Computational flexible multibody dynamics: a differential-algebraic approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Differential-Algebraic Equations Forum
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XII, 249 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642351573 9783642351570 |
Internformat
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Datensatz im Suchindex
| _version_ | 1809768723165216768 |
|---|---|
| adam_text |
PART I MATHEMATICAL MODELS
1 A POINT OF DEPARTURE 3
1.1 ELASTIC PENDULUM 4
1.1.1 SMALL ELASTIC DISPLACEMENT 5
1.1.2 FLOATING REFERENCE FRAME 6
1.1.3 GALERKIN PROJECTION 7
1.1.4 TIME INTEGRATION 8
1.2 OBJECTIVES 8
1.2.1 TREATMENT OF CONSTRAINTS 9
1.2.2 DISCRETIZATION IN SPACE AND TIME 10
1.3 OVERVIEW 10
2 RIGID MULTIBODY DYNAMICS 13
2.1 EQUATIONS OF MOTION 13
2.1.1 KINEMATICS 14
2.1.2 DYNAMICS 16
2.1.3 RELATION TO HAMILTONIAN SYSTEMS 20
2.1.4 REMARKS 20
2.2 EXAMPLES 21
2.2.1 SLIDER CRANK 21
2.2.2 NEWTON-EULER EQUATIONS 23
2.2.3 WHEEL SUSPENSION 26
2.3 DIFFERENTIAL-ALGEBRAIC EQUATIONS 28
2.3.1 BASIC TYPES OF DAES 28
2.3.2 THE INDEX 30
2.3.3 CONSTRAINT MANIFOLD AND LOCAL STATE SPACE FORM 35
2.3.4 SOLUTION INVARIANTS VERSUS CONSTRAINTS 36
2.3.5 DIFFERENTIAL-ALGEBRAIC EQUATIONS IN SADDLE POINT FORM . 38
2.3.6 REMARKS AND FURTHER REFERENCES 39
IX
HTTP://D-NB.INFO/1027239080
X CONTENTS
2.4 ANALYSIS OF THE EQUATIONS OF CONSTRAINED MECHANICAL MOTION . 39
2.4.1 INDEX AND EXISTENCE OF SOLUTIONS 40
2.4.2 MINIMAX CHARACTERIZATION OF CONSTRAINTS 42
2.4.3 INFLUENCE OF PERTURBATIONS 43
2.4.4 ALTERNATIVE FORMULATIONS 44
2.4.5 REMARKS 51
3 ELASTIC MOTION 53
3.1 BASIC EQUATIONS OF AN ELASTIC BODY 53
3.1.1 VARIATIONAL FORMULATION 53
3.1.2 EQUATIONS OF MOTION 58
3.1.3 SMOOTHNESS AND APPROPRIATE FUNCTION SPACES 59
3.1.4 THE TRACE SPACE 64
3.2 CONSTRAINTS IN LINEAR ELASTICITY 67
3.2.1 VARIATIONAL FORMULATION 68
3.2.2 APPROPRIATE FUNCTION SPACES 69
3.3 MATHEMATICAL ANALYSIS 70
3.3.1 EXISTENCE OF SOLUTIONS 71
3.3.2 INFLUENCE OF PERTURBATIONS 76
3.3.3 REMARKS 79
3.4 RELATED MATHEMATICAL MODELS 80
3.4.1 DOMAIN DECOMPOSITION 80
3.4.2 DYNAMIC CONTACT 82
3.4.3 INCOMPRESSIBLE ELASTIC BODY 84
4 FLEXIBLE MULTIBODY DYNAMICS 87
4.1 FLOATING REFERENCE FRAME 87
4.1.1 VARIATIONAL FORMULATION 88
4.1.2 EQUATIONS OF UNCONSTRAINED MOTION 90
4.1.3 EXTENSIONS AND SPECIAL CASES 93
4.2 CONSTRAINTS 97
4.2.1 WEAK FORM OF EQUATIONS OF CONSTRAINED MOTION 97
4.2.2 MODELING JOINTS 99
4.2.3 REMARKS 103
4.3 FLEXIBLE MULTIBODY SYSTEM 104
4.3.1 VARIATIONAL FORMULATION 104
4.3.2 EQUATIONS OF MOTION 106
4.4 SPECIAL BODIES 109
4.4.1 PLANE STRAIN AND PLANE STRESS 109
4.4.2 BEAM MODEL 110
4.5 EXAMPLES 112
4.5.1 SLIDER CRANK 112
4.5.2 TRUCK MODEL 115
4.5.3 PANTOGRAPH AND CATENARY 117
4.6 SUMMARY OF KEY FORMULAS IN PART I 120
CONTENTS XI
PART II NUMERICAL METHODS
5 SPATIAL DISCRETIZATION 125
5.1 FINITE ELEMENT APPROXIMATION OF ELASTIC BODY 125
5.1.1 UNCONSTRAINED EQUATIONS 126
5.1.2 CONSTRAINED EQUATIONS OF MOTION 129
5.1.3 REMARKS 138
5.2 SPATIAL DISCRETIZATION OF FLEXIBLE MULTIBODY SYSTEM 139
5.2.1 GALERKIN PROJECTION FOR FLOATING REFERENCE FRAME 139
5.2.2 FLEXIBLE MULTIBODY SYSTEM 143
5.2.3 MODEL REDUCTION 146
5.3 EXAMPLES 150
5.3.1 SLIDER CRANK WITH ELASTIC CONNECTING ROD 150
5.3.2 LOADING AREA OF PLANAR TRUCK MODEL 153
5.3.3 PANTOGRAPH AND CATENARY 156
6 STIFF MECHANICAL SYSTEM 159
6.1 ELASTIC PENDULUM REVISITED 160
6.2 GENERAL FRAMEWORK 161
6.3 STATE SPACE FORM 163
6.3.1 ASYMPTOTIC EXPANSION 163
6.3.2 ELASTIC PENDULUM 167
6.3.3 REMARKS 168
6.4 THE DIFFERENTIAL-ALGEBRAIC CASE 169
6.4.1 STRUCTURE-PRESERVING LOCAL PARAMETRIZATION 170
6.4.2 COMPUTATIONAL METHOD 172
7 TIME INTEGRATION METHODS 173
7.1 OVERVIEW ON TIME INTEGRATION METHODS 173
