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Foundations of Geometric Continuum Mechanics

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Cover of 'Foundations of Geometric Continuum Mechanics'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Prelude: Finite-Dimensional Systems
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    Chapter 3 Simplices in Affine Spaces and Their Boundaries
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    Chapter 4 Uniform Fluxes in Affine Spaces
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    Chapter 5 From Uniform Fluxes to Exterior Algebra
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    Chapter 6 Smooth Analysis on Manifolds: A Short Review
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    Chapter 7 Interlude: Smooth Distributions of Defects
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    Chapter 8 Smooth Fluxes
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    Chapter 9 Frames, Body Points, and Spacetime Structure
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    Chapter 10 Stresses
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    Chapter 11 Smooth Electromagnetism on Manifolds
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    Chapter 12 The Elasticity Problem
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    Chapter 13 Symmetry and Dynamics
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    Chapter 14 Banachable Spaces of Sections of Vector Bundles over Compact Manifolds
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    Chapter 15 Manifolds of Sections and Embeddings
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    Chapter 16 The General Framework for Global Analytic Stress Theory
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    Chapter 17 Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals
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    Chapter 18 de Rham Currents
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    Chapter 19 Interlude: Singular Distributions of Defects in Bodies
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    Chapter 20 Vector-Valued Currents
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    Chapter 21 The Representation of Forces by Stresses and Hyperstresses
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    Chapter 22 Simple Forces and Stresses
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    Chapter 23 Whitney’s Geometric Integration Theory and Non-smooth Bodies
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    Chapter 24 Optimal Fields and Load Capacity of Bodies
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Title
Foundations of Geometric Continuum Mechanics
Published by
Springer International Publishing, August 2023
DOI 10.1007/978-3-031-35655-1
ISBNs
978-3-03-135654-4, 978-3-03-135655-1
Authors

Segev, Reuven

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