Existence and regularity for nonlinear elastic self-contact problems:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Bonn
[Math.-Naturwiss. Fak. der Univ.]
2002
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| Series: | Bonner mathematische Schriften
349 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 127 S. Ill. : 21 cm |
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Record in the Search Index
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| adam_text | Titel: Existence and regularity for nonlinear elastic self-contact problems
Autor: Mosel, Heiko von der
Jahr: 2002
Contents
Introduction *
1 Global curvature ^
1.1 Definition and basic properties.................^
1.2 Regularity.............................15
1.3 Limit cases........................................................^
1.4 Excluded volume constraint...................22
1.5 Functional properties.......................24
1.6 Proofs for Chapter 1.......................26
2 Framed curves and elastic rods 56
2.1 framed curves ....................................................56
2.2 Rod theory............................60
2.3 Local and global injectivity......................................65
2.4 Topological constraints......................68
3 Existence results 76
3.1 Abstract existence theorem......................................76
3.2 Energy minimizing elastic rods..................................78
3.2.1 Rods with shear and extension..........................78
3-2.2 Unshearable, inextensible case ..........................80
3.2.3 Extensible rods without shear............................83
3.2.4 Existence of ideal knots..................................84
4 Euler-Lagrange equations 87
4.1 The variational problem in the unshearable inextensible case 87
4.2 Euler-Lagrange equations........................................88
4.2.1 Modified variational problem............................90
4.2.2 Reduction of the modified problem......................94
4.2.3 Differentiability of the centreline and the directors . . 96
2
CONTENTS 3
4.2.4 Differentiability of the energy............................97
4.2.5 Differentiability of the boundary constraints ..........99
4.2.6 Differentiability of the self-contact constraint.....101
4.2.7 Proof of the Euler-Lagrange equations.........105
5 Regularity 108
5.1 Structure of the contact forces .................108
5.2 Transversality...........................Ill
5.3 Higher regularity.........................113
6 Appendix 117
6.1 Differential of the frame.....................117
6.2 Clarke s generalized gradients..................120
Bibliography 123
|
| any_adam_object | 1 |
| author | Mosel, Heiko von der |
| author_facet | Mosel, Heiko von der |
| author_role | aut |
| author_sort | Mosel, Heiko von der |
| author_variant | h v d m hvd hvdm |
| building | Verbundindex |
| bvnumber | BV015312023 |
| classification_rvk | SI 180 |
| classification_tum | MAT 532d MAT 492d |
| ctrlnum | (OCoLC)634631091 (DE-599)BVBBV015312023 |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-09T19:09:10Z |
| institution | BVB |
| language | English |
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| spelling | Mosel, Heiko von der Verfasser aut Existence and regularity for nonlinear elastic self-contact problems Heiko von der Mosel Bonn [Math.-Naturwiss. Fak. der Univ.] 2002 127 S. Ill. : 21 cm txt rdacontent n rdamedia nc rdacarrier Bonner mathematische Schriften 349 Zugl.: Bonn, Univ., Habil.-Schr., 2001 Energiefunktional (DE-588)4324274-1 gnd rswk-swf Euler-Lagrange-Gleichung (DE-588)4700698-5 gnd rswk-swf Elastizität (DE-588)4014159-7 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Euler-Lagrange-Gleichung (DE-588)4700698-5 s Elastizität (DE-588)4014159-7 s Energiefunktional (DE-588)4324274-1 s Variationsrechnung (DE-588)4062355-5 s DE-604 Bonner mathematische Schriften 349 (DE-604)BV000001610 349 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010100991&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mosel, Heiko von der Existence and regularity for nonlinear elastic self-contact problems Bonner mathematische Schriften Energiefunktional (DE-588)4324274-1 gnd Euler-Lagrange-Gleichung (DE-588)4700698-5 gnd Elastizität (DE-588)4014159-7 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4324274-1 (DE-588)4700698-5 (DE-588)4014159-7 (DE-588)4062355-5 (DE-588)4113937-9 |
| title | Existence and regularity for nonlinear elastic self-contact problems |
| title_auth | Existence and regularity for nonlinear elastic self-contact problems |
| title_exact_search | Existence and regularity for nonlinear elastic self-contact problems |
| title_full | Existence and regularity for nonlinear elastic self-contact problems Heiko von der Mosel |
| title_fullStr | Existence and regularity for nonlinear elastic self-contact problems Heiko von der Mosel |
| title_full_unstemmed | Existence and regularity for nonlinear elastic self-contact problems Heiko von der Mosel |
| title_short | Existence and regularity for nonlinear elastic self-contact problems |
| title_sort | existence and regularity for nonlinear elastic self contact problems |
| topic | Energiefunktional (DE-588)4324274-1 gnd Euler-Lagrange-Gleichung (DE-588)4700698-5 gnd Elastizität (DE-588)4014159-7 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Energiefunktional Euler-Lagrange-Gleichung Elastizität Variationsrechnung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010100991&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001610 |
| work_keys_str_mv | AT moselheikovonder existenceandregularityfornonlinearelasticselfcontactproblems |