Computational contact mechanics: geometrically exact theory for arbitrary shaped bodies
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Lecture notes in applied and computational mechanics
67 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXI, 443 S. graph. Darst. |
| ISBN: | 9783642315305 |
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MARC
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| 100 | 1 | |a Konyukhov, Alexander |e Verfasser |0 (DE-588)143486306 |4 aut | |
| 245 | 1 | 0 | |a Computational contact mechanics |b geometrically exact theory for arbitrary shaped bodies |c Alexander Konyukhov and Karl Schweizerhof |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XXI, 443 S. |b graph. Darst. | ||
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| 490 | 1 | |a Lecture notes in applied and computational mechanics |v 67 | |
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| 700 | 1 | |a Schweizerhof, Karl |e Verfasser |4 aut | |
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IMAGE 1
C O N T E N T S
1 I N T R O D U C T I O N 1
1.1 OVERVIEW OF APPROACHES T O MODEL CONTACT PROBLEMS 1
1.2 DISCUSSION - WHY COVARIANT APPROACH? 13
1.3 O N GEOMETRICAL APPROACHES IN CONTACT MECHANICS 17
1.4 GOALS AND STRUCTURE OF THE BOOK 17
1.4.1 STRUCTURE OF THE CURRENT BOOK 18
2 DIFFERENTIAL G E O M E T R Y O F SURFACES A N D C U R V E S 25
2.1 DEFINITION OF THE SURFACE AND ITS GEOMETRICAL CHARACTERISTICS 25
2.1.1 THE FUNDAMENTAL TENSORS AND PROPERTY OF T H E SURFACE 26
2.1.2 STUDY THE LOCAL SURFACE STRUCTURE 28
2.1.3 DIFFERENTIAL OPERATIONS IN THE SURFACE COORDINATE SYSTEM 31
2.2 DEFINITION OF THE CURVE IN 3D AND ITS GEOMETRICAL CHARACTERISTICS 33
2.2.1 DEFINITION OF A LOCAL COORDINATE (SERRET-FRENET) SYSTEM.
SERRET-FRENET FORMULAS 34
3 C L O S E S T P O I N T P R O J E C T I O N P R O C E D U R E A N D C
O R R E S P O N D I N G CURVILINEAR C O O R D I N A T E S Y S T E M 35
3.1 CLOSEST POINT PROJECTION PROCEDURE FOR ARBITRARY SURFACES 35
3.1.1 FORMULATION OF THE CLOSEST POINT PROJECTION PROCEDURE IN
GEOMETRICAL TERMS 38
3.1.2 PROXIMITY CRITERIA FOR DIFFERENT SURFACES 41
3.2 SOLVABILITY OF THE C P P PROCEDURE FOR SURFACES - ALLOWABLE AND
NON-ALLOWABLE DOMAINS 44
3.2.1 REDUCTION T O 2D PLANE GEOMETRY - SOLVABILITY CRITERIA AND
UNIQUENESS 44
HTTP://D-NB.INFO/102301646X
IMAGE 2
X I V
CONTENTS
3.2.2 PROXIMITY DOMAIN FOR GLOBALLY C-CONTINUOUS SURFACE IN 3D 47
3.2.3 REFERENCE EXAMPLE: PROJECTION DOMAIN FOR A HYPERBOLICAL SURFACE 49
3.3 CLOSEST POINT PROJECTION PROCEDURE FOR POINT-TO-CURVE PROJECTION AND
CORRESPONDING PROJECTION DOMAIN 50
3.4 CLOSEST POINT PROJECTION PROCEDURE FOR CURVE-TO-CURVE CONTACT AND
DEFINITION OF LOCAL COORDINATE SYSTEMS 53
