Mathematical elasticity

C. von Westenholz (Eds.)0444828915, 9780444828910, 9780585474175, 0444702598, 0444825703

The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the “small” parameter.

---

Table of contents :
Content:
Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages vii-viii

Chapter 1 Topological Preliminaries
Pages 3-18

Chapter 2 Differential Calculus on Rn
Pages 19-41

Chapter 3 Differentiable Manifolds
Pages 45-58

Chapter 4 Differential Calculus on Manifolds
Pages 59-83

Chapter 5 Lie Groups
Pages 84-115

Chapter 6 Fiber Bundles
Pages 116-137

Chapter 7 Basic Concepts of Differential Forms
Pages 141-207

Chapter 8 Frobenius Theory
Pages 208-256

Chapter 9 Integration of Differential Forms
Pages 259-292

Chapter 10 The de Rham Cohomology
Pages 293-331

Chapter 11 Connections on Fiber Bundles
Pages 335-386

Chapter 12 Hamiltonian Mechanics and Geometry
Pages 389-439

Chapter 13 General Theory of Relativity
Pages 440-482

Bibliography
Pages 483-484

Subject Index
Pages 485-487