Reduction methods in finite element analysis of nonlinear structural dynamics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hannover
IBNM
2006
|
| Series: | Research reports / Institut für Baumechanik und Numerische Mechanik, Universität Hannover : F
[20]06,2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Hannover, Univ., Diss., 2006 |
| Physical Description: | X, 147 S. graph. Darst. |
| ISBN: | 3935732171 9783935732178 |
Staff View
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| adam_text | HAUPTREFERENT: PROF. DR.-ING. P. WRIGGERS KORREFERENT: PROF. DR.-ING. E.
RAMM DOKTORAND: DIPL.-ING. H. SPIESS REDUCTION METHODS IN FINITE ELEMENT
ANALYSIS OF NONLINEAR STRUCTURAL DYNAMICS VON DER FAKULTAT FUR
BAUINGENIEURWESEN UND GEODASIE DER UNIVERSITAT HANNOVER ZUR ERIANGUNG
DES GRADES EINES DOKTOR-INGENIEUR GENEHMIGTE DISSERTATION VON DIPL.-ING.
H. SPIESS HANNOVER 2006 TAG DER EINREICHUNG: 02. 11.2005 TAG DER MUNDL.
PRIIFUNG: 10.02.2006 INSTITUT FUR BAUMECHANIK UND II I 16410888 CONTENTS
1 INTRODUCTION 1 1.1 MOTIVATION 1 1.2 STATE OF THE ART 2 1.3 STRUCTURE
OF THIS WORK 2 2 FINITE ELEMENT ANALYSIS IN NONLINEAR STRUCTURAL
DYNAMICS 3 2.1 BASIC CONTINUUM MECHANICS 3 2.1.1 KINEMATICS 3 2.1.2
STRESSES 5 2.1.3 CONSTITUTIVE EQUATIONS 5 2.1.4 CONSERVATION OF MOMENTUM
6 2.1.5 INITIAL BOUNDARY VALUE PROBLEM OF STRUCTURAL DYNAMICS 7 2.2
FINITE ELEMENT METHOD 8 2.2.1 DISCRETIZATION 8 2.2.2 WEAK FORM OF
EQUILIBRIUM 8 2.2.3 ISOPARAMETRIC ELEMENTS 9 2.2.4 ASSEMBLY 11 2.2.5
DISCRETE INITIAL BOUNDARY VALUE PROBLEM 11 2.3 LINEAR DYNAMICS 12 2.3.1
MODAL ANALYSIS 13 2.4 TIME INTEGRATION 13 2.4.1 THE NEWMARK ALGORITHM 14
2.4.2 SOLUTION OF THE NONLINEAR EQUATION 16 2.4.3 STABILITY AND ERRORS
20 3 REDUCTION METHODS - OVERVIEW 21 3.1 DYNAMIC CONDENSATION 21 3.2
MODAL METHODS 22 3.2.1 MODE SUPERPOSITION AND MODE TRUNCATION FOR LINEAR
SYSTEMS . . . 23 3.2.2 TANGENT SPECTRUM METHOD 24 3.2.3 PSEUDO FORCE
METHOD 25 3.2.4 DIRECT UPDATE OF EIGENVECTORS 26 3.2.5 MODAL DERIVATIVES
27 3.3 TRANSFORMATION METHODS USING A GENERAL BASIS 28 3.4 OTHER
APPROACHES 28 VI CONTENTS 4 PROJECTION-BASED REDUCTION METHODS WITH
GENERAL BASIS 29 4.1 PROJECTION TO A SUBSPACE 29 4.1.1 REDUCED INITIAL
BOUNDARY VALUE PROBLEM 30 4.1.2 BASIS VECTORS 31 4.1.3 SUBSPACE AND FULL
SOLUTION SPACE 32 4.2 SOLUTION OF THE REDUCED PROBLEM 33 4.3 EFFICIENCY
33 4.3.1 ESTIMATION OF COMPUTATIONAL EFFORT 34 4.3.2 DIRECT ASSEMBLY OF
REDUCED MATRICES AND VECTORS 35 4.3.3 SOLUTION IN THE SUBSPACE WITH THE
BFGS METHOD 37 4.4 ACCURACY, ERRORS AND ERROR MEASURES 37 4.4.1
DISPLACEMENT ERROR 38 4.4.2 BAD REPRESENTATION OF THE LOAD VECTOR 39
