Trimming, mapping, and optimization in isogeometric analysis of shell structures:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Hochschulschrift/Dissertation Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Aachen
Shaker
2013
|
| Schriftenreihe: | Schriftenreihe des Lehrstuhls für Statik TU München
20 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026905586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | IX, 176 S. Ill., graph. Darst. |
| ISBN: | 9783844023107 |
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| 100 | 1 | |a Schmidt, Robert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Trimming, mapping, and optimization in isogeometric analysis of shell structures |c Robert Schmidt |
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Datensatz im Suchindex
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|---|---|
| DE-BY-TUM_katkey | 1969200 |
| DE-BY-TUM_location | Mag |
| DE-BY-TUM_media_number | 040007976852 |
| _version_ | 1821935175620100097 |
| adam_text | TABLE OF CONTENTS
ABSTRACT III
ZUSAMMENFASSUNG IV
1 INTRODUCTION 1
1.1 MOTIVATION 1
1.2 CONTRIBUTIONS 3
1.3 OUTLINE 3
2 THEORETICAL BASICS OF NURBS 5
2.1 HISTORICAL BACKGROUND 5
2.2 B-SPLINES 7
2.2.1 PARAMETRIC DOMAIN 7
2.2.2 BASIS FUNCTION 7
2.2.3 GEOMETRY ENTITIES 8
2.3 NURBS 9
2.3.1 DEFINITION 9
2.3.2 CONTINUITY 11
2.4 TRIMMED NURBS 12
3 BASICS OF MECHANICS 17
3.1 STRUCTURAL MECHANICS 17
3.1.1 KINEMATICS 17
3.1.2 CONSTITUTIVE EQUATION 19
3.1.3 BOUNDARY VALUE PROBLEM 19
3.2 THE FINITE ELEMENT METHOD 20
3.2.1 WEAK FORM 20
3.2.2 DISCRETIZATION 21
4 ISOGEOMETRIC ANALYSIS 25
4.1 ATTRIBUTES 25
4.2 ELEMENT DEFINITION AND INTEGRATION 28
4.3 REFINEMENT 28
4.4 ELEMENT FORMULATION 30
4.4.1 ASSUMPTIONS 30
4.4.2 KINEMATICS 30
4.4.3 FE-EQUATIONS 32
HTTP://D-NB.INFO/1042680477
VIII TABLE OF CONTENTS
5 COUPLING OF NONCONFORMING DISCRETIZATIONS 33
5.1 COUPLING METHODS 33
5.1.1 INTERPOLATION METHOD 33
5.1.2 DISCRETE LEAST-SQUARES METHOD 34
5.1.3 WEIGHTED-RESIDUAL METHOD 35
5.2 FIELD APPROXIMATION 36
5.3 MAPPING QUANTITIES 37
5.3.1 STATE MAPPING 37
5.3.2 FORCE MAPPING 37
5.4 NUMERICAL INVESTIGATIONS 38
5.4.1 STATE MAPPING 40
5.4.2 FORCE MAPPING 42
5.5 CONCLUDING REMARKS 51
6 ISOGEOMETRIC ANALYSIS OF TRIMMED NURBS SURFACES 53
6.1 BASIC IDEAS OF THE METHOD 53
6.2 ALGORITHMIC FORMULATION 54
6.3 ASSESSMENT OF THE RECONSTRUCTION 61
6.4 FINITE ELEMENT EQUATIONS 62
6.5 BOUNDARY CONDITIONS 66
6.5.1 NEUMANN 66
6.5.2 DIRICHLET 67
6.6 CONDITIONING OF THE SYSTEM MATRIX 68
6.6.1 PROBLEM DESCRIPTION 68
6.6.2 PRECONDITIONING 69
6.6.3 PLATE EXAMPLE 70
6.6.4 CONCLUDING REMARKS 71
6.7 BENCHMARKING 71
6.7.1 CANTILEVER PLATE 72
6.7.2 CANTILEVER PLATE WITH CURVED EDGE 72
6.7.3 TRIMMED CYLINDER SHELL 75
6.7.4 DOUBLY-CURVED SURFACE 75
7 ISOGEOMETRIC ANALYSIS OF TRIMMED MULTI-PATCHES 81
7.1 C-CONTINUITY 81
7.2 G -CONTINUITY 84
7.3 BENCHMARKING 86
7.3.1 TENSION TEST 86
7.3.2 CANTILEVER PLATE 88
7.3.3 TRIMMED QUARTER-CYLINDERS 90
7.3.4 TRIMMED HEMISPHERE 90
8 ISOGEOMETRIC ANALYSIS AND TRIANGULAR BEZIER SHELL ELEMENTS 95
8.1 TRIANGULAR BEZIER FUNCTIONS 96
8.2 ELEMENT FORMULATION * * * 98
8.3 INTEGRATION 99
8.4 CONTINUITY ENFORCEMENT 99
8.5 BENCHMARKING 100
8.5.1 SCORDELIS-LO ROOF 100
8.5.2 PINCHED CYLINDER 101
TABLE OF CONTENTS IX
8.5.3 PINCHED HEMISPHERE 104
8.5.4 BENDING A CANTILEVER PLATE TO A CYLINDER 104
8.5.5 PULLOUT OF AN OPEN-ENDED CYLINDRICAL SHELL 105
8.6 ANALYSIS OF TRIMMED NURBS SURFACES 108
8.6.1 INFINITE PLATE WITH HOLE 109
8.6.2 WIDE-SPANNING ROOF-LIKE STRUCTURE 109
8.7 CONCLUDING REMARKS ILL
