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Introduction to the Theory of Elasticity

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ISBN-10: 0486442411

ISBN-13: 9780486442419

Edition: 2005

Authors: N. Fox, R. J. Atkin

List price: $18.95
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Description:

This accessible text requires minimal mathematical background and provides a firm foundation for more advanced studies. Topics include deformation and stress, the derivation of the equations of finite elasticity, and the formulation of infinitesimal elasticity with application to some two- and three-dimensional static problems and elastic waves. Solutions. 1980 edition.
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Book details

List price: $18.95
Copyright year: 2005
Publisher: Dover Publications, Incorporated
Publication date: 11/21/2005
Binding: Paperback
Pages: 245
Size: 5.47" wide x 8.50" long x 0.55" tall
Weight: 0.594
Language: English

Preface
Deformation and stress
Motion. Material and spatial coordinates
The material time derivative
The deformation-gradient tensor
Strain tensors
Homogeneous deformation
Non-homogeneous deformations
The displacement vector and infinitesimal strain tensor
Geometrical interpretation of the infinitesimal strains
The continuity equation
The stress vector and body force
Principles of linear and angular momentum. The stress tensor
Principal stresses. Principal axes of stress. Stress invariants
The energy-balance equation
Piola stresses
Cylindrical and spherical polar coordinates
Examples
Finite elasticity: constitutive theory
Constitutive equations
Invariance under superposed rigid-body motions
Invariance of the strain energy under superposed rigid-body motions
The stress tensor in terms of the strain-energy function
Material symmetry. Strain-energy function for an isotropic material
The stress tensor for an isotropic material
Cauchy elasticity
Incompressible elastic materials
Forms of the strain-energy function
Examples
Exact solutions
Basic equations. Boundary conditions
Inverse method
Homogeneous deformations
Pure homogeneous deformation of a compressible material
Pure homogeneous deformation of an incompressible material
Experiments
Simple shear of a compressible material
Simple shear of an incompressible material
Non-homogeneous deformations
Simple torsion of a circular cylinder. Theory
Simple torsion of a circular cylinder. Experiment
Extension and torsion of a circular cylinder. Theory
Extension and torsion of a circular cylinder. Experiment
Examples
Infinitesimal theory
Equations of motion
Stress-strain relations
Formulation of the infinitesimal theory of elasticity
Equation for the displacement vector
Compatibility equations for the components of the infinitesimal strain tensor
Energy equations and uniqueness of solution
Pure homogeneous deformations
Values of the elastic constants
Spherical symmetry
The Boussinesq-Papkovitch-Neuber solution
Concentrated loads
Isolated point force in an infinite medium
Isolated point force on a plane boundary
Examples
Anti-plane strain, plane strain, and generalised plane stress
Basic equations
Anti-plane strain
Plane strain. Equations for the stress field
The Airy stress function
Complex representation of the Airy stress function
Determination of the displacement field
Force on a section of the boundary
Equivalence of function pairs [psi], X
Generalised plane stress
Formulation of boundary-value problems
Multiply connected regions
Infinite regions
Isolated point force
Examples
Extension, torsion, and bending
The deformation of long cylinders
Extension
Torsion of a circular cylinder
Torsion of cylinders of arbitrary cross-section
The Prandtl stress function and the lines of shearing stress
Maximum shearing stress
Force and couple resultants on a cross-section
Torsion of a cylinder with elliptical cross-section
Torsion of a cylinder of equilateral-triangular cross-section
Bending by terminal couples
The Euler-Bernoulli law
Examples
Elastic waves
One-dimensional wave equation. Notion of a plane wave
Plane harmonic waves
Elastic body waves
Potential function representation
Reflection of P-waves
Reflection of SV-waves
Reflection and refraction of plane harmonic waves
Rayleigh waves
Love waves
Examples
Answers to examples
References and suggestions for further reading
Index