Variational principles of continuum mechanics / Victor L. Berdichevsky.

Format:

Book

Author/Creator:

Berdichevskiĭ, V. L. (Viktor Lʹvovich)

Contributor:

Hazel M. Hussong Fund.

Series:

Interaction of mechanics and mathematics series

Interaction of mechanics and mathematics

Language:

English

Subjects (All):

Continuum mechanics.

Continuum mechanics--Mathematics.

Variational principles.

Mathematics.

Physical Description:

2 volumes : illustrations ; 24 cm.

Place of Publication:

Berlin ; New York : Springer, [2009]

Summary:

The Interaction of Mechanics and Mathematics (IMM) series publishes advanced textbooks and introductory scientific monographs devoted to modern research in the wide area of mechanics. The authors are distinguished specialists with international reputation in their field of expertise. The books are intended to serve as modern guides in their fields and anticipated to be accessible to advanced graduate students. IMM books are planned to be comprehensive reviews developed to the cutting edge of their respective field and to list the major references.

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems.

Berdichevsky's work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given.

This book, the second volume, describes how the variational approach can be applied to constructing models of continuum media, such as the theory of elastic plates, shells and beams; shallow water theory; heterogeneous mixtures; granular materials; and turbulence. It goes on to apply the variational approach to asymptotical analysis of problems with small parameters, such as the derivation of the theory of elastic plates, shells and beams from three-dimensional elasticity theory; and the basics of homogenization theory. A theory of stochastic variational problems is considered in detail too, along with applications to the homogenization of continua with random microstructures.

Contents:

1. Fundamentals

2. Applications.

Notes:

Includes bibliographical references and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

9783540884668

3540884661

9783540884682

3540884688

9783540884651

3540884653

OCLC:

269435364