Mechanics Of Continuous Media

From the reviews: "The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. [...] It will be very useful for both mathematicians and physicists." EMS Newsletter

This volume is written by Academician Sedov who is considered by many as the leading scientist in mechanics in the USSR. This latest fourth edition helps the reader in a relatively short time to master and acquire fully the essence of many geometrical and mechanical theories.

Physics of Continuous Media: A Collection of Problems with Solutions for Physics Students contains a set of problems with detailed and rigorous solutions. Aimed at undergraduate and postgraduate students in physics and applied mathematics, the book is a complementary text for standard courses on the physics of continuous media. With its assortment of standard problems for beginners, variations on a theme, and original problems based on new trends and theories in the physics under investigation, this book aids in the understanding of practical aspects of the subject. Topics discussed include vectors, tensors, and Fourier transformations; dielectric waves in media; natural optical activity; Cherenkov radiation; nonlinear interaction of waves; dynamics of ideal fluids and the motion of viscous fluids; convection; turbulence and acoustic and shock waves; the theory of elasticity; and the mechanics of liquid crystals.

This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.

Mechanics of Continuous Media and Analysis of Structures is a six-chapter book that begins by elucidating the mechanics of solid continuous media. The text then describes the finite elements method, which undoubtedly dominates the methods used for structural analysis. Subsequent chapters explain the variational principles in linear elasticity, vibration of linear structure, non-linear deformations, and the shell theory. This book will be valuable to all those who need certain theoretical developments in mechanics, including mechanical engineers, economists, and mathematicians.

Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.