Adaptive numerical integration of dynamical contact problems
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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Cuvillier
2010 [erschienen] 2011
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| Ausgabe: | 1. Aufl. |
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| 245 | 1 | 0 | |a Adaptive numerical integration of dynamical contact problems |c Corinna Klapproth |
| 246 | 1 | 3 | |a Adaptive numerische Integration von dynamischen Kontaktproblemen |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Göttingen |b Cuvillier |c 2010 [erschienen] 2011 | |
| 300 | |a II, 160, XV S. |b graph. Darst. | ||
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| 500 | |a Nebentitel: Adaptive numerische Integration von dynamischen Kontaktproblemen | ||
| 502 | |a Berlin, Freie Univ., Diss., 2011 | ||
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| 912 | |a ebook | ||
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Datensatz im Suchindex
| _version_ | 1819752454728712192 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
INTRODUCTION 1
1. THE MOTION OF THE HUMAN KNEE AS A DYNAMICAL CONTACT PROBLEM 5 1.1.
THE HUMAN KNEE 5
1.2. BASICS OF THE MATHEMATICAL MODEL 6
1.3. STRONG AND VARIATIONAL PROBLEM 11
1.4. CONSERVATION PROPERTIES AND PERSISTENCY CONDITION 16
2. NEWMARK METHODS 23
2.1. CLASSICAL NEWMARK METHOD 25
2.2. CONTACT-IMPLICIT NEWMARK METHOD 28
2.3. CONTACT-STABILIZED NEWMARK METHOD 29
2.4. IMPROVED CONTACT-STABILIZED NEWMARK METHOD 32
2.5. NUMERICAL COMPARISON 36
3. A PERTURBATION RESULT - VISCOSITY AND PHYSICAL ENERGY NORM 45 3.1.
ELASTICITY 46
3.2. VISCOELASTICITY 48
3.3. INTERPRETATION OF THE STABILITY CONDITION 53
3.4. APPROXIMATIONS OF THE SIGNORINI CONDITION 57
4. CONSISTENCY - BOUNDED VARIATION 59
4.1. NEWMARK METHODS IN FUNCTION SPACE 59
4.2. CONSISTENCY ERROR IN PHYSICAL ENERGY NORM 66
4.3. CONSISTENCY ERROR IN A DISCRETE DISPLACEMENT NORM 78
4.4. CONSISTENCY ERROR FOR PERMANENT ACTIVE CONTACT 82
5. CONVERGENCE THEORY 91
5.1. DISCRETE PERTURBATION RESULTS 91
5.1.1. A DISCRETE PERTURBATION RESULT IN DISCRETE DISPLACEMENT NORM 92
5.1.2. DISCRETE STABILITY CONDITION 94
5.1.3. A DISCRETE PERTURBATION RESULT IN PHYSICAL ENERGY NORM . .. 99
5.2. CONVERGENCE 103
5.2.1. CONVERGENCE IN PHYSICAL ENERGY NORM 106
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1012589536
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
5.2.2. CONVERGENCE IN DISCRETE DISPLACEMENT NORM 108
6. ADAPTIVE TIMESTEP CONTROL 111
6.1. TOWARDS AN ASYMPTOTIC ERROR EXPANSION I LL
6.1.1. CONICAL DERIVATIVE 112
6.1.2. EXTENSION OF EXTRAPOLATION TECHNIQUES 114
6.1.3. CONSTRUCTION OF A HIGHER-ORDER SCHEME 116
6.1.4. DISCUSSION OF CONSISTENCY ORDER 124
6.2. TIMESTEP CONTROL 127
6.2.1. ERROR ESTIMATOR IN THE ABSENCE OF CONTACT 128
6.2.2. ERROR ESTIMATOR IN THE PRESENCE OF CONTACT 129
6.2.3. COMBINED TIMESTEP STRATEGY 131
6.3. GLOBAL DISCRETIZATION ERROR 134
7. NUMERICAL RESULTS 137
7.1. HERTZIAN CONTACT PROBLEM 137
7.2. MOTION OF THE HUMAN KNEE 142
CONCLUSION 149
A. INEQUALITIES 151
B. INTERPRETATION OF CONTACT STRESSES 153
B.I. AN ABSTRACT TRACE THEOREM 153
B.2. LOCALIZATION ON ACTIVE CONTACT BOUNDARIES 154
B.3. LOCALIZATION ON CRITICAL CONTACT BOUNDARIES 156
B.4. INTERPRETATION OF DISCRETE CONTACT STRESSES 158
LIST OF SYMBOLS I
BIBLIOGRAPHY XII
DANKSAGUNG XIII
ZUSAMMENFASSUNG XV
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| any_adam_object | 1 |
| author | Klapproth, Corinna 1982- |
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| author_facet | Klapproth, Corinna 1982- |
| author_role | aut |
| author_sort | Klapproth, Corinna 1982- |
| author_variant | c k ck |
| building | Verbundindex |
| bvnumber | BV037490822 |
| collection | ebook |
| ctrlnum | (OCoLC)780101172 (DE-599)BVBBV037490822 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV037490822 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T01:13:37Z |
| institution | BVB |
| isbn | 9783869557694 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022642150 |
| oclc_num | 780101172 |
| open_access_boolean | 1 |
| owner | DE-188 DE-634 DE-706 |
| owner_facet | DE-188 DE-634 DE-706 |
| physical | II, 160, XV S. graph. Darst. |
| psigel | ebook |
| publishDate | 2010 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cuvillier |
| record_format | marc |
| spellingShingle | Klapproth, Corinna 1982- Adaptive numerical integration of dynamical contact problems Numerische Integration (DE-588)4172168-8 gnd Gehen (DE-588)4140871-8 gnd Kontaktkraft (DE-588)4192757-6 gnd Viskoelastisches Medium (DE-588)4426217-6 gnd |
| subject_GND | (DE-588)4172168-8 (DE-588)4140871-8 (DE-588)4192757-6 (DE-588)4426217-6 (DE-588)4113937-9 |
| title | Adaptive numerical integration of dynamical contact problems |
| title_alt | Adaptive numerische Integration von dynamischen Kontaktproblemen |
| title_auth | Adaptive numerical integration of dynamical contact problems |
| title_exact_search | Adaptive numerical integration of dynamical contact problems |
| title_full | Adaptive numerical integration of dynamical contact problems Corinna Klapproth |
| title_fullStr | Adaptive numerical integration of dynamical contact problems Corinna Klapproth |
| title_full_unstemmed | Adaptive numerical integration of dynamical contact problems Corinna Klapproth |
| title_short | Adaptive numerical integration of dynamical contact problems |
| title_sort | adaptive numerical integration of dynamical contact problems |
| topic | Numerische Integration (DE-588)4172168-8 gnd Gehen (DE-588)4140871-8 gnd Kontaktkraft (DE-588)4192757-6 gnd Viskoelastisches Medium (DE-588)4426217-6 gnd |
| topic_facet | Numerische Integration Gehen Kontaktkraft Viskoelastisches Medium Hochschulschrift |
| url | http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000023096 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022642150&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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