Model reduction in nonlinear finite element method for engineering structures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Hannover
Inst. für Kontinuumsmechanik
2015
|
| Series: | Leibniz-Universität Hannover, Institut für Kontinuumsmechanik
B ; 15,2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 99 S. graph. Darst. 21 cm |
| ISBN: | 9783941302150 |
Staff View
MARC
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Record in the Search Index
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| adam_text | LIST OF CONTENTS
ABSTRACT I
ZUSAMMENFASSUNG I
ACKNOWLEDGEMENTS III
LIST OF CONTENTS V
LIST OF TABLES VIII
LIST OF FIGURES IX
CHAPTER 1 INTRODUCTION 1
1.1 MOTIVATION 1
1.2 STATE OF THE ART 1
1.3 OBJECTIVES 3
1.4 THE ORGANIZATION OF THE THESIS 3
CHAPTER 2 INTRODUCTION TO NONLINEAR FINITE ELEMENT METHOD U
2.1 SOLID AND STRUCTURAL NONLINEARITIES 5
2.2 PRINCIPLES OF NONLINEAR FEM 5
2.3 TIME INTEGRATION METHODS: 11
2.4 SOLUTION METHODS OF NONLINEAR STRUCTURAL MECHANICS SYSTEMS 13
2.4.1 NEWTON-RAPHSON METHOD 13
2.4.2 QUASI-NEWTON METHOD 14
2.4.3 ARC-LENGTH METHOD 15
CHAPTER 3 REDUCED ORDER MODEL BASED ON PROJECTION 17
3.1 INTRODUCTION 17
3.2 REDUCED ORDER MODEL 17
3.3 DIMENSION REDUCTION IS
3.4 COMPUTATIONAL COMPLEXITY OF DIMENSIONALITY REDUCTION 20
3.5 AN ERROR ESTIMATION OF DIMENSIONALITY REDUCTION 20
3.6 SUBSPACE BASIS 21
3.7 REDUCED ORDER MODEL TECHNIQUES 22
3.7.1 DIMENSIONAL REDUCTION TECHNIQUES 22
3.7.1.1 MODAL METHOD 22
3.7.1.2 LOAD DEPENDENT RITZ METHOD 23
3.7.1.3 PROPER ORTHOGONAL DECOMPOSITION (POD) 23
3.7.2 SPATIAL-COMPLEXITY REDUCTION TECHNIQUES 25
HTTP://D-NB.INFO/1071958968
3.7.2.1 DISCRETE EMPIRICAL INTERPOLATION METHOD (DEIM) 25
3.7.2.2 A PRIORI HYPER-REDUCTION 2G
3.7.2.3 MISSING POINT ESTIMATION (MPE) 27
CHAPTER 4 PROPOSED APPROACHES OF REDUCED ORDER MODEL 31
4.1 INTRODUCTION 31
4.2 REDUCED ORDER MODEL AND THE NECESSITY OF AN ADAPTIVITY 31
4.3 AN ADAPTIVE REDUCED ORDER MODEL 35
4.3.1 AN ADAPTIVE STRATEGY 35
4.3.1.1 AN ITERATIVE ADAPTIVITY-ERROR ANALYSIS 3G
4.3.1.2 AN INCREMENTAL ADAPTIVITY 37
4.3.2 AN ADAPTIVE REDUCED ORDER MODEL BASED ON POD & BFGS METHOD
3S
4.3.3 AN ADAPTIVE REDUCED ORDER MODE BY PROPER SNAPSHOTS SELECTION
(PSS) METHOD 52
4.3.3.1 PSS TO ENRICH THE PROJECTION MATRIX (PSSE) 54
4.3.3.2 PSS TO REDUCE THE PROJECTION MATRIX (PSSR) 54
4.3.3.3 PSS S TOLERANCE AND WEIGHTED SNAPSHOTS 54
4.4 AN ADAPTIVE HYPER-REDUCED ORDER MODEL G4
4.4.1 THE DYNAMIC-POD G5
4.4.2 WEIGHTED SNAPSHOTS G5
CHAPTER 5 MACHINE LEARNING APPROACH 75
5.1 SUPPORT VECTOR MACHINE (SVM) 75
5.1.1 SUPPORT VECTOR FOR CLASSIFICATION 75
5.1.2 SUPPORT VECTOR FOR REGRESSION 79
5.1.3 MULTI-OUTPUT SUPPORT VECTOR REGRESSION (M-SVR.) 81
5.1.4 NUMERICAL EXAMPLE OF M-SVR S3
CHAPTER G COMPARISON. CONCLUSIONS AND RECOMMENDATIONS 87
6.1.1 COMPARISON OF DIFFERENT APPROACHES 87
G. 1.2 CONCLUSIONS SS
6.1.3 LIMITATIONS AND FUTURE RESEARCH 89
APPENDICES 91
A. PROGRAMMING DETAILS 91
B. PARAMETERS RELATED TO ADAPTIVE MODEL ORDER REDUCTION (POD&BFGS) 91
C. PARAMETERS RELATED TO ADAPTIVE MODEL ORDER REDUCTION (PSS) 91
BIBLIOGRAPHY
|
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| dewey-full | 620.1050151825 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.1050151825 |
