Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Stuttgart
Fraunhofer Verlag
2023
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | xiii, 153 Seiten Illustrationen, Diagramme 21 cm x 14.8 cm |
| ISBN: | 9783839619728 3839619726 |
Internformat
MARC
| LEADER | 00000nam a22000008c 4500 | ||
|---|---|---|---|
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| 016 | 7 | |a 1318560063 |2 DE-101 | |
| 020 | |a 9783839619728 |c : EUR 79.00 (DE), EUR 81.30 (AT), CHF 121.70 (freier Preis) |9 978-3-8396-1972-8 | ||
| 020 | |a 3839619726 |9 3-8396-1972-6 | ||
| 024 | 3 | |a 9783839619728 | |
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| 100 | 1 | |a Falconi, Riccardo |e Verfasser |0 (DE-588)1332891772 |4 aut | |
| 245 | 1 | 0 | |a Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact |c Riccardo Falconi |
| 264 | 1 | |a Stuttgart |b Fraunhofer Verlag |c 2023 | |
| 300 | |a xiii, 153 Seiten |b Illustrationen, Diagramme |c 21 cm x 14.8 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |b Dissertation |c Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |d 2023 | ||
| 650 | 0 | 7 | |a Elastizität |0 (DE-588)4014159-7 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Textilien |0 (DE-588)4059615-1 |2 gnd |9 rswk-swf |
| 653 | |a Periodic Unfolding Method | ||
| 653 | |a Homogenization | ||
| 653 | |a Dimension reduction | ||
| 653 | |a Linear Elasticity | ||
| 653 | |a Sobolev spaces | ||
| 653 | |a Textile Structures Modeling | ||
| 653 | |a Funktionalanalyse Mathematiker | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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Datensatz im Suchindex
| _version_ | 1817696770248933376 |
|---|---|
| adam_text |
VIII
CONTENTS
ABSTRACT
.
III
ABSTRACT
.
V
ACKNOWLEDGEMENTS
.
VII
1
INTRODUCTION
.
1
1.1
FIRST
PART:
NEW
TOOLS
FOR
THE
PERIODIC
UNFOLDING
.
2
1.2
SECOND
PART:
CLASSIFICATION
AND
HOMOGENIZATION
OF
TEXTILE
STRUCTURES
.
.
4
2
PRELIMINARIES
.
9
2.1
THE
PERIODIC
UNFOLDING
METHOD
.
9
2.1.1
ASYMPTOTIC
BEHAVIOR
OF
(ISOTROPICALLY)
BOUNDED
FUNCTIONS
.
11
2.2
THE
APPROXIMATION
OF
FUNCTIONS
TO
LINEAR
AND
CUBIC
INTERPOLATES
.
12
2.2.1
THE
N-LINEAR
INTERPOLATION
.
14
2.2.2
THE
N-CUBIC
INTERPOLATION
.
16
3
NEW
TOOL:
PERIODIC
UNFOLDING
FOR
ANISOTROPICALLY
BOUNDED
FUNCTIONS
.
23
3.1
SPACE
PARTITION
AND
ANISOTROPY
OF
THE
FUNCTIONS
.
23
3.2
THE
TWO-STEP
UNFOLDING
.
25
3.3
ASYMPTOTIC
BEHAVIOR
OF
ANISOTROPICALLY
BOUNDED
SEQUENCES
.
26
3.4
APPLICATION:
HOMOGENIZATION
IN
AN
ANISOTROPIC
ENVIRONMENT
.
29
4
NEW
TOOL:
PERIODIC
UNFOLDING
FOR
FUNCTIONS
DEFINED
ON
LATTICES
.
37
4.1
THE
PERIODIC
LATTICE
STRUCTURE
.
37
4.1.1
THE
UNFOLDING
OPERATOR
FOR
LATTICES
.
39
4.2
PERIODIC
UNFOLDING
FOR
SEQUENCES
DEFINED
AS
N-LINEAR
INTERPOLATES
ON
LATTICES
.
40
4.3
HOW
TO
UNFOLD
SEQUENCES
DEFINED
ON
PERIODIC
LATTICE
STRUCTURES
.
