Cosserat Theories: Shells, Rods and Points [electronic resource] / by M.B. Rubin.
This book presents a unified hierarchical formulation of theories for three-dimensional continua, two-dimensional shells, one-dimensional rods, and zero-dimensional points. Moreover, it is shown that a Cosserat point can be used like a finite element for the numerical solution of problems in continu...
Saved in:
| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht :
Springer Netherlands,
2000.
|
| Series: | Solid mechanics and its applications ;
79. |
| Subjects: |
MARC
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| 245 | 1 | 0 | |a Cosserat Theories: Shells, Rods and Points |h [electronic resource] / |c by M.B. Rubin. |
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| 490 | 1 | |a Solid Mechanics and Its Applications, |x 0925-0042 ; |v 79 | |
| 505 | 0 | |a 1 Introduction -- 2 Basic Tensor Operations in Curvilinear Coordinates -- 3 Three-Dimensional Continua -- 4 Cosserat Shells -- 5 Cosserat Rods -- 6 Cosserat Points -- 7 Numerical Solutions using Cosserat Theories -- 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. | |
| 520 | |a This book presents a unified hierarchical formulation of theories for three-dimensional continua, two-dimensional shells, one-dimensional rods, and zero-dimensional points. Moreover, it is shown that a Cosserat point can be used like a finite element for the numerical solution of problems in continuum mechanics. One objective of this book is to allow readers with varying backgrounds easy access to fundamental understanding of these powerful Cosserat theories. Therefore, the mathematical presentation has been simplified and a number of example problems have been solved. Also, complete specific constitutive equations for nonlinear orthotropic elastic structures have been presented in terms of easily identifiable material constants. This book can be used as a graduate text in continuum mechanics or as an invaluable reference for researchers in nonlinear structural mechanics. | ||
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