Ebook: Elasticity

This is a first year graduate textbook in Linear Elasticity. It is written with the practical engineering reader in mind, dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Emphasis is placed on engineering applications of elasticity and examples are generally worked through to final expressions for the stress and displacement fields in order to explore the engineering consequences of the results.

The topics covered are chosen with a view to modern research applications in fracture mechanics, composite materials, tribology and numerical methods. Thus, significant attention is given to crack and contact problems, problems involving interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems.

This third edition includes new chapters on complex variable methods, variational methods and three-dimensional solutions for the prismatic bar. Other detailed changes have been made throughout the work, many suggested by users of earlier editions.

The new edition includes over 300 end-of-chapter problems, expressed wherever possible in the form they would arise in engineering - i.e. as a body of a given geometry subjected to prescribed loading - instead of inviting the student to 'verify' that a given candidate stress function is appropriate to the problem. Solution of these problems is considerably facilitated by the use of modern symbolic mathematical languages such as Maple and Mathematica. Electronic files and hints on this method of solution, as well as further supplementary software are available for download via the webpage for this volume on www.springer.com.

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This is a first year graduate textbook in Linear Elasticity. It is written with the practical engineering reader in mind, dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Emphasis is placed on engineering applications of elasticity and examples are generally worked through to final expressions for the stress and displacement fields in order to explore the engineering consequences of the results.

The topics covered are chosen with a view to modern research applications in fracture mechanics, composite materials, tribology and numerical methods. Thus, significant attention is given to crack and contact problems, problems involving interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems.

This third edition includes new chapters on complex variable methods, variational methods and three-dimensional solutions for the prismatic bar. Other detailed changes have been made throughout the work, many suggested by users of earlier editions.

The new edition includes over 300 end-of-chapter problems, expressed wherever possible in the form they would arise in engineering - i.e. as a body of a given geometry subjected to prescribed loading - instead of inviting the student to 'verify' that a given candidate stress function is appropriate to the problem. Solution of these problems is considerably facilitated by the use of modern symbolic mathematical languages such as Maple and Mathematica. Electronic files and hints on this method of solution, as well as further supplementary software are available for download via the webpage for this volume on www.springer.com.

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This is a first year graduate textbook in Linear Elasticity. It is written with the practical engineering reader in mind, dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Emphasis is placed on engineering applications of elasticity and examples are generally worked through to final expressions for the stress and displacement fields in order to explore the engineering consequences of the results.

The topics covered are chosen with a view to modern research applications in fracture mechanics, composite materials, tribology and numerical methods. Thus, significant attention is given to crack and contact problems, problems involving interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems.

This third edition includes new chapters on complex variable methods, variational methods and three-dimensional solutions for the prismatic bar. Other detailed changes have been made throughout the work, many suggested by users of earlier editions.

The new edition includes over 300 end-of-chapter problems, expressed wherever possible in the form they would arise in engineering - i.e. as a body of a given geometry subjected to prescribed loading - instead of inviting the student to 'verify' that a given candidate stress function is appropriate to the problem. Solution of these problems is considerably facilitated by the use of modern symbolic mathematical languages such as Maple and Mathematica. Electronic files and hints on this method of solution, as well as further supplementary software are available for download via the webpage for this volume on www.springer.com.

