Cosserat theories : shells, rods, and points /

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Bibliographic Details
Author / Creator:	Rubin, M. B.
Imprint:	Dordrecht ; Boston : Kluwer Academic Publishers, c2000.
Description:	xv, 480 p. : ill. ; 25 cm.
Language:	English
Series:	Solid mechanics and its applications ; v. 79
Subject:	Continuum mechanics. Continuum mechanics.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/4424967

Hidden Bibliographic Details
ISBN:	0792364899 (alk. paper)
Notes:	Includes bibliographical references and index.

Table of Contents:

Preface
Chapter 1. Introduction
1.1. The basic idea of a Cosserat model
1.2. A brief outline of the book
1.3. Notation
Chapter 2. Basic Tensor Operations in Curvilinear Coordinates
2.1. Covariant and contravariant base vectors
2.2. Base tensors and components of tensors
2.3. Basic tensor operations
2.4. Covariant differentiation and Christoffel symbols
Chapter 3. Three-Dimensional Continua
3.1. Configurations and motion
3.2. Balance laws
3.3. Invariance under superposed rigid body motions
3.4. Mechanical power
3.5. An alternative derivation of the balance laws
3.6. An averaged form of the balance of linear momentum
3.7. Anisotropic nonlinear elastic materials
3.8. Constraints
3.9. Initial and boundary conditions
3.10. Material Symmetry
3.11. Isotropic nonlinear elastic materials
3.12. A small strain theory
3.13. Small deformations superimposed on a large deformation
3.14. Pure bending of an orthotropic rectangular parallelepiped
3.15. Torsion of an orthotropic rectangular parallelepiped
3.16. Forced shearing vibrations of an orthotropic rectangular parallelepiped
3.17. Free isochoric vibrations of an isotropic cube
3.18. An orthotropic rectangular parallelepiped loaded by its own weight
3.19. An isotropic circular cylinder loaded by its own weight
3.20. Plane strain free vibrations of an isotropic solid circular cylinder
3.21. Dissipation inequality and material damping
Chapter 4. Cosserat Shells
4.1. Description of a shell structure
4.2. The Cosserat model of a shell
4.3. Derivation of the balance laws from the three-dimensional theory
4.4. Balance laws by the direct approach
4.5. Invariance under superposed rigid body motions
4.6. Mechanical power
4.7. An alternative derivation of the balance laws
4.8. Anisotropic nonlinear elastic shells
4.9. Constraints
4.10. Initial and boundary conditions
4.11. Further restrictions on constitutive equations for shells constructed from homogeneous anisotropic nonlinear elastic materials
4.12. A small strain theory
4.13. Small deformations superimposed on a large deformation
4.14. Pure bending of an orthotropic rectangular plate
4.15. Torsion of an orthotropic rectangular plate
4.16. Forced shearing vibrations of an orthotropic rectangular plate
4.17. Free isochoric vibrations of an isotropic cube
4.18. An orthotropic rectangular plate loaded by its own weight
4.19. Elastic shells
4.20. Plane strain expansion of an isotropic circular cylindrical shell
4.21. Plane strain free vibrations of an isotropic solid circular cylinder
4.22. Expansion of an isotropic spherical shell
4.23. Free vibrations of an isotropic solid sphere
4.24. An isotropic circular cylindrical shell loaded by its own weight
4.25. Isotropic nonlinear elastic shells
4.26. A simple derivation of the local equations for shells
4.27. A brief summary of the equations for shells
4.28. Generalized membranes and membrane-like shells
4.29. Simple membranes
4.30. Expansion of an incompressible isotropic spherical shell
4.31. Bending of an orthotropic plate into a circular cylindrical surface
4.3. Linear theory of an isotropic plate
4.33. Dissipation inequality and material damping
Chapter 5. Cosserat Rods
5.1. Description of a rod structure
5.2. The Cosserat model of a rod
5.3. Derivation of the balance laws from the three-dimensional theory
5.4. Balance laws by the direct approach