43
4.3.1
A
FIRST
DECOMPOSITION
.
43
4.3.2
A
COMMUTATIVE
DIAGRAM:
FROM
LATTICE
TO
RN,
AND
TO
LATTICE
AGAIN
44
4.4
ASYMPTOTIC
BEHAVIOR
OF
SEQUENCES
WITH
BOUND
UP
TO
THE
FIRST
DERIVATIVES
44
4.4.1
SEQUENCES
ISOTROPICALLY
BOUNDED
ON
LATTICES
.
45
4.4.2
SEQUENCES
ANISOTROPICALLY
BOUNDED
ON
LATTICES
.
47
4.5
ASYMPTOTIC
BEHAVIOR
OF
SEQUENCES
WITH
BOUND
UP
TO
THE
SECOND
DERIVA
TIVES
.
49
4.5.1
THE
PROBLEM
OF
MIXED
DERIVATIVES
.
49
4.5.2
UNFOLDING
VIA
N-CUBIC
INTERPOLATION
.
50
4.5.3
UNFOLDING
VIA
KNOWN
RESULTS
FOR
SEQUENCES
BOUNDED
IN
W1P
.
.
53
4.6
APPLICATION:
HOMOGENIZATION
ON
A
PERIODIC
LATTICE
STRUCTURE
.
57
5
CLASSIFICATION
OF
TEXTILE
STRUCTURES
IN
LINEAR
ELASTICITY
REGIMES
.
63
IX
5.1
PARAMETERIZATION
OF
A
CURVED
ROD
.
63
5.2
DECOMPOSITION
OF
A
CURVED
ROD'S
DISPLACEMENT
.
65
5.2.1
THE
LINEARIZED
STRAIN
TENSOR
ASSOCIATED
WITH
THE
DISPLACEMENT
.
66
5.3
A
NEW
DECOMPOSITION
FOR
THE
DISPLACEMENT
.
67
5.3.1
PROPERTIES
OF
THE
INTERPOLATING
FUNCTIONS
.
68
5.3.2
THE
PRIME
DECOMPOSITION
.
69
5.3.3
THE
LINEARIZED
STRAIN
TENSOR
ASSOCIATED
WITH
THE
PRIME
DECOM
POSITION
.
71
5.4
THE
TEXTILE
STRUCTURE
AND
NATURAL
ASSUMPTIONS
.
72
5.4.1
THE
WOVEN
STRUCTURE
.
72
5.4.2
BOUNDARY
CONDITIONS
.
74
5.4.3
CONTACT
AND
NON-PENETRATION
CONDITIONS
.
74
5.5
WELL
POSEDNESS
OF
THE
ELASTICITY
PROBLEM
.
75
5.5.1
SET
OF
ADMISSIBLE
DISPLACEMENTS
.
75
5.5.2
THE
PROBLEM
IN
LINEAR
ELASTICITY
.
75
5.6
ESTIMATES
FOR
THE
DISPLACEMENTS
FIELDS
.
77
5.6.1
FUNDAMENTAL
ESTIMATES
.
77
5.6.2
CONTACT
AND
NON-PENETRATION
ESTIMATES
.
77
5.6.3
OUTER-PLANE
FIELDS'
ESTIMATES
IN
THE
WHOLE
DOMAIN
0
.
78
5.6.4
IN-PLANE
FIELDS'
ESTIMATES
IN
THE
WHOLE
DOMAIN
Q
.
79
5.6.5
OTHER
IMPORTANT
ESTIMATES
.
81
5.7
CHOICE
OF
THE
PARAMETERS
.
82
5.7.1
DIFFERENT
TYPE
OF
R
=
K8
TEXTILES
IN
LINEAR
REGIME
(L|U||T
~
85/2)
.
84
6
TEXTILES
WITH
STRONG
CONTACT
AND
VERY
LOOSE
CONTACT
.
87
6.1
TEXTILES
WITH
VERY
STRONG
CONTACT
.
