 10.2 Complex Formulation of the Plane Elasticity ProblemCover
  • 10.3 Resultant Boundary ConditionsCover
  • 10.4 General Structure of the Complex PotentialsCover
  • 10.5 Circular Domain ExamplesCover
  • 10.6 Plane and Half-Plane ProblemsCover
  • 10.7 Applications Using the Method of Conformal MappingCover
  • 10.8 Applications to Fracture MechanicsCover
  • 10.9 Westergaard Method for Crack AnalysisCover
  • ReferencesCover
  • ExercisesCover
  • 11. Anisotropic Elasticity283
  • 11.1 Basic ConceptsCover
  • 11.2 Material SymmetryCover
  • 11.3 Restrictions on Elastic ModuliCover
  • 11.4 Torsion of a Solid Possessing a Plane of Material SymmetryCover
  • 11.5 Plane Deformation ProblemsCover
  • 11.6 Applications to Fracture MechanicsCover
  • ReferencesCover
  • ExercisesCover
  • 12. Thermoelasticity319
  • 12.1 Heat Conduction and the Energy EquationCover
  • 12.2 General Uncoupled FormulationCover
  • 12.3 Two-Dimensional FormulationCover
  • 12.4 Displacement Potential SolutionCover
  • 12.5 Stress Function FormulationCover
  • 12.6 Polar Coordinate FormulationCover
  • 12.7 Radially Symmetric ProblemsCover
  • 12.8 Complex Variable Methods for Plane ProblemsCover
  • ReferencesCover
  • ExercisesCover
  • 13. Displacement Potentials and Stress Functions347
  • 13.1 Helmholtz Displacement Vector RepresentationCover
  • 13.2 Lamé’s Strain PotentialCover
  • 13.3 Galerkin Vector RepresentationCover
  • 13.4 Papkovich-Neuber RepresentationCover
  • 13.5 Spherical Coordinate FormulationsCover
  • 13.6 Stress FunctionsCover
  • ReferencesCover
  • ExercisesCover
  • 14. Micromechanics Applications371
  • 14.1 Dislocation ModelingCover
  • 14.2 Singular Stress StatesCover
  • 14.3 Elasticity Theory with Distributed CracksCover
  • 14.4 Micropolar/Couple-Stress ElasticityCover
  • 14.5 Elasticity Theory with VoidsCover
  • 14.6 Doublet MechanicsCover
  • ReferencesCover
  • ExercisesCover
  • 15. Numerical Finite and Boundary Element Methods413
  • 15.1 Basics of the Finite Element MethodCover
  • 15.2 Approximating Functions for Two-Dimensional Linear Triangular ElementsCover
  • 15.3 Virtual Work Formulation for Plane ElasticityCover
  • 15.4 FEM Problem ApplicationCover
  • 15.5 FEM Code ApplicationsCover
  • 15.6 Boundary Element FormulationCover
  • ReferencesCover
  • ExercisesCover
  • Appendix A: Basic Field Equations in Cartesian, Cylindrical, and Spherical CoordinatesCover
  • Strain-Displacement RelationsCover
  • Equilibrium EquationsCover
  • Hooke’s LawCover
  • Equilibrium Equations in Terms of Displacements (Navier’s Equations)Cover
  • Appendix B: Transformation of Field Variables Between Cartesian, Cylindrical, and Spherical ComponenCover
  • Cylindrical Components from CartesianCover
  • Spherical Components from CylindricalCover
  • Spherical Components From CartesianCover
  • Appendix C: MATLAB PrimerCover
  • C.1 Getting StartedCover
  • C.2 ExamplesCover
  • ReferenceCover
  • IndexCover
Book details
  • Vendor Elsevier S & T
  • SKU 9780126058116
  • ISBN-13 9780080477473
  • Author Sadd, Martin H.
  • Category Technology & Engineering
  • Subject Materials Science

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Description eBook delivery & access Reviews
Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. Complemented by an online Solutions Manual and companion website, and including MatLab codes and coding, this text is an excellent book teaching guide.

- Contains exercises for student engagement as well as the integration and use of MATLAB Software

- Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of