Elasticity
Subtitle: theory, applications, and numerics
Publisher: Elsevier Science
Published: 2010
Place of publication: Oxford
Language: eng
Format: [electronic resource] :
Number of pages: 474
ISBN-13: 9780080477473
Subjects: Thermodynamics; Elasticity; Acceleration (Mechanics); Wire rope -- Testing
Notes: Description based upon print version of record.

10.1 Review of Complex Variable Theory
Table of contents: title: Cover; Frontmatter; Half Title Page; Title Page; Copyright; Preface; Contents; About the Author; Part I: Foundations and Elementary Applications; 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; Exercises; 2. Deformation: Displacements and Strains; title: 2.1 General Deformations2.2 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; Exercises; 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 and Deviatoric Stresses; 3.6 Equilibrium Equations; 3.7 Relations in Curvilinear Cylindrical and Spherical Coordinates; References; Exercises; title: 4. Material Behavior-Linear Elastic Solids4.1 Material Characterization; 4.3 Physical Meaning of Elastic Moduli; 4.4 Thermoelastic Constitutive Relations; References; Exercises; 5. Formulation and Solution Strategies; 5.1 Review of Field Equations; 5.2 Boundary Conditions and Fundamental Problem Clasifications; 5.3 Stress Formulation; 5.4 Displacement Formulation; 5.5 Principle of Superposition; 5.7 General Solution Strategies; References; Exercises; 6. Strain Energy and Related Principles; 6.1 Strain Energy; 6.2 Uniqueness of the Elasticity Boundary-Value Problem; title: 6.3 Bounds on the Elastic Constants6.4 Related Integral Theorems; 6.5 Principle of Virtual Work; 6.6 Principles of Minimum Potential and Complementary Energy; 6.7 Rayleigh-Ritz Method; References; Exercises; 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; Exercises; 8. Two-Dimensional Problem Solution; 8.1 Cartesian Coordinate Solutions Using Polynomials; 8.2 Cartesian Coordinate Solutions Using Fourier Methods; title: 8.3 General Solutions in Polar Coordinates8.4 Polar Coordinate Solutions; References; Exercises; 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; Exercises; Part II: Advanced Applications; 10. Complex Variable Methods