87
6.1.1
FINAL
DECOMPOSITION
OF
THE
DISPLACEMENT
IN
THE
IN-PLANE
COM
PONENT
.
87
6.1.2
FINAL
DECOMPOSITION
OF
THE
DISPLACEMENT
IN
THE
IN-PLANE
COM
PONENT
.
90
6.1.3
APRIORI
CONCLUSIONS
.
92
6.2
TEXTILES
WITH
VERY
LOOSE
CONTACT
.
92
6.2.1
FINAL
DECOMPOSITION
OF
THE
DISPLACEMENT
IN
THE
OUTER-PLANE
COMPONENT
.
93
6.2.2
NEW
ASSUMPTION:
THE
GLUED
CONDITIONS
.
93
6.2.3
FINAL
DECOMPOSITION
OF
THE
DISPLACEMENT
IN
THE
IN-PLANE
COM
PONENT
AND
A
PRIORI
CONCLUSIONS
.
95
7
TEXTILES
WITH
LOOSE
CONTACT
.
97
7.1
FINAL
DECOMPOSITION
OF
THE
DISPLACEMENTS
.
97
7.1.1
.
IN
THE
OUTER-PLANE
COMPONENT
.
97
7.1.2
.
THE
IN-PLANE
COMPONENT
.
97
7.1.3
FINAL
SPLIT
OF
THE
IN-PLANE
"CENTERLINE"
DISPLACEMENTS
.
99
7.2
THE
SUFFICIENT
APPLIED
STRESS
TO
STAY
IN
A
LINEAR
REGIME
.
102
7.3
WEAK
CONVERGENCE
OF
THE
DISPLACEMENT
FIELDS
VIA
UNFOLDING
.
103
7.3.1
THE
UNFOLDING
OPERATORS
FOR
A
TEXTILE
WITH
CONTACT
SLIDING
.
103
7.3.2
LIMIT
DISPLACEMENT
FIELDS
VIA
THE
MIDDLE
LINE
UNFOLDING
OPERATOR
105
7.3.3
LIMIT
OF
THE
STRAIN
TENSOR'S
FIELDS
VIA
GLOBAL
UNFOLDING
OPERATOR
109
7.3.4
UNFOLDED
LIMIT
OF
THE
FRAME
.
111
7.3.5
FORM
OF
THE
LIMIT
STRAIN
TENSORS
FOR
THE
WARPING
.
112
7.3.6
FORM
OF
THE
LIMIT
STRAIN
TENSORS
.
112
X
7.3.7
UNFOLD
OF
THE
CONTACT
CONDITIONS
VIA
CONTACT
UNFOLDING
OPERATOR
114
7.3.8
THE
DISPLACEMENTS
LIMIT
SET
.
119
7.4
STRONG
CONVERGENCE
OF
THE
TEST
FUNCTIONS
VIA
UNFOLDING
.
120
7.4.1
CONSTRUCTION
OF
THE
TEST
FUNCTIONS
.
120
7.4.2
LIMIT
STRAIN
TENSORS
FOR
THE
TEST
FUNCTIONS
.
121
7.4.3
CONTACT
CONDITIONS
FOR
THE
TEST
FUNCTIONS
.
122
7.5
STUDY
OF
THE
LIMIT
PROBLEM
.
123
7.5.1
THE
UNFOLDED
LIMIT
PROBLEM
.
124
7.5.2
THE
MICROSCOPIC
CELL
PROBLEM
.
126
7.5.3
THE
HOMOGENIZING
OPERATOR
AND
THE
MACROSCOPIC
CELL
PROBLEM
.
127
8
CONCLUSIONS
.
131
8.1
RESULTS
OF
THE
EXTENSION
OF
THE
UNFOLDING
METHOD
.
131
8.2
MACROSCOPIC
BEHAVIOR
OF
R
=
K8
TEXTILES
ACCORDING
TO
THE
CONTACT
STRENGTH
H
131
8.2.1
.
RESULTS
(KNOWN)
FOR
A
TEXTILE
WITH
CONTACT
G
E
~
84G
OR
HIGHER
.
.
132
8.2.2
.
