Elasticity and geometry: from hair curls to the non-linear response of shells
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2010
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | X, 586 S. Ill., graph. Darst. |
| ISBN: | 9780198506256 |
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MARC
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| 245 | 1 | 0 | |a Elasticity and geometry |b from hair curls to the non-linear response of shells |c B. Audoly ; Y. Pomeau |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2010 | |
| 300 | |a X, 586 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020534486 | ||
Record in the Search Index
| _version_ | 1804143221216903168 |
|---|---|
| adam_text | Contents
1
Introduction
1
1.1 Outline 1
1.2
Notations
and conventions
3
1.3
Mathematical background
9
2
Three-dimensional elasticity
17
2.1
Introduction
17
2.2
Strain
18
2.3
Stress
33
2.4
Hookean elasticity
42
2.5
Stress and strain for finite displacements
47
2.6
Conclusion
56
References
56
PART I RODS
3
Equations for elastic rods
59
3.1
Introduction
59
3.2
Geometry of a deformed rod. Darboux vector
61
3.3
Flexion
63
3.4
Twist
73
3.5
Energy
79
3.6
Equilibrium:
Kirchhoff
equations
82
3.7
Inextensibility. validity of
Kirchhoff
model
90
3.8
Mathematical analogy with the spinning top
92
3.9
The localized helix: an explicit solution
96
3.10
Conclusion
102
References
102
4
Mechanics of the human hair
105
4.1
Dimensional analysis
106
4.2
Equilibrium equations
109
4.3
Weak gravity 111
4.4
Strong gravity
114
4.5
Extensions of the model
124
4.6
Conclusion
129
References
130
5
Rippled leaves, uncoiled springs
132
5.1
Introduction
132
5.2
Governing equations
141
5.3
Helical solutions
143
5.4
Godet
solutions
147
viii Contents
5.5
Conclusion
153
References
154
PART II PLATES
6
The equations for elastic
plates
157
6.1
Bending
versus
stretching energy
158
6.2
Gauss
Theorema
egregium
161
6.3
Developable surfaces
176
6.4
Membranes: stretching energy
184
6.5
Equilibrium: the
Föppl-von Karman
equations
192
6.6
Elastic energy
199
6.7
Narrow plates: consistency with the theory of rods
205
6.8
Discussion
210
6.9
Conclusion
212
References
213
7
End effects in plate buckling
214
7.1
A historical background on end effects
214
7.2
Geometry
215
7.3
Governing equations
217
7.4
Linear stability analysis
221
7.5
Buckling amplitude near threshold
224
7.6
Wavenumber selection by end effects
231
7.7
Experiments
247
7.8
Conclusion
249
References
249
8
Finite amplitude buckling of a strip
251
8.1
A short review on buckling
252
8.2
The experiments
253
8.3
Equations for the compressed strip
256
8.4
Linear stability
260
8.5
The
Euler
column, an exact solution
265
8.6
Transition from finite to infinite wavelengths
273
8.7
Linear stability of the
Euler
column
282
8.8
Extension of the diagram
296
8.9
Comparison with buckling experiments
311
8.10
Application: interpretation of delamination
patterns
314
8.11
Limitations and extensions of the model
318
8.12
Conclusion
321
References
322
9
Crumpled paper
325
9.1
Introduction
325
9.2
Conical singularities
326
9.3
Ridge singularities
350
Contents ix
9.4
Conclusion
366
References
357
10
Fractal buckling near edges
369
10.1
Case of residual stress near a free edge
371
10.2
Case of a clamped edge
384
10.3
Summary and conclusion
398
References
398
PART III SHELLS
11
Geometric rigidity of surfaces
403
11.1
Introduction
404
11.2
Infinitesimal bendings of a weakly curved surface 40G
11.3
Infinitesimal bendings: an intrinsic approach
408
11.4
Minimal surfaces,
Weierstrass
transform
415
11.5
Surfaces of revolution
416
11.6
Crowns: interpretation of rigidity, extension to arbitrary surfaces
429
11.7
Conclusion
432
References
433
12
Shells of revolution
435
12.1
Geometry
436
12.2
Constitutive relations
442
12.3
Equilibrium of membranes
444
12.4
Equilibrium of shells
448
12.5
Conclusion, extensions
452
References
453
13
The elastic torus
454
13.1
Introduction
454
13.2
Mechanical problem
457
13.3
Linearized membrane theory
460
13.4
Boundary layer equations
464
13.5
The curious case of pressurized circular toroidal shells
471
13.6
Boundary layer solution for moderate nonlinearity
473
13.7
Boundary layer solution for weak nonlinearity
475
13.8
Boundary layer solution for strong nonlinearity
486
13.9
Conclusion
-187
References
ΊΜ
14
Spherical shell pushed by a wall
490
14.1
Introduction
-W
14.2
A short account of Hertz contact theory
492
14.3
Point-like force on a spherical shell
194
14.4
Spherical shell pushed by a plane: overview
198
14.5
Equation for spherical shells r>02
14.6
Spherical shell pushed by a plane: disc-like contact
510
χ
Contents
14.7
Spherical shell pushed by a plane: circular contact
521
14.8
Stability of disc-like contact, transition to circular contact
532
References
543
Appendix A Calculus of variations: a worked example
546
A.I Model problem: the
Elastica
546
A.