4.4.3 REMAINING RESIDUAL OF FULL SYSTEM 40 4.4.4 TRUNCATION ERROR 41
4.4.5 CONVERGENCE OF THE NEWTON ITERATION 42 4.4.6 COMPARISON OF
DIFFERENT ERROR MEASURES 45 4.4.7 DISCRETIZATION-DEPENDENCE OF ERROR
MEASURES 45 5 REDUCTION BASED ON LOAD-DEPENDENT RITZ VECTORS 48 5.1
LOAD-DEPENDENT RITZ VECTOR BASIS 48 5.1.1 COMPUTATION OF THE BASIS
VECTORS 48 5.1.2 DIFFERENT START VECTORS 49 5.1.3 LANCZOS VECTORS 50
5.1.4 MODIFICATIONS OF THE BASIS GENERATION 50 5.1.5 TRUNCATION CRITERIA
51 5.1.6 EXAMPLE 52 5.2 BASIS UPDATES 54 5.2.1 UPDATES AT REGULAR TIME
INTERVALS 55 5.2.2 UPDATES BASED ON ERROR MEASURES 56 5.2.3 AUTOMATIC
SWITCHING BETWEEN FULL AND REDUCED SOLUTION SPACE .... 58 5.3
DERIVATIVES OF LOAD-DEPENDENT RITZ VECTORS 59 5.3.1 DERIVATIVES WITH
RESPECT TO REDUCED COORDINATES 59 5.3.2 TIME DERIVATIVES OF RITZ VECTORS
61 5.3.3 DISREGARD OF THE ORTHONORMALIZATION PROCESS 64 5.3.4 EXAMPLE 66
6 REDUCTION BASED ON POD VECTORS 71 6.1 PROPER ORTHOGONAL DECOMPOSITION
71 6.1.1 PROPER ORTHOGONAL DECOMPOSITION OF GIVEN DATA 71 6.1.2
OPTIMALITY OF THE POD SUBSPACE 73 6.1.3 METHOD OF SNAPSHOTS 74 6.1.4 POD
BASIS IN A REDUCTION METHOD 76 6.1.5 EXAMPLE 78 6.2 USING POD FOR
ANALYSIS OF DIFFERENT LOAD CASES 81 6.3 INCREMENTAL SUBSPACE ADAPTATION
(ISA) 84 CONTENTS VII 6.3.1 COMPUTATIONAL PROCEDURE 84 6.3.2 COMPUTATION
OF THE POD BASIS 86 6.3.3 EXAMPLE 88 6.4 SIMPLE SUBSPACE EXTENSION (SSE)
101 6.4.1 EXAMPLE 103 7 EXAMPLES 105 7.1 TWO-DIMENSIONAL T-BEAM 106 7.2
THREE-DIMENSIONAL T-BEAM 108 7.3 FLAT DOME ILL 7.3.1 PROBLEM DESCRIPTION
ILL 7.3.2 EIGENMODES AND POD VECTORS 113 7.3.3 COMPUTATIONS WITH
LOAD-DEPENDENT RITZ VECTORS 115 7.3.4 COMPUTATIONS WITH POD BASED
METHODS 117 7.3.5 RESULTS FOR A HIGHER LOAD 119 7.4 CUP BEARING 121
7.4.1 PROBLEM DESCRIPTION 121 7.4.2 COMPUTATIONS WITH LOAD-DEPENDENT
RITZ VECTORS 124 7.4.3 COMPUTATIONS WITH POD BASED METHODS 126 7.4.4
HIGHER LOAD 126 7.5 BELL 128 7.5.1 PROBLEM DESCRIPTION 128 7.5.2
COMPUTATIONS WITH LOAD-DEPENDENT RITZ VECTORS 130 7.5.3 COMPUTATIONS
BASED ON POD VECTORS 132 7.6 EXAMPLE SUMMARY 133 8 SUMMARY AND
CONCLUSIONS 134 A FETA - A FINITE ELEMENT PROGRAM FOR TRANSIENT ANALYSIS
136 A.I FEATURES 136 A.2 PROGRAMMING DETAILS 136 A.2.1 DEVELOPMENT
ENVIRONMENT 137 A.2.2 PROGRAM STRUCTURE 138 A.2.3 NUMERICAL LIBRARIES
138 RESEARCH REPORTS, IBNM 149
|
| adam_txt |
HAUPTREFERENT: PROF. DR.-ING. P. WRIGGERS KORREFERENT: PROF. DR.-ING. E.
RAMM DOKTORAND: DIPL.-ING. H. SPIESS REDUCTION METHODS IN FINITE ELEMENT
ANALYSIS OF NONLINEAR STRUCTURAL DYNAMICS VON DER FAKULTAT FUR
BAUINGENIEURWESEN UND GEODASIE DER UNIVERSITAT HANNOVER ZUR ERIANGUNG
DES GRADES EINES DOKTOR-INGENIEUR GENEHMIGTE DISSERTATION VON DIPL.-ING.