RESULTS
(KNOWN)
FOR
A
TEXTILE
WITH
CONTACT
G
E
~
83G
.
133
8.2.3
NEW
RESULTS
FOR
A
TEXTILE
WITH
CONTACT
GE
~
82G
134
8.2.4
THE
TRIVIAL
CASE
OF
A
TEXTILE
WITH
CONTACT
GE
~
EG
.
135
A
TECHNICAL
LEMMAS
.
137
A.1
.ABOUT
THE
PERIODIC
UNFOLDING
FOR
ANISOTROPICALLY
BOUNDED
SEQUENCES
137
A.2
.ABOUT
THE
PERIODIC
UNFOLDING
FOR
LATTICES
.
139
B
ADDITIONAL
RESULTS
ABOUT
ANISOTROPICALLY
BOUNDED
FUNCTIONS
.
.141
C
PROOF
OF
A
BETTER
BOUND
FOR
ESTIMATE
(5.37)
IN
LEMMA
19
.
145
BIBLIOGRAPHY
.
151 |
| any_adam_object | 1 |
| author | Falconi, Riccardo |
| author_GND | (DE-588)1332891772 |
| author_facet | Falconi, Riccardo |
| author_role | aut |
| author_sort | Falconi, Riccardo |
| author_variant | r f rf |
| building | Verbundindex |
| bvnumber | BV049878058 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)1466910097 (DE-599)DNB1318560063 |
| discipline | Mathematik |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV049878058 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T13:12:04Z |
| institution | BVB |
| institution_GND | (DE-588)10126139-1 (DE-588)4786605-6 |
| isbn | 9783839619728 3839619726 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035217488 |
| oclc_num | 1466910097 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xiii, 153 Seiten Illustrationen, Diagramme 21 cm x 14.8 cm |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Fraunhofer Verlag |
| record_format | marc |
| spelling | Falconi, Riccardo Verfasser (DE-588)1332891772 aut Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact Riccardo Falconi Stuttgart Fraunhofer Verlag 2023 xiii, 153 Seiten Illustrationen, Diagramme 21 cm x 14.8 cm txt rdacontent n rdamedia nc rdacarrier Dissertation Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau 2023 Elastizität (DE-588)4014159-7 gnd rswk-swf Struktur (DE-588)4058125-1 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Textilien (DE-588)4059615-1 gnd rswk-swf Periodic Unfolding Method Homogenization Dimension reduction Linear Elasticity Sobolev spaces Textile Structures Modeling Funktionalanalyse Mathematiker (DE-588)4113937-9 Hochschulschrift gnd-content Textilien (DE-588)4059615-1 s Struktur (DE-588)4058125-1 s Elastizität (DE-588)4014159-7 s DE-604 Funktionalanalysis (DE-588)4018916-8 s Fraunhofer-Institut für Techno- und Wirtschaftsmathematik Sonstige (DE-588)10126139-1 oth Fraunhofer IRB-Verlag (DE-588)4786605-6 pbl X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=e702ac7598db4cada2980438851f5c02&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035217488&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20240207 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Falconi, Riccardo Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact Elastizität (DE-588)4014159-7 gnd Struktur (DE-588)4058125-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd Textilien (DE-588)4059615-1 gnd |
| subject_GND | (DE-588)4014159-7 (DE-588)4058125-1 (DE-588)4018916-8 (DE-588)4059615-1 (DE-588)4113937-9 |
| title | Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact |
| title_auth | Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact |
| title_exact_search | Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact |
| title_full | Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact Riccardo Falconi |
| title_fullStr | Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact Riccardo Falconi |
| title_full_unstemmed | Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact Riccardo Falconi |
| title_short | Homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact |
| title_sort | homogenization and dimension reduction for periodic textiles made of linear elastic yarns with sliding contact |
| topic | Elastizität (DE-588)4014159-7 gnd Struktur (DE-588)4058125-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd Textilien (DE-588)4059615-1 gnd |
| topic_facet | Elastizität Struktur Funktionalanalysis Textilien Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=e702ac7598db4cada2980438851f5c02&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035217488&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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