Through its inclusion of specific applications, The Mathematical Theory of Elasticity, Second Edition continues to provide a bridge between the theory and applications of elasticity. It presents classical as well as more recent results, including those obtained by the authors and their colleagues. Revised and improved, this edition incorporates additional examples and the latest research results.
New to the Second Edition
- Exposition of the application of Laplace transforms, the Dirac delta function, and the Heaviside function
- Presentation of the Cherkaev, Lurie, and Milton (CLM) stress invariance theorem that is widely used to determine the effective moduli of elastic composites
- The Cauchy relations in elasticity
- A body force analogy for the transient thermal stresses
- A three-part table of Laplace transforms
- An appendix that explores recent developments in thermoelasticity
Although emphasis is placed on the problems of elastodynamics and thermoelastodynamics, the text also covers elastostatics and thermoelastostatics. It discusses the fundamentals of linear elasticity and applications, including kinematics, motion and equilibrium, constitutive relations, formulation of problems, and variational principles. It also explains how to solve various boundary value problems of one, two, and three dimensions.
This professional reference includes access to a solutions manual for those wishing to adopt the book for instructional purposes.
Updated, improved, expanded, revised, this second edition graduate text supplants the first, which was published in 2004. The intent is still to provide coverage of both theory and applications using lots of examples and problems of interest to a wide range of readers. Students preparing PhD theses, grad students needing a text that provides classical as well as recent results, and researchers in continuum mechanics are among the expected audience for this one-volume resource. Coverage includes elastostatics, thermoelastostics, elastodynamics, and thermoelastodynamics; special emphasis is on the latter two areas, given that most texts deal mainly with the first two. New to this edition is coverage of the application of Laplace transforms, the Dirac delta function, and the Heaviside function; the Cherkaev, Lurie, and Milton (CLM) stress invariance theorem; and recent developments in thermoelasticity. Hetnarski and Ignaczak both have long experience in the field, and they include results from their own research in this volume. --SciTech Book News, February 2011 Praise for the First Edition The text is written in an elegant mathematical style. --CHOICE ! a complete and modern course on this fundamental field of continuum mechanics ! combines the accuracy of mathematical formulations and proofs of basic theorems with the educational aspects ! the book is strongly recommended for graduate students of technical universities, especially to students of applied and computational mechanics. The book is also very useful to those preparing Ph.D. theses, and to all scientists conducting research, who need a background in solid mechanics. --Journal of Thermal Stresses, 29, 2006 An advanced approach to the subject in both contents and style. It is highly recommended to graduate students, engineers and scientists. --ZAMM-Journal of Applied Mathematics and Mechanics, Vol. 42, No. 2
HISTORICAL NOTE, THEORY, EXAMPLES, AND PROBLEMS Creators of the Theory of Elasticity Historical Note: Creators of the Theory of Elasticity Mathematical Preliminaries Vectors and Tensors Scalar, Vector, and Tensor Fields Integral Theorems Fundamentals of Linear Elasticity Kinematics Motion and Equilibrium Constitutive Relations Formulation of Problems of Elasticity Boundary Value Problems of Elastostatics Initial-Boundary Value Problems of Elastodynamics Variational Formulation of Elastostatics Minimum Principles Variational Principles Variational Principles of Elastodynamics The Hamilton--Kirchhoff Principle Gurtin's Convolutional Variational Principles Complete Solutions of Elasticity Complete Solutions of Elastostatics Complete Solutions of Elastodynamics Formulation of Two-Dimensional Problems Two-Dimensional Problems of Elastostatics Two-Dimensional Problems of Elastodynamics APPLICATIONS AND PROBLEMS Solutions to Particular Three-Dimensional Boundary Value Problems of Elastostatics Three-Dimensional Solutions of Isothermal Elastostatics Three-Dimensional Solutions of Nonisothermal Elastostatics Torsion Problem Solutions to Particular Two-Dimensional Boundary Value Problems of Elastostatics Two-Dimensional Solutions of Isothermal Elastostatics Two-Dimensional Solutions of Nonisothermal Elastostatics Solutions to Particular Three-Dimensional Initial-Boundary Value Problems of Elastodynamics Three-Dimensional Solutions of Isothermal Elastodynamics Three-Dimensional Solutions of Nonisothermal Elastodynamics Saint-Venant's Principle of Elastodynamics in Terms of Stresses Solutions to Particular Two-Dimensional Initial-Boundary Value Problems of Elastodynamics Two-Dimensional Solutions of Isothermal Elastodynamics Two-Dimensional Solutions of Nonisothermal Elastodynamics One-Dimensional Solutions of Elastodynamics One-Dimensional Solutions of Isothermal Elastodynamics One-Dimensional Solutions of Nonisothermal Elastodynamics APPENDIX: COUPLED AND GENERALIZED THERMOELASTICITY NAME INDEX SUBJECT INDEX Problems and References appear at the end of each chapter.