7.1.1 ALTERNATIVE FORMULATIONS OF THE EQUATIONS OF MOTION . . 174
7.1.2 BASIC DISCRETIZATION SCHEMES 175
7.2 BDF AND IMPLICIT RUNGE-KUTTA METHODS 180
7.2.1 BACKWARD DIFFERENTIATION FORMULAS 180
7.2.2 ERROR ANALYSIS 182
7.2.3 IMPLICIT RUNGE-KUTTA METHODS OF COLLOCATION TYPE . 186
7.2.4 APPLICATION TO DIFFERENTIAL-ALGEBRAIC EQUATIONS 188
7.2.5 SOLVING CONSTRAINED MECHANICAL SYSTEMS IN PRACTICE . . 190
7.3 ORDER REDUCTION FOR STIFF MECHANICAL SYSTEMS 193
7.3.1 BEAM UNDER POINT LOAD 193
7.3.2 A MODEL PROBLEM 195
7.3.3 RUNGE-KUTTA METHODS 196
7.3.4 ROSENBROCK-WANNER METHODS 202
7.3.5 BDF METHODS 206
7.3.6 A NONLINEAR TEST EQUATION 207
7.3.7 REMARKS 208
XII CONTENTS
7.4 SPECIAL INTEGRATION METHODS 208
7.4.1 GENERALIZED-A METHOD 209
7.4.2 A VARIANT OF THE IMPLICIT MIDPOINT RULE 212
8 NUMERICAL CASE STUDIES 217
8.1 SLIDER CRANK I 217
8.2 SLIDER CRANK II 222
8.3 PANTOGRAPH AND CATENARY 228
8.4 PLANAR TRUCK MODEL 230
8.5 3D TRAILER FRAME 233
REFERENCES 239
INDEX 247 |
| any_adam_object | 1 |
| author | Simeon, Bernd |
| author_GND | (DE-588)112623115 |
| author_facet | Simeon, Bernd |
| author_role | aut |
| author_sort | Simeon, Bernd |
| author_variant | b s bs |
| building | Verbundindex |
| bvnumber | BV041139626 |
| classification_rvk | SK 520 SK 900 UF 1950 |
| ctrlnum | (OCoLC)864602704 (DE-599)DNB1027239080 |
| dewey-full | 620.104 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.104 |
| dewey-search | 620.104 |
| dewey-sort | 3620.104 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Mathematik |
| format | Book |
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| spelling | Simeon, Bernd Verfasser (DE-588)112623115 aut Computational flexible multibody dynamics a differential-algebraic approach Bernd Simeon Berlin [u.a.] Springer 2013 XII, 249 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Differential-Algebraic Equations Forum Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Mehrkörpersystem (DE-588)4038390-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Mehrkörpersystem (DE-588)4038390-8 s Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-35158-7 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4168066&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026115294&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simeon, Bernd Computational flexible multibody dynamics a differential-algebraic approach Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Mehrkörpersystem (DE-588)4038390-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4229517-8 (DE-588)4038390-8 (DE-588)4128130-5 |
| title | Computational flexible multibody dynamics a differential-algebraic approach |
| title_auth | Computational flexible multibody dynamics a differential-algebraic approach |
| title_exact_search | Computational flexible multibody dynamics a differential-algebraic approach |
| title_full | Computational flexible multibody dynamics a differential-algebraic approach Bernd Simeon |
| title_fullStr | Computational flexible multibody dynamics a differential-algebraic approach Bernd Simeon |
| title_full_unstemmed | Computational flexible multibody dynamics a differential-algebraic approach Bernd Simeon |
| title_short | Computational flexible multibody dynamics |
| title_sort | computational flexible multibody dynamics a differential algebraic approach |
| title_sub | a differential-algebraic approach |
| topic | Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Mehrkörpersystem (DE-588)4038390-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Differential-algebraisches Gleichungssystem Mehrkörpersystem Numerisches Verfahren |
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