Variational principles of continuum mechanics
著者
書誌事項
Variational principles of continuum mechanics
（Interaction of mechanics and mathematics）
Springer, c2009
- 1. fundamentals
- 2. applications
大学図書館所蔵 件 / 全15件
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1: fundamentalsBERD/10/2-1033212010000421,
2: applicationsBERD/10/2-2033212010000433 -
1. fundamentals423.1||BER200028522374,
2. applications423.1||BER200028522383 -
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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1. fundamentals ISBN 9783540884668
内容説明
Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.
目次
Fundamentals.- Variational Principles.- Thermodynamics.- Continuum Mechanics.- Principle of Least Action in Continuum Mechanics.- Direct Methods of Calculus of Variations.- Variational features of classical continuum models.- Statics of a Geometrically Linear Elastic Body.- Statics of a Geometrically Nonlinear Elastic Body.- Dynamics of Elastic Bodies.- Ideal Incompressible Fluid.- Ideal Compressible Fluid.- Steady Motion of Ideal Fluid and Elastic Body.- Principle of Least Dissipation.- Motion of Rigid Bodies in Fluids.
- 巻冊次
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2. applications ISBN 9783540884682
内容説明
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.
目次
Some Applications of Variational Methods to Development.- Theory of Elastic Plates and Shells.- Elastic Beams.- Some Stochastic Variational Problems.- Homogenization.- Homogenization of Random Structures: a Closer View.- Some Other Applications.
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