Tensor Analysis and Continuum Mechanics

ISBN-13: 9789048161904 / Angielski / Miękka / 2010 / 591 str.

Y. R. Talpaert

Opis

This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc ..

Spis treści

Preface. 1: Tensors. 1. First steps with tensors. 2. Operations of tensors. 3. Euclidean vector space. 4. Exterior algebra. 5. Point spaces. Exercises. 2 : Lagrangian and Eulerian Descriptions. 1. Lagrangian description. 2. Eulerian description. Exercises. 3 : Deformations. 1. Homogeneous transformation. 2. Tangential homogeneous transformation. 3. Infinitesimal transformation. Exercises. 4: Kinematics of Continua. 1. Lagrangian kinematics. 2. Eulerian kinematics. 3. Material derivatives of circulation, flux, and volume. Exercises. 5: Fundamental Laws: Principle of Virtual Work. 1. Conservation of mass and continuity equation. 2. Fundamental laws of dynamics. 3. Theorem of kinetic energy. 4. Study of stresses. 5. Principle of virtual work. 6. Thermomechanics and balance equations. Exercises. 6: Linear Elasticity. 1. Elasticity and tests. 2. Generalized Hooke's law in linear elasticity. 3. Equations and principles in elastostatics. 4. Classical problems. Exercises. Summary of Formulae. Bibliography. Glossary of Symbols. Index.