Foundations of Geometric Continuum Mechanics Geometry and Duality in Continuum Mechanics
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in...
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| Format: | eBook |
| Language: | English |
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Cham
Birkhäuser
2023, 2023
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| Edition: | 1st ed. 2023 |
| Series: | Advances in Continuum Mechanics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 1. Introduction
- 2. Prelude: Finite Dimensional Systems
- Part I Algebraic Theory: Uniform Fluxes
- 3. Simplices in Affine Spaces and Their Boundaries
- 4. Uniform Fluxes in Affine Spaces
- 5. From Uniform Fluxes to Exterior Algebra
- Part II: Smooth Theory
- 6. Smooth Analysis on Manifolds: A Short Review
- 7. Interlude: Smooth Distributions of Defects
- 8. Smooth Fluxes
- 9. Frames, Body Points, and Spacetime Structure
- 10. Stresses
- 11. Smooth Electromagnetism on Manifolds
- 12. The Elasticity Problem
- 13. Symmetry and Dynamics
- Part III Non-Smooth, Global Theories
- 14. Banachable Space of Sections of Vector Bundles over Compact Manifolds
- 15. Manifolds of Sections and Embeddings
- 16. The General Framework for Global Analytic Stress Theory
- 17. Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals
- 18. de Rham Currents
- 19. Interlude: Singular Distributions of Defects in Bodies
- 20. Vector-Valued Currents
- 21. The Representation of Forces by Stresses and Hyperstresses
- 22. Simple Forces and Stresses
- 23. Whitney's Geometric Integration Theory and Non-Smooth Bodies
- 24. Optimal Fields and Load Capacity of Bodies
- Index