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