H. SPIESS HANNOVER 2006 TAG DER EINREICHUNG: 02. 11.2005 TAG DER MUNDL.
PRIIFUNG: 10.02.2006 INSTITUT FUR BAUMECHANIK UND II I 16410888 CONTENTS
1 INTRODUCTION 1 1.1 MOTIVATION 1 1.2 STATE OF THE ART 2 1.3 STRUCTURE
OF THIS WORK 2 2 FINITE ELEMENT ANALYSIS IN NONLINEAR STRUCTURAL
DYNAMICS 3 2.1 BASIC CONTINUUM MECHANICS 3 2.1.1 KINEMATICS 3 2.1.2
STRESSES 5 2.1.3 CONSTITUTIVE EQUATIONS 5 2.1.4 CONSERVATION OF MOMENTUM
6 2.1.5 INITIAL BOUNDARY VALUE PROBLEM OF STRUCTURAL DYNAMICS 7 2.2
FINITE ELEMENT METHOD 8 2.2.1 DISCRETIZATION 8 2.2.2 WEAK FORM OF
EQUILIBRIUM 8 2.2.3 ISOPARAMETRIC ELEMENTS 9 2.2.4 ASSEMBLY 11 2.2.5
DISCRETE INITIAL BOUNDARY VALUE PROBLEM 11 2.3 LINEAR DYNAMICS 12 2.3.1
MODAL ANALYSIS 13 2.4 TIME INTEGRATION 13 2.4.1 THE NEWMARK ALGORITHM 14
2.4.2 SOLUTION OF THE NONLINEAR EQUATION 16 2.4.3 STABILITY AND ERRORS
20 3 REDUCTION METHODS - OVERVIEW 21 3.1 DYNAMIC CONDENSATION 21 3.2
MODAL METHODS 22 3.2.1 MODE SUPERPOSITION AND MODE TRUNCATION FOR LINEAR
SYSTEMS . . . 23 3.2.2 TANGENT SPECTRUM METHOD 24 3.2.3 PSEUDO FORCE
METHOD 25 3.2.4 DIRECT UPDATE OF EIGENVECTORS 26 3.2.5 MODAL DERIVATIVES
27 3.3 TRANSFORMATION METHODS USING A GENERAL BASIS 28 3.4 OTHER
APPROACHES 28 VI CONTENTS 4 PROJECTION-BASED REDUCTION METHODS WITH
GENERAL BASIS 29 4.1 PROJECTION TO A SUBSPACE 29 4.1.1 REDUCED INITIAL
BOUNDARY VALUE PROBLEM 30 4.1.2 BASIS VECTORS 31 4.1.3 SUBSPACE AND FULL
SOLUTION SPACE 32 4.2 SOLUTION OF THE REDUCED PROBLEM 33 4.3 EFFICIENCY
33 4.3.1 ESTIMATION OF COMPUTATIONAL EFFORT 34 4.3.2 DIRECT ASSEMBLY OF
REDUCED MATRICES AND VECTORS 35 4.3.3 SOLUTION IN THE SUBSPACE WITH THE
BFGS METHOD 37 4.4 ACCURACY, ERRORS AND ERROR MEASURES 37 4.4.1
DISPLACEMENT ERROR 38 4.4.2 BAD REPRESENTATION OF THE LOAD VECTOR 39
4.4.3 REMAINING RESIDUAL OF FULL SYSTEM 40 4.4.4 TRUNCATION ERROR 41
4.4.5 CONVERGENCE OF THE NEWTON ITERATION 42 4.4.6 COMPARISON OF
DIFFERENT ERROR MEASURES 45 4.4.7 DISCRETIZATION-DEPENDENCE OF ERROR
MEASURES 45 5 REDUCTION BASED ON LOAD-DEPENDENT RITZ VECTORS 48 5.1
LOAD-DEPENDENT RITZ VECTOR BASIS 48 5.1.1 COMPUTATION OF THE BASIS
VECTORS 48 5.1.2 DIFFERENT START VECTORS 49 5.1.3 LANCZOS VECTORS 50
5.1.4 MODIFICATIONS OF THE BASIS GENERATION 50 5.1.5 TRUNCATION CRITERIA
51 5.1.6 EXAMPLE 52 5.2 BASIS UPDATES 54 5.2.1 UPDATES AT REGULAR TIME
INTERVALS 55 5.2.2 UPDATES BASED ON ERROR MEASURES 56 5.2.3 AUTOMATIC
SWITCHING BETWEEN FULL AND REDUCED SOLUTION SPACE . 58 5.3
DERIVATIVES OF LOAD-DEPENDENT RITZ VECTORS 59 5.3.1 DERIVATIVES WITH
RESPECT TO REDUCED COORDINATES 59 5.3.2 TIME DERIVATIVES OF RITZ VECTORS
61 5.3.3 DISREGARD OF THE ORTHONORMALIZATION PROCESS 64 5.3.4 EXAMPLE 66
6 REDUCTION BASED ON POD VECTORS 71 6.1 PROPER ORTHOGONAL DECOMPOSITION
71 6.1.1 PROPER ORTHOGONAL DECOMPOSITION OF GIVEN DATA 71 6.1.2
OPTIMALITY OF THE POD SUBSPACE 73 6.1.3 METHOD OF SNAPSHOTS 74 6.1.4 POD
BASIS IN A REDUCTION METHOD 76 6.1.5 EXAMPLE 78 6.2 USING POD FOR
ANALYSIS OF DIFFERENT LOAD CASES 81 6.3 INCREMENTAL SUBSPACE ADAPTATION
(ISA) 84 CONTENTS VII 6.3.1 COMPUTATIONAL PROCEDURE 84 6.3.2 COMPUTATION
OF THE POD BASIS 86 6.3.3 EXAMPLE 88 6.4 SIMPLE SUBSPACE EXTENSION (SSE)
101 6.4.1 EXAMPLE 103 7 EXAMPLES 105 7.1 TWO-DIMENSIONAL T-BEAM 106 7.2
THREE-DIMENSIONAL T-BEAM 108 7.3 FLAT DOME ILL 7.3.1 PROBLEM DESCRIPTION
ILL 7.3.2 EIGENMODES AND POD VECTORS 113 7.3.3 COMPUTATIONS WITH
LOAD-DEPENDENT RITZ VECTORS 115 7.3.4 COMPUTATIONS WITH POD BASED