9 ISOGEOMETRIC SHAPE OPTIMIZATION 115
9.1 OPTIMIZATION PROBLEM 116
9.2 ISOGEOMETRIC OPTIMIZATION CONCEPT 117
9.3 SENSITIVITY ANALYSIS 118
9.3.1 DISCRETE SEMI-ANALYTICAL SENSITIVITIES 120
9.3.2 GRADIENT OF THE OBJECTIVE FUNCTION 120
9.3.3 STUDY ON SENSITIVITY WEIGHTING 122
9.4 STUDY ON THE DIRECTIONAL DEPENDENCY OF OPTIMAL SOLUTIONS 124
9.4.1 SQUARE PLATE 124
9.4.2 CIRCULAR DISK 125
10 ISOGEOMETRIC SHAPE OPTIMIZATION WITH MULTI-PATCHES 131
10.1 PROBLEM STATEMENT 131
10.2 CONSTRAINT FORMULATION 132
10.2.1 CONTINUITY CONSTRAINT 134
10.3 PERPETUATION OF GEOMETRIC CONTINUITY 135
10.4 ENFORCEMENT OF GEOMETRIC CONTINUITY 136
10.5 COMPARISON BETWEEN SINGLE PATCH AND MULTI-PATCHES 139
10.6 NONCONFORMING OPTIMIZATION MODELS 142
10.6.1 CHOICE OF INTEGRATION DOMAIN 145
10.6.2 PERPETUATION OF TANGENT CONTINUITY 146
10.6.3 ENFORCEMENT OF TANGENT CONTINUITY 148
11 CONCLUSION 155
APPENDIX A GEOMETRIC DATA OF MODELS 159
APPENDIX B INTEGRATION POINTS FOR POLYNOMIALS ON TRIANGULAR DOMAINS 161
BIBLIOGRAPHY 167
|
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| genre_facet | Hochschulschrift |
| id | DE-604.BV041459195 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:47:50Z |
| institution | BVB |
| isbn | 9783844023107 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026905586 |
| oclc_num | 867153941 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-12 |
| owner_facet | DE-91 DE-BY-TUM DE-12 |
| physical | IX, 176 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Shaker |
| record_format | marc |
| series | Schriftenreihe des Lehrstuhls für Statik TU München |
| series2 | Schriftenreihe des Lehrstuhls für Statik TU München |
| spellingShingle | Schmidt, Robert Trimming, mapping, and optimization in isogeometric analysis of shell structures Schriftenreihe des Lehrstuhls für Statik TU München CAD (DE-588)4069794-0 gnd Isogeometrische Analyse (DE-588)7718401-4 gnd NURBS (DE-588)4376916-0 gnd Gestaltoptimierung (DE-588)4329076-0 gnd Dünne Schale (DE-588)4150826-9 gnd |
| subject_GND | (DE-588)4069794-0 (DE-588)7718401-4 (DE-588)4376916-0 (DE-588)4329076-0 (DE-588)4150826-9 (DE-588)4113937-9 |
| title | Trimming, mapping, and optimization in isogeometric analysis of shell structures |
| title_auth | Trimming, mapping, and optimization in isogeometric analysis of shell structures |
| title_exact_search | Trimming, mapping, and optimization in isogeometric analysis of shell structures |
| title_full | Trimming, mapping, and optimization in isogeometric analysis of shell structures Robert Schmidt |
| title_fullStr | Trimming, mapping, and optimization in isogeometric analysis of shell structures Robert Schmidt |
| title_full_unstemmed | Trimming, mapping, and optimization in isogeometric analysis of shell structures Robert Schmidt |
| title_short | Trimming, mapping, and optimization in isogeometric analysis of shell structures |
| title_sort | trimming mapping and optimization in isogeometric analysis of shell structures |
| topic | CAD (DE-588)4069794-0 gnd Isogeometrische Analyse (DE-588)7718401-4 gnd NURBS (DE-588)4376916-0 gnd Gestaltoptimierung (DE-588)4329076-0 gnd Dünne Schale (DE-588)4150826-9 gnd |
| topic_facet | CAD Isogeometrische Analyse NURBS Gestaltoptimierung Dünne Schale Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026905586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035420927 |
| work_keys_str_mv | AT schmidtrobert trimmingmappingandoptimizationinisogeometricanalysisofshellstructures |
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