3.4.1 DEFINITION OF A LOCAL COORDINATE SYSTEM ATTACHED T O A CURVE 55
3.4.2 ANALYSIS OF UNIQUENESS AND EXISTENCE OF SOLUTIONS FOR THE CPP:
DEFINITION OF A PROJECTION DOMAIN 56
3.4.3 COMPUTATIONAL ISSUES OF THE C P P PROCEDURE 62
4 G E O M E T R Y A N D K I N E M A T I C S O F C O N T A C T 63
4.1 KINEMATICS OF THE SURFACE-TO-SURFACE INTERACTION 63
4.1.1 LOCAL SURFACE COORDINATE SYSTEM 64
4.1.2 SPATIAL CURVILINEAR LOCAL COORDINATE SYSTEM AND ITS
CHARACTERISTICS 64
4.1.3 MEASURE OF CONTACT INTERACTION FOR SURFACE-TO-SURFACE CONTACT 66
4.1.4 SPATIAL BASIS VECTORS AND METRIC TENSOR 66
4.1.5 MOTION OF A SLAVE POINT 71
4.1.6 GEOMETRICAL INTERPRETATION OF COVARIANT DERIVATIVE AND NUMERICAL
REALIZATION 74
4.1.7 VARIATION AND ITS LINEARIZATION 77
4.1.8 VARIATION S A N D ITS LINEARIZATION 79
4.2 KINEMATICS OF 2D CONTACT INTERACTION 83
4.2.1 CLOSEST POINT PROJECTION PROCEDURE AND CORRESPONDING COORDINATE
SYSTEM 84
4.2.2 2D CONTACT KINEMATICS 91
4.2.3 LINEARIZATION OF VARIATIONS 5( AND 92
4.3 KINEMATICS OF SEGMENT (DEFORMABLE)-TO-ANALYTICAL (RIGID) SURFACES
CONTACT (STAS) - TWO STRATEGIES 95
4.3.1 RIGID SURFACE IS A "SLAVE" SURFACE 95
4.3.2 RIGID SURFACE IS A "MASTER" SURFACE 97
4.3.3 SURFACES ALLOWING A CLOSED FORM SOLUTION FOR THE PENETRATION 98
4.4 KINEMATICS OF POINT-TO-CURVE INTERACTION 105
4.5 KINEMATICS OF CURVE-TO-CURVE INTERACTION 107
4.5.1 DEVELOPMENT OF BEAM-TO-BEAM AND EDGE-TO-EDGE CONTACT 108
4.5.2 MEASURES OF CONTACT INTERACTION 109
4.5.3 RATES AND VARIATIONS OF MEASURES FOR CONTACT INTERACTION 112
IMAGE 3
CONTENTS X V
4.5.4 LINEARIZATION IN A COVARIANT FORM OF VARIATIONS FOR CONTACT
MEASURES 113
4.6 KINEMATICS OF THE CURVE-TO-RIGID-SURFACE INTERACTION 115
5 W E A K FORMULATION O F C O N T A C T C O N D I T I O N S 119
5.1 WEAK FORMULATION OF THE SURFACE-TO-SURFACE CONTACT 119
5.2 WEAK FORMULATION OF 2D CONTACT INTERACTION 122
5.3 WEAK FORMULATION FOR POINT-TO-CURVE CONTACT 122
5.4 WEAK FORMULATION FOR CURVE-TO-CURVE CONTACT 123
5.5 WEAK FORMULATION FOR CURVE-TO-RIGID SURFACE CONTACT 127 5.6 NITSCHE
AND LAGRANGIAN FORMULATIONS OF NON-FRICTIONAL CONTACT PROBLEMS 128
5.6.1 CHOICE OF THE LAGRANGE MULTIPLIER SET 130
5.6.2 PHYSICAL MEANING OF THE NON-PENETRATION TERMS 130 5.6.3 TYPES OF
THE NITSCHE APPROACH 132
6 C O N T A C T C O N S T R A I N T S A N D C O N S T I T U T I V E E Q
U A T I O N S FOR C O N T A C T TRACTIONS 135
6.1 SURFACE-TO-SURFACE CONTACT - NON-FRICTIONAL CASE AND ISOTROPIC
COULOMB'S FRICTIONAL CASE 136
6.1.1 CONTACT CONSTRAINTS FOR NORMAL CONTACT CONDITIONS 136
6.1.2 TANGENTIAL CONTACT CONDITIONS. EVOLUTION EQUATIONS 138
6.1.3 RETURN-MAPPING SCHEME FOR THE REAL TANGENTIAL TRACTION 140
6.1.4 INTEGRATION OF EVOLUTION EQUATIONS. GEOMETRICAL INTERPRETATION OF
