Differential Geometry and Kinematics of Continua
Nonfiction, Science & Nature, Mathematics, Geometry, Applied
| Author: | John D Clayton | ISBN: | 9789814616058 |
| Publisher: | World Scientific Publishing Company | Publication: | July 31, 2014 |
| Imprint: | WSPC | Language: | English |
| Author: | John D Clayton |
| ISBN: | 9789814616058 |
| Publisher: | World Scientific Publishing Company |
| Publication: | July 31, 2014 |
| Imprint: | WSPC |
| Language: | English |
This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided.
Contents:
- Introduction
- Geometric Fundamentals
- Kinematics of Integrable Deformation
- Geometry of Anholonomic Deformation
- Kinematics of Anholonomic Deformation
- List of Symbols
- Bibliography
- Index
Readership: Researchers in mathematical physics and engineering mechanics.
Key Features:
- Presentation of mathematical operations and examples in anholonomic space associated with a multiplicative decomposition (e.g., of the gradient of motion) is more general and comprehensive than any given elsewhere and contains original ideas and new results
- Line-by-line derivations are frequent and exhaustive, to facilitate practice and enable verification of final results
- General analysis is given in generic curvilinear coordinates; particular sections deal with applications and examples in Cartesian, cylindrical, spherical, and convected coordinates. Indicial and direct notations of tensor calculus enable connections with historic and modern literature, respectively
This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided.
Contents:
- Introduction
- Geometric Fundamentals
- Kinematics of Integrable Deformation
- Geometry of Anholonomic Deformation
- Kinematics of Anholonomic Deformation
- List of Symbols
- Bibliography
- Index
Readership: Researchers in mathematical physics and engineering mechanics.
Key Features:
- Presentation of mathematical operations and examples in anholonomic space associated with a multiplicative decomposition (e.g., of the gradient of motion) is more general and comprehensive than any given elsewhere and contains original ideas and new results
- Line-by-line derivations are frequent and exhaustive, to facilitate practice and enable verification of final results
- General analysis is given in generic curvilinear coordinates; particular sections deal with applications and examples in Cartesian, cylindrical, spherical, and convected coordinates. Indicial and direct notations of tensor calculus enable connections with historic and modern literature, respectively
