Three-Dimensional Elasticity, Volume 20This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible. |
Contents
Geometrical and other preliminaries | 3 |
The equations of equilibrium and the principle | 57 |
Exercises | 85 |
Hyperelasticity | 137 |
The boundary value problems of threedimensional | 199 |
Existence theory based on the implicit function | 269 |
function theorem | 299 |
Au¹f | 336 |
Existence theory based on the minimization of | 345 |
| 409 | |
| 435 | |
Common terms and phrases
a₁ applied body force applied forces applied surface force assume assumption axiom boundary condition boundary value problem Cauchy stress tensor Ciarlet Cof F condition of place constitutive equation continuous converges convex function defined definition deformed configuration denote density differentiable displacement-traction problem domain in R³ elastic material equivalent Exercise existence results FEM³ given gradient Green's formula Hence hyperelastic material inequality injective isotropic Lamé constants lower semi-continuous mapping f matrix minimizer nonlinear normed vector space notation open set open subset Piola-Kirchhoff stress tensor polyconvex proof of Theorem pure displacement problem pure traction problem reference configuration relation Remark response function satisfies Sect sequence Show smooth Sobolev space solution St Venant-Kirchhoff material stored energy function strain tensor symmetric tensor field topology vector field Vo(x x₁ Γ₁
References to this book
The Mathematical Theory of Finite Element Methods Susanne Brenner,L. Ridgway Scott Limited preview - 2002 |
Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear ... E. Zeidler No preview available - 1989 |