THE RETURN-MAPPING SCHEME 142
6.2 GENERALIZATION OF COULOMB FRICTION LAW INTO COMPLEX CONTACT
INTERFACE LAW 143
6.2.1 VECTOR FORM OF THE ISOTROPIC EQUATIONS 143
6.2.2 GENERAL INTERFACE MODEL 144
6.2.3 ANISOTROPIC YIELD FUNCTION 146
6.2.4 TENSOR REPRESENTATIONS FOR ANISOTROPY 148
6.3 DERIVATION OF T H E ANISOTROPIC ADHESION-FRICTION CONTACT PROBLEM
VIA THE PRINCIPLE OF MAXIMUM DISSIPATION 156
6.3.1 CONTINUOUS FORMULATION 157
6.3.2 INCREMENTAL FORMULATION 158
6.3.3 SPECIFICATION OF INITIAL CONDITIONS FOR T H E RETURN-MAPPING
SCHEME 161
6.3.4 DERIVATION OF T H E SLIDING INCREMENTAL DISPLACEMENT A SL A N D
UPDATE SCHEME FOR THE HISTORY VARIABLES 161
6.3.5 COMPUTATIONAL ASPECTS FOR FURTHER IMPLEMENTATION CONSIDERING
NONLINEAR AND CONSTANT TENSORS 163
IMAGE 4
CONTENTS
6.3.6 GEOMETRICAL INTERPRETATION OF THE SOLUTION PROCESS. . 164 6.3.7
RHEOLOGICAL MODEL OF THE ORTHOTROPIC ADHESIONFRICTION PROBLEM 167
6.4 ANALYSIS OF VARIOUS MODELS FOR ANISOTROPIC FRICTION AND ADHESION 168
6.4.1 ORTHOTROPIC COULOMB FRICTION LAW 169
6.4.2 MODEL FOR ORTHOTROPIC CONTACT INTERFACES INCLUDING BOTH ADHESION
AND FRICTION 171
6.4.3 RECOVERING CIRCULAR MOTION FOR POLAR ORTHOTROPY . . . . 172 6.5 2D
CONTACT PROBLEMS - EVOLUTION EQUATIONS FOR CONTACT TRACTIONS 173
6.6 CONSTITUTIVE EQUATIONS FOR POINT-TO-CURVE CONTACT INTERACTION 174
6.7 CURVE-TO-CURVE CONTACT - CONSTITUTIVE EQUATIONS FOR CONTACT
TRACTIONS 175
6.7.1 NORMAL CONTACT. SPECIFICATION OF CONSTITUTIVE LAWS FOR THE
TRACTION N COUPLED WITH CONTACT CONSTRAINTS FOR THE VARIABLE R 176
6.7.2 TANGENTIAL CONTACT. SPECIFICATION OF CONSTITUTIVE LAWS FOR
TRACTIONS T J COUPLED WITH CONTACT CONSTRAINTS FOR T H E VARIABLES S J
178
6.7.3 ROTATIONAL CONTACT. SPECIFICATION OF A CONSTITUTIVE LAW FOR THE
ROTATIONAL MOMENT M J COUPLED WITH CONTACT CONSTRAINTS FOR THE VARIABLES
.PI 180
6.8 CURVE-TO-CURVE CONTACT: RATE OF CONTACT FORCES IN A COVARIANT FORM
181
6.8.1 COVARIANT FORM FOR STICKING 182
6.8.2 COVARIANT FORM FOR SLIDING 182
6.9 CURVE-TO-RIGID SURFACE CONTACT - TRANSFORMATION OF THE CONTACT
FORCES 182
LINEARIZATION O F T H E W E A K F O R M S - TANGENT M A T R I C E S IN A
COVARIANT F O R M 185
7.1 LINEARIZATION OF THE WEAK FORM FOR THE SURFACE-TO-SURFACE CONTACT
185
7.1.1 LINEARIZATION OF THE NORMAL CONTACT P A R T 5 W ^ 187
7.1.2 TANGENT MATRICES FOR THE NORMAL CONTACT P A R T 5W C N 188
7.1.3 LINEARIZATION OF THE TANGENTIAL CONTACT P A R T 5 W J - CASE OF
STICKING 190
7.1.4 LINEARIZATION OF THE TANGENTIAL CONTACT P A R T 5 W J - CASE OF
SLIDING 192
7.2 LINEARIZATION OF THE WEAK FORM FOR THE 2D CASE 194
7.2.1 TANGENT MATRIX FOR THE NORMAL P A R T 195
7.2.2 TANGENT MATRIX FOR THE TANGENTIAL P A R T 196
IMAGE 5
CONTENTS X V I I
