| Description |
1 online resource (vi, 352 pages) : color illustrations |
| Contents |
Foreword; Translation of Michael Sadowsky's Paper "An Elementary Proof for the Existence of a Developable Möbius Band and the Attribution of the Geometric Problem to a Variational Problem"; Abstract; References; Translation and Interpretation of Michael Sadowsky's Paper "Theory of Elastically Bendable Inextensible Bands with Applications to the Möbius Band"; Abstract; De nition of the Term Band Through Kinematic Properties; Rope or Wire; Band |
|
Conclusions from the Kinematical De nition of a Band: Determination of the Virtual Torsion of the Accompanying Triad t, n, and b of the Midline Compatible with the Kinematical Properties of the BandThe Equations of Static Equilibrium and the Differential Equations of a Möbius Band; A Peculiar Implication for the Shape of a Möbius Band; Acknowledgements; Appendix: Interpretation and Explanation of Sect. 4 of Sadowsky's Paper; References; Translation of Michael Sadowsky's Paper "The Differential Equations of the Möbius Band"; Abstract; References |
|
"Wunderlich, Meet Kirchhoff": A General and Uni ed Description of Elastic Ribbons and Thin RodsAbstract; Introduction; Geometry of a Developable Ribbon; Developable Transformation from Reference to Current Con guration; Edge Functions; Constraints Expressing Developability; Area Element; Curvature Tensor of the Deformed Ribbon; Elastic Energy; Equations of Equilibrium; Principle of Virtual Work for a Ribbon; Equations of Equilibrium; Complete Set of Equations for an Elastic Ribbon; Special Cases; Naturally Straight, Rectangular Ribbons; Sadowsky's Limit: Narrow Rectangular Ribbons |
|
Helical RibbonsIllustrations; Buckling of a Cylindrical Ribbon; Overcurved and Undercurved Annular Ribbons; 3D Kirigami from 2D Cut-Out Patterns; Conclusion; Acknowledgements; Appendix: Curvature Tensor of a Developable Surface; References; Equilibrium Shapes with Stress Localisation for Inextensible Elastic Möbius and Other Strips; Abstract; Introduction; Geometry of a Developable Strip; Edge of Regression; The Energy Functional; Variational Principle and Equilibrium Equations; Variational Principle; Equations in the Original Variables kappa, eta; Hamiltonian; Symmetries |
| Summary |
Recent developments in biology and nanotechnology have stimulated a rapidly growing interest in the mechanics of thin, flexible ribbons and Mobius bands. This edited volume contains English translations of four seminal papers on this topic, all originally written in German; of these, Michael A. Sadowsky published the first in 1929, followed by two others in 1930, and Walter Wunderlich published the last in 1962. The volume also contains invited, peer-reviewed, original research articles on related topics. Previously published in the Journal of Elasticity, Volume 119, Issue 1-2, 2015 |
| Analysis |
engineering |
|
computational science |
|
membranen |
|
membranes |
|
nanotechnologie |
|
nanotechnology |
|
mechanica |
|
mechanics |
|
materialen |
|
materials |
|
Engineering (General) |
|
Techniek (algemeen) |
| Notes |
"Previously published in Journal of Elasticity, volume 119, issues 1-2, 2015." |
|
English |
|
Online resource; title from PDF title page (EBSCO, viewed August 20, 2015) |
| Subject |
Conformal geometry.
|
|
Mechanics -- Mathematics
|
|
MATHEMATICS -- Geometry -- General.
|
|
Conformal geometry
|
|
Mechanics -- Mathematics
|
| Form |
Electronic book
|
| Author |
Fosdick, Roger, editor.
|
|
Fried, Eliot, editor.
|
| ISBN |
9789401773003 |
|
9401773009 |
|
