Mathematical Elasticity, Three Volume Set

The Mathematical Elasticity set is a modern treatise on elasticity that includes three self-contained volumes: Three-Dimensional Elasticity, Theory of Plates, and Theory of Shells. It provides proofs, detailed surveys of prerequisites, and problems for teaching and self-study. The books are suitable for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics.

Format: Paperback / softback
Length: 1546 pages
Publication date: 30 November 2022
Publisher: Society for Industrial & Applied Mathematics,U.S.

The Mathematical Elasticity set is a comprehensive and authoritative collection of three self-contained volumes that delve into the realm of elasticity, offering a modern and comprehensive treatise on this fundamental concept in mathematics. Comprising a total of 1,500 pages, this set provides a comprehensive overview of three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume is meticulously crafted to cater to advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics, as well as continuum mechanics.

Three-Dimensional Elasticity:

This first volume delves into the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It encompasses a wide range of topics, including the study of solid bodies, fluids, and elastic materials in three dimensions. The book employs advanced mathematical techniques, such as differential equations, integral equations, and asymptotic methods, to develop and analyze models of elastic behavior. It provides a rigorous mathematical foundation for understanding the deformation, stress, and strain in three-dimensional structures.

Theory of Plates:

The second volume, Theory of Plates, focuses on the mathematical justification of classical two-dimensional linear plate and shallow shell theories. It employs asymptotic methods to derive and validate these theories, providing a rigorous mathematical framework for understanding the behavior of plates and shells under various loading conditions. The book covers topics such as plate bending, membrane stresses, and shell stability, and it serves as a valuable resource for researchers and engineers working in the field of structural analysis and design.

Theory of Shells:

The final volume, Theory of Shells, aims to demonstrate how asymptotic methods provide a rigorous mathematical justification of classical two-dimensional linear shell theories. It covers membrane, generalized membrane, and flexural shell theories, providing a comprehensive understanding of the behavior of these structures under various loading conditions. The book employs advanced mathematical techniques, including perturbation analysis, boundary value problems, and asymptotic expansions, to develop and analyze models of shell behavior.

These classic textbooks are widely recognized as essential resources for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics, as well as continuum mechanics. They are suitable for courses in mathematical elasticity, the theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

The Mathematical Elasticity set is a testament to the enduring significance of elasticity in modern mathematics and its applications. By presenting a comprehensive and up-to-date treatment of three-dimensional elasticity, the theory of plates, and the theory of shells, this set serves as a valuable tool for advancing knowledge and understanding in these fields. Whether you are a student, researcher, or professional seeking to deepen your expertise in elasticity, this set is an indispensable resource that will undoubtedly enhance your understanding and appreciation of this fundamental concept.

ISBN-13: 9781611976939