7.3 LINEARIZATION OF THE WEAK FORM FOR THE SURFACE-TO-SURFACE CONTACT -
CASE OF COUPLED ANISOTROPIC ADHESION-FRICTION INTERFACES 197
7.3.1 LINEARIZATION OF THE TANGENTIAL P A R T 5 W J 198
7.4 LINEARIZATION OF THE WEAK FORM FOR POINT-TO-CURVE INTERACTION 202
7.5 LINEARIZATION OF THE WEAK FORM FOR CURVE-TO-CURVE CONTACT 202
7.5.1 FIRST PART, REPRESENTING GEOMETRICAL NONLINEARITY . . . 203 7.5.2
CONSTITUTIVE P A R T FOR STICKING 204
7.5.3 CONSTITUTIVE P A R T FOR TANGENTIAL SLIDING 205
7.5.4 LINEARIZED P A R T FOR ROTATIONAL SLIDING 206
7.6 LINEARIZATION OF THE WEAK FORM FOR CURVE-TO-RIGID SURFACE CONTACT
207
8 SURFACE-TO-SURFACE C O N T A C T - VARIOUS A S P E C T S FOR I M P L E
M E N T A T I O N S W I T H I N T H E F I N I T E E L E M E N T M E T H
O D 209
8.1 FINITE ELEMENT DISCRETIZATION FOR VARIOUS CONTACT APPROACHES - NTS,
STS AND STAS CONTACT ELEMENTS 209
8.1.1 NODE-TO-SEGMENT (NTS) CONTACT APPROACH 210
8.1.2 SEGMENT-TO-SEGMENT (STS) CONTACT APPROACH 211 8.1.3
SEGMENT-TO-ANALYTICAL SURFACE (STAS) CONTACT APPROACH 213
8.2 VARIOUS APPROXIMATIONS OF CONTACT SURFACES DEFINED BY FINITE
ELEMENTS 214
8.2.1 QUADRILATERAL SEGMENT WITH LINEAR APPROXIMATION. . 214 8.2.2
CLOSED FORM SOLUTION FOR C P P PROCEDURE FOR LINEAR SEGMENT 214
8.2.3 QUADRILATERAL SEGMENT WITH QUADRATIC LAGRANGIAN APPROXIMATION 216
8.2.4 SURFACE SMOOTHING TECHNIQUES IN A COVARIANT APPROACH 217
8.3 NON FRICTIONAL CONTACT ANALYSIS: NODE-TO-SEGMENT APPROACH 230
8.3.1 BENDING OF A BEAM OVER A RIGID CYLINDER 231
8.3.2 BENDING OF A BEAM OVER A RIGID SPHERE 234
8.3.3 DISCUSSION 234
8.4 NON FRICTIONAL CONTACT ANALYSIS: LARGE PENETRATION ALGORITHM 235
8.4.1 LARGE PENETRATION ALGORITHM - GENERAL CONSIDERATIONS 236
8.4.2 NUMERICAL EXAMPLES 239
8.4.3 WEDGE PLATE INDENTED INTO CANTILEVER PLATE 239
8.4.4 SEMICIRCULAR PLATE INDENTED INTO RECTANGULAR PLATE 241
IMAGE 6
XVIII
CONTENTS
8.4.5 BENDING OF A BEAM OVER A RIGID CYLINDER 243
8.4.6 BENDING OF A BEAM OVER A RIGID SPHERE 246
8.4.7 DISCUSSION 249
8.5 FRICTIONAL CONTACT ANALYSIS: NODE-TO-SEGMENT APPROACH . . . 249
8.5.1 GLOBAL SOLUTION SCHEME. SUMMARY OF THE RESULTS . . . . 250 8.5.2
SLIDING OF A BLOCK. LINEAR APPROXIMATION OF T H E CONTACT SURFACES. TWO
TYPES OF A FRICTIONAL
CONTACT PROBLEM 250
8.5.3 SLIDING OF A BLOCK. QUADRATICAL APPROXIMATION OF THE CONTACT
SURFACES 257
8.5.4 DISCUSSION 262
8.6 COMPUTATION OF CONTACT INTEGRALS - MORTAR TYPE CONTACT 263
8.6.1 CONVERGENCE TEST FOR THE INTEGRATION ALGORITHM: COMPUTATION OF THE
ENERGY ASSOCIATED WITH T H E PENALTY FUNCTIONAL 264
8.6.2 INTEGRATION SCHEMES WITH SUBDOMAINS 265
8.7 SEGMENT-TO-SEGMENT (MORTAR) APPROACH: ANALYSIS OF T H E P A T C H
TEST 268
8.7.1 CLASSICAL CONTACT P A T C H TEST - LINEAR APPROXIMATIONS 269
