Variational Principles of Continuum Mechanics

by Berdichevsky, Victor L.

• ISBN13: 9783540884682
• ISBN10: 3540884688
• eBook ISBN(s): 9783540884699
• Format: Paperback
• Copyright: 2009-10-04
• Publisher: Springer Nature
• More Book Details
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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.

Table of Contents

Some Applications of Variational Methods to Development of Continuum Mechanics Models
Theory of Elastic Plates and Shells	p. 589
Preliminaries from Geometry of Surfaces	p. 590
Classical Shell Theory: Phenomenological Approach	p. 598
Plates	p. 620
Derivation of Classical Shell Theory from Three-Dimensional Elasticity	p. 626
Short Wave Extrapolation	p. 640
Refined Shell Theories	p. 642
Theory of Anisotropic Heterogeneous Shells	p. 665
Laminated Plates	p. 679
Sandwich Plates	p. 688
Nonlinear Theory of Hard-Skin Plates and Shells	p. 701
Elastic Beams	p. 715
Phenomenological Approach	p. 715
Variational Problem for Energy Density	p. 725
Asymptotic Analysis of the Energy Functional of Three-Dimensional Elasticity	p. 741
Some Stochastic Variational Problems	p. 751
Stochastic Variational Problems	p. 751
Stochastic Quadratic Functionals	p. 756
Extreme Values of Energy	p. 761
Probability Distribution of Energy: Gaussian Excitation	p. 768
Probability Distribution of Energy: Small Excitations	p. 771
Probability Distribution of Energy: Large Excitations	p. 789
Probability Distribution of Linear Functionals of Minimizers	p. 797
Variational Principle for Probability Densities	p. 801
Homogenization	p. 817
The Problem of Homogenization	p. 817
Homogenization of Periodic Structures	p. 818
Some Non-asymptotic Features of Homogenization Problem	p. 833
Homogenization of Random Structures	p. 840
Homogenization in One-Dimensional Problems	p. 849
A One-Dimensional Nonlinear Homogenization Problem: Spring Theory	p. 856
Two-Dimensional Structures	p. 862
Two-Dimensional Incompressible Elastic Composites	p. 875
Some Three-Dimensional Homogenization Problems	p. 883
Estimates of Effective Characteristics of Random Cell Structures in Terms of that for Periodic Structures	p. 892
Homogenization of Random Structures: a Closer View	p. 899
More on Kozlov's Cell Problem	p. 899
Variational Principle for Probability Densities	p. 918
Equations for Probability Densities	p. 922
Approximations of Probability Densities	p. 927
The Choice of Probabilistic Measure	p. 931
Entropy of Microstructure	p. 934
Temperature of Microstructure	p. 939
Entropy of an Elastic Bar	p. 943
Some Other Applications	p. 961
Shallow Water Theory	p. 961
Models of Heterogeneous Mixtures	p. 966
A Granular Material Model	p. 976
A Turbulence Model	p. 978
Bibliographic Comments	p. 987
Bibliography	p. 991
Index	p. 1005
Notation	p. 1011
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