The Mathematical Theory of Elasticity

Through its inclusion of specific applications, this text continues to provide a bridge between the theory and applications of elasticity. Revised and enhanced, this second edition is fully updated with additional examples and the latest research results. It presents an exposition of the application of Laplace transforms, the Dirac delta function, and the Heaviside function, and offers a presentation of the CLM stress invariance theorem that is widely used to determine the effective moduli of elastic composites. This edition also includes a three-part table of Laplace transforms and a new appendix that explores recent developments in thermoelasticity.

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.