2
Discretization of energy using a Riemann sum
548
A.3 Calculus of variations: the Euler-Lagrange method
549
A.
4
Handling additional constraints
550
A.
5
Linear stability analysis
551
A.
6
Exact solution
552
References
557
Appendix
В
Boundary and interior layers
558
B.I Layer at an interior point
558
B.2 Layers near a boundary
565
References
567
Appendix
С
The geometry of helices
569
Appendix
D
Derivation of the plate equations by formal
expansion from
3D
elasticity
571
D.I Introduction
571
D.2 Scaling assumptions
573
D.3 Basic equations
573
D.4 Expansion of the basic quantities
575
D.5 Solution at leading order
576
D.6 Conclusion
581
References
581
Index
583
|
| any_adam_object | 1 |
| author | Audoly, Basile Pomeau, Yves 1942- |
| author_GND | (DE-588)1170093558 (DE-588)1170093825 |
| author_facet | Audoly, Basile Pomeau, Yves 1942- |
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| author_sort | Audoly, Basile |
| author_variant | b a ba y p yp |
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| classification_rvk | UF 3000 SK 600 |
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| dewey-full | 531.3820151636 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.3820151636 |
| dewey-search | 531.3820151636 |
| dewey-sort | 3531.3820151636 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV036614304 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:13Z |
| institution | BVB |
| isbn | 9780198506256 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020534486 |
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| physical | X, 586 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Oxford Univ. Press |
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| spelling | Audoly, Basile Verfasser (DE-588)1170093558 aut Elasticity and geometry from hair curls to the non-linear response of shells B. Audoly ; Y. Pomeau 1. publ. Oxford [u.a.] Oxford Univ. Press 2010 X, 586 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Elastizität (DE-588)4014159-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Elastizität (DE-588)4014159-7 s Geometrie (DE-588)4020236-7 s DE-604 Pomeau, Yves 1942- Verfasser (DE-588)1170093825 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020534486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Audoly, Basile Pomeau, Yves 1942- Elasticity and geometry from hair curls to the non-linear response of shells Elastizität (DE-588)4014159-7 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4014159-7 (DE-588)4020236-7 |
| title | Elasticity and geometry from hair curls to the non-linear response of shells |
| title_auth | Elasticity and geometry from hair curls to the non-linear response of shells |
| title_exact_search | Elasticity and geometry from hair curls to the non-linear response of shells |
| title_full | Elasticity and geometry from hair curls to the non-linear response of shells B. Audoly ; Y. Pomeau |
| title_fullStr | Elasticity and geometry from hair curls to the non-linear response of shells B. Audoly ; Y. Pomeau |
| title_full_unstemmed | Elasticity and geometry from hair curls to the non-linear response of shells B. Audoly ; Y. Pomeau |
| title_short | Elasticity and geometry |
| title_sort | elasticity and geometry from hair curls to the non linear response of shells |
| title_sub | from hair curls to the non-linear response of shells |
| topic | Elastizität (DE-588)4014159-7 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Elastizität Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020534486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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