| dewey-search | 620.1050151825 |
| dewey-sort | 3620.1050151825 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik |
| format | Thesis Book |
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| id | DE-604.BV042698748 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:07:40Z |
| institution | BVB |
| isbn | 9783941302150 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028130288 |
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| physical | XI, 99 S. graph. Darst. 21 cm |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Inst. für Kontinuumsmechanik |
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| series | Leibniz-Universität Hannover, Institut für Kontinuumsmechanik |
| series2 | Leibniz-Universität Hannover, Institut für Kontinuumsmechanik : B |
| spelling | Anndif, Mohamed A. A. 1984- Verfasser (DE-588)1070636029 aut Model reduction in nonlinear finite element method for engineering structures von Mohamed Ahmed Annour Anndif Hannover Inst. für Kontinuumsmechanik 2015 XI, 99 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Leibniz-Universität Hannover, Institut für Kontinuumsmechanik : B 15,2 Zugl.: Hannover, Univ., Diss., 2015 Strukturmechanik (DE-588)4126904-4 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Finite-Elemente-Methode (DE-588)4017233-8 s Strukturmechanik (DE-588)4126904-4 s DE-604 Leibniz-Universität Hannover, Institut für Kontinuumsmechanik B ; 15,2 (DE-604)BV036467379 B 15,2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028130288&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anndif, Mohamed A. A. 1984- Model reduction in nonlinear finite element method for engineering structures Leibniz-Universität Hannover, Institut für Kontinuumsmechanik Strukturmechanik (DE-588)4126904-4 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4126904-4 (DE-588)4017233-8 (DE-588)4113937-9 |
| title | Model reduction in nonlinear finite element method for engineering structures |
| title_auth | Model reduction in nonlinear finite element method for engineering structures |
| title_exact_search | Model reduction in nonlinear finite element method for engineering structures |
| title_full | Model reduction in nonlinear finite element method for engineering structures von Mohamed Ahmed Annour Anndif |
| title_fullStr | Model reduction in nonlinear finite element method for engineering structures von Mohamed Ahmed Annour Anndif |
| title_full_unstemmed | Model reduction in nonlinear finite element method for engineering structures von Mohamed Ahmed Annour Anndif |
| title_short | Model reduction in nonlinear finite element method for engineering structures |
| title_sort | model reduction in nonlinear finite element method for engineering structures |
| topic | Strukturmechanik (DE-588)4126904-4 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Strukturmechanik Finite-Elemente-Methode Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028130288&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT anndifmohamedaa modelreductioninnonlinearfiniteelementmethodforengineeringstructures |