Synopses & Reviews
This is a first year graduate textbook on linear elasticity, being based on a one semester course taught by the author at the University of Michigan. It is written with the practical engineering reader in mind, dependence on previous knowledge of solid mechanics, continuum, mechanics or mathematics being minimized. Most of the text should be readily intelligible to a reader with an undergraduate background of one or two courses in elementary strength of materials and a rudimentary knowledge of partial differentiation. 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. Problems suitable for class use are included at the end of most of the chapters. These are 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. The text is therefore written in such a way as to enable the student to approach such problems deductively. A solutions manual is available directly from the author (e-mail: jbarber@engin.umich.edu).
Review
'...this book is a very good addition to the available literature on elasticity and can be used as a textbook for the first year graduate course on linear elasticity.' Applied Mechanics Reviews, 45:12 (1992)
Synopsis
A graduate textbook, based on a course taught by the author. Placing emphasis on engineering applications, it pays special attention to crack and contact problems, interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems.
Synopsis
The subject of Elasticity can be approached from several points of view, depending on whether the practitioner is principally interested in the mathematicalstructure of the subject or in its use in engineering applications and in the latter case, whether essentially numerical or analytical methods are envisaged as the solution method. My first introduction to the subject was in response to a need for information about a specific problem in Tribology. As a practising engineer with a background only in elementary Strength of Materials, I approached that problem initially using the con- cepts of concentrated forces and superposition. Today, with a rather more extensive knowledge of analytical techniques in Elasticity, I still find it helpful to go back to these roots in the elementary theory and think through a problem physically as well as mathematically, whenever some new and unexpected feature presents difficulties in research. This way of thinking will be found to permeate this book. My engineering background will also reveal itself in a tendency to work examples through to final expressions for stresses and displacements, rather than leave the derivation at a point where the remaining manipulations would be routine. With the practical engineering reader in mind, I have endeavoured to keep to a minimum any dependence on previous knowledge of Solid Mechanics, Continuum Mechanics or Mathematics.
Table of Contents
Preface. I: General Considerations. 1. Introduction. 2. Equilibrium and Compatibility. II: Two-Dimensional Problems. 3. Plane Strain and Plane Stress. 4. Stress Function Formulation. 5. Problems in Rectangular Coordinates. 6. End Effects. 7. Body Forces. 8. Problems in Polar Coordinates. 9. Calculation of Displacements. 10. Curved Beam Problems. 11. Wedge Problems. 12. Plane Contacts Problems. 13. Forces, Dislocations and Cracks. 14. Thermoelasticity. III: Three-Dimensional Problems. 15. Displacements Function Solutions. 16. The Boussinesq Potentials. 17. Thermoelastic Displacement Potentials. 18. Singular Solutions. 19. Spherical Harmonics. 20. Axisymmetric Problems. 21. Frictionless Contact. 22. The Boundary-Value Problem. 23. The Penny-Shaped Crack. 24. The Interface Crack. 25. The Reciprocal Theorem. Index.