ELASTICITY & GEOMETRY C

1. Auflage 2010
ISBN: 978-0-19-850625-6
Verlag: ACADEMIC

Buch, Englisch, 598 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 1197 g

We experience elasticity everywhere in daily life: in the straightening or curling of hairs, the irreversible deformations of car bodies after a crash, or the bouncing of elastic balls in ping-pong or soccer. The theory of elasticity is essential to the recent developments of applied and fundamental science, such as the bio-mechanics of DNA filaments and other macro-molecules, and the animation of virtual characters in computer graphics and materials science. In this book, the emphasis is on the elasticity of thin bodies (plates, shells, rods) in connection with geometry. It covers such topics as the mechanics of hairs (curled and straight), the buckling instabilities of stressed plates, including folds and conical points appearing at larger stresses, the geometric rigidity of elastic shells, and the delamination of thin compressed films. It applies general methods of classical analysis, including advanced nonlinear aspects (bifurcation theory, boundary layer analysis), to derive detailed, fully explicit solutions to specific problems. These theoretical concepts are discussed in connection with experiments. The book is self-contained. Mathematical prerequisites are vector analysis and differential equations. The book can serve as a concrete introduction to nonlinear methods in analysis.

Zielgruppe

Students and researchers in mechanical engineering, physics, computer graphics, bio-mechanics, and applied mathematics.

Autoren/Hrsg.

Audoly, Pomeau

Audoly, Basile

Pomeau, Yves

Fachgebiete

• Naturwissenschaften Physik Mechanik
• Naturwissenschaften Physik Angewandte Physik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik
• Technische Wissenschaften Technik Allgemein Physik, Chemie für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

- 1: Introduction

- 2: Three-dimensional elasticity

- I: RODS

- 3: Equations for elastic rods

- 4: Mechanics of the human hair

- 5: Rippled leaves, uncoiled springs

- II: PLATES

- 6: The equations for elastic plates

- 7: End effects in plate buckling

- 8: Finite amplitude buckling of a strip

- 9: Crumpled paper

- 10: Fractal buckling near edges

- III: SHELLS

- 11: Geometric rigidity of surfaces

- 12: Shells of revolution

- 13: The elastic torus

- 14: Spherical shell pushed by a wall

- Appendix A: Calculus of variations: a worked example

- Appendix B: Boundary and interior layers

- Appendix C: The geometry of helices

- Appendix D: Derivation of the plate equations by formal expansion from 3D elasticity

Über Autor(innen)

Dr. Basile Audoly
Research Fellow
CNRS
Paris

Professor Yves Pomeau
Senior Researcher CNRS and Professor of Mathematics at the University of Arizona