Differential geometry applied to continuum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Aachen
Shaker
2009
|
| Schriftenreihe: | Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin
44 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 99 S. graph. Darst. 30 cm, 186 gr. |
| ISBN: | 9783832281540 |
Internformat
MARC
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| 100 | 1 | |a Aubram, Daniel |e Verfasser |0 (DE-588)1048133109 |4 aut | |
| 245 | 1 | 0 | |a Differential geometry applied to continuum mechanics |c Daniel Aubram |
| 264 | 1 | |a Aachen |b Shaker |c 2009 | |
| 300 | |a XVI, 99 S. |b graph. Darst. |c 30 cm, 186 gr. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin |v 44 | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kontinuumsmechanik |0 (DE-588)4032296-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
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Datensatz im Suchindex
| _version_ | 1804143826613305344 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE BY THE EDITOR I
PREFACE BY THE AUTHOR III
ABSTRACT V
ZUSAMMENFASSUNG VII
CONTENTS XI
LIST OF FIGURES XIII
NOTATION XV
1 INTRODUCTION 1
2 REVIEW OF LINEAR GEOMETRY 5
2.1 VECTORS AND LINEAR MAPS 5
2.2 AFFINE POINT SPACES 8
3 DIFFERENTIAL GEOMETRY 15
3.1 TOPOLOGY AND MANIFOLDS 15
3.2 THE TANGENT SPACE 19
3.3 TENSOR ALGEBRA 24
3.4 BUNDLES AND TENSOR FIELDS 30
3.4.1 SECTIONS OF FIBRE BUNDLES 30
3.4.2 ACTION OF MAPS 35
3.5 EXTERIOR ALGEBRA OF DIFFERENTIAL FORMS 40
3.6 DIFFERENTIATION ON MANIFOLDS 44
3.6.1 COVARIANT DERIVATIVE 45
3.6.2 LIE DERIVATIVE 49
3.6.3 EXTERIOR DERIVATIVE 53
3.7 INTEGRATION ON MANIFOLDS 54
3.7.1 ORIENTATION AND DETERMINANTS 54
3.7.2 STOKES THEOREM AND VOLUME MEASURES 59
4 APPLICATION: CONTINUUM MECHANICS 65
XI
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/994110510
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
4.1 MATERIAL BODY AND AMBIENT SPACE 65
4.2 DEFORMATION GRADIENT AND STRAIN MEASURES 69
4.3 LAGRANGIAN AND EULERIAN FORMULATIONS 74
4.4 CONSERVATION OF MASS AND PIOLA TRANSFORMATION 76
4.5 OBJECTIVITY AND COVARIANCE 79
4.5.1 MOTIONS, FRAMINGS, AND THE GAUGE FREEDOM 79
4.5.2 MATERIAL FRAME-INDIFFERENCE 82
4.6 ARBITRARY LAGRANGIAN-EULERIAN FORMULATION 84
4.6.1 GRID MANIFOLD AND VELOCITY FIELDS 85
4.6.2 THE GENERAL ALE OPERATOR 92
5 SUMMARY AND CONCLUSIONS 95
BIBLIOGRAPHY 97
|
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| dewey-tens | 530 - Physics |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
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| id | DE-604.BV037224235 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:53:50Z |
| institution | BVB |
| isbn | 9783832281540 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021138053 |
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| owner_facet | DE-83 |
| physical | XVI, 99 S. graph. Darst. 30 cm, 186 gr. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Shaker |
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| series | Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin |
| series2 | Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin |
| spelling | Aubram, Daniel Verfasser (DE-588)1048133109 aut Differential geometry applied to continuum mechanics Daniel Aubram Aachen Shaker 2009 XVI, 99 S. graph. Darst. 30 cm, 186 gr. txt rdacontent n rdamedia nc rdacarrier Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin 44 Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin 44 (DE-604)BV008278512 44 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021138053&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aubram, Daniel Differential geometry applied to continuum mechanics Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin Differentialgeometrie (DE-588)4012248-7 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4032296-8 |
| title | Differential geometry applied to continuum mechanics |
| title_auth | Differential geometry applied to continuum mechanics |
| title_exact_search | Differential geometry applied to continuum mechanics |
| title_full | Differential geometry applied to continuum mechanics Daniel Aubram |
| title_fullStr | Differential geometry applied to continuum mechanics Daniel Aubram |
| title_full_unstemmed | Differential geometry applied to continuum mechanics Daniel Aubram |
| title_short | Differential geometry applied to continuum mechanics |
| title_sort | differential geometry applied to continuum mechanics |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Differentialgeometrie Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021138053&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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