Content:
Front Matter....Pages 1-18
Front Matter....Pages 1-1
Introduction....Pages 3-24
Equilibrium and Compatibility....Pages 25-33
Front Matter....Pages 36-36
Plane Strain and Plane Stress....Pages 37-44
Stress Function Formulation....Pages 45-53
Problems in Rectangular Co?rdinates....Pages 55-76
End Effects....Pages 77-89
Body Forces....Pages 91-108
Problems in Polar Co?rdinates....Pages 109-122
Calculation of Displacements....Pages 123-134
Curved Beam Problems....Pages 135-148
Wedge Problems....Pages 149-170
Plane Contact Problems....Pages 171-198
Forces, Dislocations and Cracks....Pages 199-218
Thermoelasticity....Pages 219-225
Antiplane Shear....Pages 227-235
Front Matter....Pages 238-240
Torsion of a Prismatic Bar....Pages 241-257
Shear of a Prismatic Bar....Pages 259-268
Front Matter....Pages 270-272
Preliminary Mathematical Results....Pages 273-292
Application to Elasticity Problems....Pages 293-317
Front Matter....Pages 320-320
Displacement Function Solutions....Pages 321-332
Front Matter....Pages 320-320
The Boussinesq Potentials....Pages 333-345
Thermoelastic Displacement Potentials....Pages 347-361
Singular Solutions....Pages 363-376
Spherical Harmonics....Pages 377-390
Cylinders and Circular Plates....Pages 391-404
Problems in Spherical Co?rdinates....Pages 405-418
Axisymmetric Torsion....Pages 419-428
The Prismatic Bar....Pages 429-448
Frictionless Contact....Pages 449-457
The Boundary-Value Problem....Pages 459-478
The Penny-Shaped Crack....Pages 479-486
The Interface Crack....Pages 487-498
Variational Methods....Pages 499-516
The Reciprocal Theorem....Pages 517-528
Back Matter....Pages 1-6

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This is a first year graduate textbook in Linear Elasticity. It is written with the practical engineering reader in mind, dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Emphasis is placed on engineering applications of elasticity and examples are generally worked through to final expressions for the stress and displacement fields in order to explore the engineering consequences of the results.

The topics covered are chosen with a view to modern research applications in fracture mechanics, composite materials, tribology and numerical methods. Thus, significant attention is given to crack and contact problems, problems involving interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems.

This third edition includes new chapters on complex variable methods, variational methods and three-dimensional solutions for the prismatic bar. Other detailed changes have been made throughout the work, many suggested by users of earlier editions.

The new edition includes over 300 end-of-chapter problems, expressed wherever possible in the form they would arise in engineering - i.e. as a body of a given geometry subjected to prescribed loading - instead of inviting the student to 'verify' that a given candidate stress function is appropriate to the problem. Solution of these problems is considerably facilitated by the use of modern symbolic mathematical languages such as Maple and Mathematica. Electronic files and hints on this method of solution, as well as further supplementary software are available for download via the webpage for this volume on www.springer.com.

Content:
Front Matter....Pages 1-18
Front Matter....Pages 1-1
Introduction....Pages 3-24
Equilibrium and Compatibility....Pages 25-33
Front Matter....Pages 36-36
Plane Strain and Plane Stress....Pages 37-44
Stress Function Formulation....Pages 45-53
Problems in Rectangular Co?rdinates....Pages 55-76
End Effects....Pages 77-89
Body Forces....Pages 91-108
Problems in Polar Co?rdinates....Pages 109-122
Calculation of Displacements....Pages 123-134
Curved Beam Problems....Pages 135-148
Wedge Problems....Pages 149-170
Plane Contact Problems....Pages 171-198
Forces, Dislocations and Cracks....Pages 199-218
Thermoelasticity....Pages 219-225
Antiplane Shear....Pages 227-235
Front Matter....Pages 238-240
Torsion of a Prismatic Bar....Pages 241-257
Shear of a Prismatic Bar....Pages 259-268
Front Matter....Pages 270-272
Preliminary Mathematical Results....Pages 273-292
Application to Elasticity Problems....Pages 293-317
Front Matter....Pages 320-320
Displacement Function Solutions....Pages 321-332
Front Matter....Pages 320-320
The Boussinesq Potentials....Pages 333-345
Thermoelastic Displacement Potentials....Pages 347-361
Singular Solutions....Pages 363-376
Spherical Harmonics....Pages 377-390
Cylinders and Circular Plates....Pages 391-404
Problems in Spherical Co?rdinates....Pages 405-418
Axisymmetric Torsion....Pages 419-428
The Prismatic Bar....Pages 429-448
Frictionless Contact....Pages 449-457
The Boundary-Value Problem....Pages 459-478
The Penny-Shaped Crack....Pages 479-486
The Interface Crack....Pages 487-498
Variational Methods....Pages 499-516
The Reciprocal Theorem....Pages 517-528
Back Matter....Pages 1-6
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