5.5. Invariance under superposed rigid body motions
5.6. Mechanical power
5.7. An alternative derivation of the balance laws
5.8. Anisotropic nonlinear elastic rods
5.9. Constraints
5.10. Initial and boundary conditions
5.11. Further restrictions on constitutive equations for rods constructed from homogeneous anisotropic nonlinear elastic materials
5.12. A small strain theory
5.13. Small deformations superimposed on a large deformation
5.14. Pure bending of an orthotropic beam with rectangular cross-section
5.15. Torsion of an orthotropic beam with rectangular cross-section
5.16. Inhomogeneous shear of an orthotropic beam with rectangular cross-section
5.17. Forced shearing vibrations of an orthotropic beam with rectangular cross-section
5.18. Free isochoric vibrations of an isotropic cube
5.19. An orthotropic beam with rectangular cross-section loaded by its own weight
5.20. Elastic rods
5.21. Plane strain expansion of an isotropic circular cylindrical shell
5.22. Plane strain free vibrations of an isotropic solid circular cylinder
5.23. An isotropic circular cylindrical shell loaded by its own weight
5.24. Isotropic nonlinear elastic rods
5.25. A simple derivation of the local equations for rods with rectangular cross-sections
5.26. A brief summary of the equations for rods
5.27. Linearized equations for beams with rectangular cross-sections
5.28. Bernoulli-Euler rods
5.29. Timoshenko rods
5.30. Generalized strings
5.31. Simple strings
5.32. Transverse loading of an isotropic beam with a rectangular cross-section
5.33. Linearized buckling equations
5.34. An intrinsic formulation of Bernoulli-Euler rods with symmetric cross-sections
5.35. Dissipation inequality and material damping
Chapter 6. Cosserat Points
6.1. Description of a point-like structure
6.2. The Cosserat point model
6.3. Derivation of the balance laws from the three-dimensional theory
6.4. Balance laws by the direct approach
6.5. Invariance under superposed rigid body motions
6.6. Mechanical power
6.7. An alternative derivation of the balance laws
6.8. Anisotropic nonlinear elastic Cosserat points
6.9. Constraints
6.10. Initial Conditions
6.11. Further restrictions on constitutive equations for Cosserat points constructed from homogeneous anisotropic nonlinear elastic materials
6.12. A small strain theory
6.13. Small deformations superimposed on a large deformation
6.14. Forced shearing vibrations of an orthotropic rectangular parallelepiped
6.15. Free isochoric vibrations of an isotropic cube
6.16. Isotropic nonlinear elastic Cosserat points
6.17. A brief summary of the equations for Cosserat points
6.18. Dissipation inequality and material damping
Chapter 7. Numerical Solutions using Cosserat Theories
7.1. The Cosserat approach to numerical solution procedures for problems in continuum mechanics
7.2. Formulation of the numerical solution of spherically symmetric problems using the theory of a Cosserat shell
7.3. Formulation of the numerical solution of string problems using the theory of a Cosserat point
7.4. Formulation of the numerical solution of rod problems using the theory of a Cosserat point
7.5. Formulation of the numerical solution of three-dimensional problems using the theory of a Cosserat point
7.6. Formulation of the numerical solution of two-dimensional problems using the theory of a Cosserat point
Appendix A. Tensors, Tensor Products and Tensor Operations in Three Dimensions
A.1. Vectors and vector operations
A.2. Tensors as linear operators
A.3. Tensor products (special case)
A.4. Indicial notation
A.5. Tensor products (general case)
A.6. Tensor transformation relations
A.7. Additional definitions and results
Appendix B. Summary of Tensor Operations in Specific Coordinate Systems
B.1. Cylindrical polar coordinates
B.2. Spherical polar coordinates
Exercises
Acknowledgments
References
Index

Cosserat theories : shells, rods, and points /

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