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2nd Edition

The Mathematical Theory of Elasticity





ISBN 9781138374355
Published September 18, 2018 by CRC Press
837 Pages 108 B/W Illustrations

 
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Book Description

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.

Table of Contents

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.

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Author(s)

Biography

Richard B. Hetnarski, PE, is professor emeritus in the Department of Mechanical Engineering at the Rochester Institute of Technology. He has also held positions at Cornell University, NASA, and the Polish Academy of Sciences. Dr. Hetnarski is the founder and president of the International Congresses on Thermal Stresses (ICTS) and the founder and editor of the Journal of Thermal Stresses. He has published extensively in the areas of mechanics and mathematics.

Józef Ignaczak is professor emeritus in the Institute of Fundamental Technological Research of the Polish Academy of Sciences, where he was awarded the 50-year Anniversary Medal. Dr. Ignaczak has also been a recipient of the Golden Cross of Merit and the Polonia Restituta Cross (KKOOP) from the Polish State Council; the Twentieth Century Achievement Award, the Presidential Seal of Honor, the Platinum Record for Exceptional Performance, and the 2000 Millennium Medal of Honor from the American Biographical Institute (ABI); and the Honorary Achievement Award from the 1997 Symposium on Thermal Stresses. Over the years, his research has focused on the development of linear elastodynamics and dynamic coupled classical and nonclassical thermoelasticity.

Reviews

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

Support Material

Ancillaries

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