METHODS 117 7.3.5 RESULTS FOR A HIGHER LOAD 119 7.4 CUP BEARING 121
7.4.1 PROBLEM DESCRIPTION 121 7.4.2 COMPUTATIONS WITH LOAD-DEPENDENT
RITZ VECTORS 124 7.4.3 COMPUTATIONS WITH POD BASED METHODS 126 7.4.4
HIGHER LOAD 126 7.5 BELL 128 7.5.1 PROBLEM DESCRIPTION 128 7.5.2
COMPUTATIONS WITH LOAD-DEPENDENT RITZ VECTORS 130 7.5.3 COMPUTATIONS
BASED ON POD VECTORS 132 7.6 EXAMPLE SUMMARY 133 8 SUMMARY AND
CONCLUSIONS 134 A FETA - A FINITE ELEMENT PROGRAM FOR TRANSIENT ANALYSIS
136 A.I FEATURES 136 A.2 PROGRAMMING DETAILS 136 A.2.1 DEVELOPMENT
ENVIRONMENT 137 A.2.2 PROGRAM STRUCTURE 138 A.2.3 NUMERICAL LIBRARIES
138 RESEARCH REPORTS, IBNM 149 |
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| index_date | 2024-07-02T16:42:15Z |
| indexdate | 2024-07-09T20:53:33Z |
| institution | BVB |
| isbn | 3935732171 9783935732178 |
| language | English |
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| series2 | Research reports / Institut für Baumechanik und Numerische Mechanik, Universität Hannover : F |
| spelling | Spiess, Holger 1973- Verfasser (DE-588)132600668 aut Reduction methods in finite element analysis of nonlinear structural dynamics H. Spiess Hannover IBNM 2006 X, 147 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Research reports / Institut für Baumechanik und Numerische Mechanik, Universität Hannover : F [20]06,2 Zugl.: Hannover, Univ., Diss., 2006 Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Strukturdynamik (DE-588)4226174-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Strukturdynamik (DE-588)4226174-0 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Institut für Baumechanik und Numerische Mechanik, Universität Hannover Research reports F ; [20]06,2 (DE-604)BV012930351 2006,2 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015469897&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spiess, Holger 1973- Reduction methods in finite element analysis of nonlinear structural dynamics Finite-Elemente-Methode (DE-588)4017233-8 gnd Strukturdynamik (DE-588)4226174-0 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4226174-0 (DE-588)4113937-9 |
| title | Reduction methods in finite element analysis of nonlinear structural dynamics |
| title_auth | Reduction methods in finite element analysis of nonlinear structural dynamics |
| title_exact_search | Reduction methods in finite element analysis of nonlinear structural dynamics |
| title_exact_search_txtP | Reduction methods in finite element analysis of nonlinear structural dynamics |
| title_full | Reduction methods in finite element analysis of nonlinear structural dynamics H. Spiess |
| title_fullStr | Reduction methods in finite element analysis of nonlinear structural dynamics H. Spiess |
| title_full_unstemmed | Reduction methods in finite element analysis of nonlinear structural dynamics H. Spiess |
| title_short | Reduction methods in finite element analysis of nonlinear structural dynamics |
| title_sort | reduction methods in finite element analysis of nonlinear structural dynamics |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd Strukturdynamik (DE-588)4226174-0 gnd |
| topic_facet | Finite-Elemente-Methode Strukturdynamik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015469897&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012930351 |
| work_keys_str_mv | AT spiessholger reductionmethodsinfiniteelementanalysisofnonlinearstructuraldynamics |