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Elasticity and Geometry
From hair curls to the non-linear response of shells
Basile Audoly and Yves Pomeau
600 pages
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150 line, 30 halftone b/w illustrations
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246x171mm
978-0-19-850625-6
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Hardback
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24 June 2010
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- Covers a wide range of problems (rods, plates, shells) and applications
- Accessible to readers without background in mechanics, minimal mathematical pre-requisites
- Detailed, fully explicit solutions to practical problems
- Rigorous mathematical arguments supported by an intuitive presentation
- Can serve as an introduction to elasticity and nonlinear science
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.Readership: Students and researchers in mechanical engineering,
physics, computer graphics, bio-mechanics, and applied mathematics.
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Basile Audoly, CNRS and Université Pierre et Marie Curie, Paris VI, France, and Yves Pomeau, CNRS, Ecole Normale Supérieure, Paris, and University of Arizona, Tucson, USA
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"A most welcome addition to the literature with a refreshingly new approach, first in that it discusses in depth how the differential geometry of surfaces is connected with the theory of elastic plates and shells, second in that, as a consequence of this perspective, it sheds new light and understanding on practical problems." - Philippe Ciarlet, City University of Hong Kong
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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
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The specification in this catalogue, including without limitation price, format, extent, number of illustrations, and month of publication, was as accurate as possible at the time the catalogue was compiled. Occasionally, due to the nature of some contractual restrictions, we are unable to ship a specific product to a particular territory. Jacket images are provisional and liable to change before publication.
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