The Mathematical Theory of Elasticity SECOND EDITION

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.

HISTORICAL NOTE, THEORY, EXAMPLES, AND PROBLEMSCreators of the Theory of ElasticityHistorical Note: Creators of the Theory of Elasticity Mathematical PreliminariesVectors and TensorsScalar, Vector, and Tensor FieldsIntegral Theorems Fundamentals of Linear ElasticityKinematicsMotion and EquilibriumConstitutive Relations Formulation of Problems of ElasticityBoundary Value Problems of ElastostaticsInitial-Boundary Value Problems of Elastodynamics Variational Formulation of ElastostaticsMinimum PrinciplesVariational Principles Variational Principles of ElastodynamicsThe Hamilton–Kirchhoff Principle Gurtin’s Convolutional Variational Principles Complete Solutions of ElasticityComplete Solutions of Elastostatics Complete Solutions of Elastodynamics Formulation of Two-Dimensional ProblemsTwo-Dimensional Problems of Elastostatics Two-Dimensional Problems of Elastodynamics APPLICATIONS AND PROBLEMSSolutions to Particular Three-Dimensional Boundary Value Problems of ElastostaticsThree-Dimensional Solutions of Isothermal ElastostaticsThree-Dimensional Solutions of Nonisothermal ElastostaticsTorsion Problem Solutions to Particular Two-Dimensional Boundary Value Problems of ElastostaticsTwo-Dimensional Solutions of Isothermal ElastostaticsTwo-Dimensional Solutions of Nonisothermal Elastostatics Solutions to Particular Three-Dimensional Initial-Boundary Value Problems of ElastodynamicsThree-Dimensional Solutions of Isothermal ElastodynamicsThree-Dimensional Solutions of Nonisothermal ElastodynamicsSaint-Venant’s Principle of Elastodynamics in Terms of Stresses Solutions to Particular Two-Dimensional Initial-Boundary Value Problems of ElastodynamicsTwo-Dimensional Solutions of Isothermal ElastodynamicsTwo-Dimensional Solutions of Nonisothermal Elastodynamics One-Dimensional Solutions of ElastodynamicsOne-Dimensional Solutions of Isothermal ElastodynamicsOne-Dimensional Solutions of Nonisothermal Elastodynamics APPENDIX: COUPLED AND GENERALIZED THERMOELASTICITY NAME INDEXSUBJECT INDEX Problems and References appear at the end of each chapter.

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.