Mathematical theory of elasticity

This book is devoted to the classical theory of linear elasticity in which both the elastostatics and elastodynamics are discussed. The theory is presented in a modern continuum mechanics setting using direct notation as well as cartesian co-ordinates. Each chapter, except for the first one on the history of elasticity, contains examples with full solutions that illustrate the theory introduced. Also, each chapter except for the first one is supplemented by a set of problems with answers and hints. The book provides new general theorems and applications of elasticity that are complementary to the classical results such as: 3D Compatibility Related Variational Principle of Elastostatics, Pure Stress Treatment of Elastodynamics, Tensorial Classification of Elastic Waves and the Stress Energy Partition Formula for the Classical surface-wave in a semi-space. Due to its explanatory style the book could be useful for graduate students and for beginners in the application of elasticity theory to engineering problems. It may also be useful for researchers in the modern theory of continuum mechanics.

Creators of the Theory of Elasticity. Mathematical Preliminaries. Fundamentals of Linear Elasticity. Formulation of Problems of Elasticurt. Variational Formulation of Elastostatics. Variational Principles of Elastodynamics. Complete Solutions of Elasticity. Formulation of Two-dimensional Problems. Solutions to Particular 3D Boundary Value Problems of Elastostatics. Solutions to Particular 2D Boundary Value Problems of Elastostatics. Solutions to Particular 3D Initial-Boundary Value Problems of Elastodynamics. Solutions to Particular 2D Initial-boundary Value Problems of Elastodynamics. One-dimensional Solutions of Elastodynamics