An Introduction to the Theory of Elasticity

 
 
Dover Publications (Verlag)
  • 1. Auflage
  • |
  • erschienen am 20. Februar 2013
  • |
  • 272 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-0-486-15099-4 (ISBN)
 
Thanks to intense research activity in the field of continuum mechanics, the teaching of subjects such as elasticity theory has attained a high degree of clarity and simplicity. This introductory volume offers upper-level undergraduates a perspective based on modern developments that also takes into account the limited mathematical tools they are likely to have at their disposal. It also places special emphasis on areas that students often find difficult upon first encounter. An Introduction to the Theory of Elasticity provides an accessible guide to the subject in a form that will instill a firm foundation for more advanced study.The topics covered include a general discussion of deformation and stress, the derivation of the equations of finite elasticity with some exact solutions, and the formulation of infinitesimal elasticity with application to some two- and three-dimensional static problems and elastic waves. Answers to examples appear at the end of the book.
  • Englisch
  • New York
  • |
  • USA
  • Höhe: 216 mm
  • |
  • Breite: 137 mm
  • 13,78 MB
978-0-486-15099-4 (9780486150994)
0486150992 (0486150992)
weitere Ausgaben werden ermittelt
R. J. Atkin and N. Fox
  • Title Page
  • Copyright Page
  • Table of Contents
  • Preface
  • 1 - Deformation and stress
  • 1.1 Motion. Material and spatial coordinates
  • 1.2 The material time derivative
  • 1.3 The deformation-gradient tensor
  • 1.4 Strain tensors
  • 1.5 Homogeneous deformation
  • 1.6 Non-homogeneous deformations
  • 1.7 The displacement vector and infinitesimal strain tensor
  • 1.8 Geometrical interpretation of the infinitesimal strains
  • 1.9 The continuity equation
  • 1.10 The stress vector and body force
  • 1.11 Principles of linear and angular momentum. The stress tensor
  • 1.12 Principal stresses. Principal axes of stress. Stress invariants
  • 1.13 The energy-balance equation
  • 1.14 Piola stresses
  • 1.15 Cylindrical and spherical polar coordinates
  • 2 - Finite elasticity: constitutive theory
  • 2.1 Constitutive equations
  • 2.2 Invariance under superposed rigid-body motions
  • 2.3 Invariance of the strain energy under superposed rigid-body motions
  • 2.4 The stress tensor in terms of the strain-energy function
  • 2.5 Material symmetry. Strain-energy function for an isotropic material
  • 2.6 The stress tensor for an isotropic material
  • 2.7 Cauchy elasticity
  • 2.8 Incompressible elastic materials
  • 2.9 Forms of the strain-energy function
  • 3 - Exact solutions
  • 3.1 Basic equations. Boundary conditions
  • 3.2 Inverse method
  • 3.3 Homogeneous deformations
  • 3.4 Pure homogeneous deformation of a compressible material
  • 3.5 Pure homogeneous deformation of an incompressible material
  • 3.6 Experiments
  • 3.7 Simple shear of a compressible material
  • 3.8 Simple shear of an incompressible material
  • 3.9 Non-homogeneous deformations
  • 3.10 Simple torsion of a circular cylinder. Theory
  • 3.11 Simple torsion of a circular cylinder. Experiment
  • 3.12 Extension and torsion of a circular cylinder. Theory
  • 3.13 Extension and torsion of a circular cylinder. Experiment
  • 4 - Infinitesimal theory
  • 4.1 Equations of motion
  • 4.2 Stress-strain relations
  • 4.3 Formulation of the infinitesimal theory of elasticity
  • 4.4 Equation for the displacement vector
  • 4.5 Compatibility equations for the components of the infinitesimal strain tensor
  • 4.6 Energy equations and uniqueness of solution
  • 4.7 Pure homogeneous deformations
  • 4.8 Values of the elastic constants
  • 4.9 Spherical symmetry
  • 4.10 The Boussinesq-Papkovitch-Neuber solution
  • 4.11 Concentrated loads
  • 4.12 Isolated point force in an infinite medium
  • 4.13 Isolated point force on a plane boundary
  • 5 - Anti-plane strain, plane strain, and generalised plane stress
  • 5.1 Basic equations
  • 5.2 Anti-plane strain
  • 5.3 Plane strain. Equations for the tress field
  • 5.4 The Airy stress function
  • 5.5 Complex representation of the Airy stress function
  • 5.6 Determination of the displacement field
  • 5.7 Force on a section of the boundary
  • 5.8 Equivalence of function pairs ?, ?
  • 5.9 Generalised plane stress
  • 5.10 Formulation of boundary-value problems
  • 5.11 Multiply connected regions
  • 5.12 Infinite regions
  • 5.13 Isolated point force
  • 6 - Extension, torsion, and bending
  • 6.1 The deformation of long cylinders
  • 6.2 Extension
  • 6.3 Torsion of a circular cylinder
  • 6.4 Torsion of cylinders of arbitrary cross-section
  • 6.5 The Prandtl stress function and the lines of shearing stress
  • 6.6 Maximum shearing stress
  • 6.7 Force and couple resultants on a cross-section
  • 6.8 Torsion of a cylinder with elliptical cross-section
  • 6.9 Torsion of a cylinder of equilateraltriangular cross-section
  • 6.10 Bending by terminal couples
  • 6.11 The Euler-Bernoulli law
  • 7 - Elastic waves
  • 7.1 One-dimensional wave equation. Notion of a plane wave
  • 7.2 Plane harmonic waves
  • 7.3 Elastic body waves
  • 7.4 Potential function representation
  • 7.5 Reflection of P-waves
  • 7.6 Reflection of SV-waves
  • 7.7 Reflection and refraction of plane harmonic waves
  • 7.8 Rayleigh waves
  • 7.9 Love waves
  • Answers
  • References and suggestions for further reading
  • Index
  • CATALOG OF DOVER BOOKS

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