8.7.2 CONTACT P A T C H TEST WITH SMOOTH SURFACES 271
8.8 SEGMENT-TO-ANALYTICAL SURFACE (STAS) APPROACH: VARIOUS APPLICATIONS
272
8.8.1 LARGE SLIDING ON A RIGID PARABOLIC CYLINDER 273
8.8.2 FREE BENDING OF A METAL SHEET ON TWO CYLINDERS . . . . 275
8.8.3 DEEP DRAWING OF A CYLINDRICAL P O T - COMBINATION OF STAS CONTACT
ELEMENTS 281
8.8.4 DEEP DRAWING - TEST FOR THE QUALITY OF SHELL ELEMENTS AS WELL AS
FOR T H E QUALITY OF THE CONTACT ALGORITHM 282
8.8.5 DISCUSSION 286
8.9 IMPLEMENTATION OF T H E NITSCHE APPROACHE 287
8.9.1 GAUSS POINT-WISE SUBSTITUTED FORMULATION 287
8.9.2 BUBNOV-GALERKIN-WISE PARTIAL SUBSTITUTED FORMULATION 288
' 8.9.3 NUMERICAL EXAMPLE 289
9 S P E C I A L C A S E O F I M P L E M E N T A T I O N - R E D U C T I
O N I N T O 2 D C A S E 293
9.1 FINITE ELEMENT IMPLEMENTATION OF 2D CONTACT INTERACTION 293
9.1.1 LINEAR NTS CONTACT ELEMENT 294
9.1.2 CLOSED FORM SOLUTION FOR C P P PROCEDURE 295
9.1.3 RETURN-MAPPING SCHEME - 2D CASE 296
IMAGE 7
CONTENTS X I X
9.1.4 TREATMENT OF SPECIAL CASES 297
9.1.5 UPDATE OF THE SLIDING DISPLACEMENTS IN THE CASE OF REVERSIBLE
LOADING 298
9.1.6 CROSSING A N ELEMENT BOUNDARY - CONTINUOUS INTEGRATION SCHEME 299
9.1.7 REMARKS ON ADDITIONAL DEVELOPMENTS 300
9.2 FRICTIONAL CONTACT ANALYSIS: REQUIREMENTS OF SPECIAL ALGORITHMS 304
9.2.1 SLIDING OF A BLOCK. LINEAR APPROXIMATION OF T H E CONTACT
SURFACES. REVERSIBLE LOADING PROCESS 304
9.2.2 DRAWING OF AN ELASTIC STRIP INTO A CHANNEL WITH SHARP CORNERS 308
9.3 DISCUSSION 313
10 I M P L E M E N T A T I O N O F C O N T A C T A L G O R I T H M S W I
T H H I G H ORDER F E 315
10.1 INTRODUCTION 315
10.2 FINITE ELEMENT IMPLEMENTATION OF HIGH ORDER CONTACT F E 317
10.2.1 COMPUTATION OF CONTACT INTEGRALS 319
10.2.2 CONTACT LAYER - RIGID SURFACE (CLRS) FINITE ELEMENT 319
10.2.3 CONTACT LAYER - CONTACT LAYER (CLCL) FINITE ELEMENT 320
10.2.4 LAGRANGE MULTIPLIER METHOD FOR NORMAL TRACTION . . . . 322 10.2.5
GLOBAL SOLUTION SCHEME 323
10.3 NUMERICAL EXAMPLES FOR HIGH ORDER CONTACT LAYER FINITE ELEMENTS 323
10.3.1 LOADING CASE 1. CONTACT ZONE WITHIN ONE ELEMENT 325
10.3.2 LOADING CASE 2. CONTACT ZONE WITHIN SEVERAL ELEMENTS 326
10.3.3 DISCUSSION 329
11 A N I S O T R O P I C ADHESION-FRICTION M O D E L S - S O M E
PARTICULAR D E T A I L S O F I M P L E M E N T A T I O N A N D N U M E R
I C A L E X A M P L E S 331
11.1 INTRODUCTION 331
11.1.1 VARIOUS MODELS FOR FRICTION 331
11.1.2 AVAILABLE FINITE ELEMENT MODELS 333
11.2 EXAMPLES OF THE FINITE ELEMENT IMPLEMENTATION OF T H E COUPLED
ANISOTROPIC ADHESION-FRICTION MODEL 334
11.2.1 POINT-TO-ANALYTICAL SURFACE CONTACT ELEMENT. LINEAR SURFACE
APPROXIMATION OF A DEFORMABLE BODY 335
IMAGE 8
X X
CONTENTS
11.2.2 POINT-TO-ANALYTICAL SURFACE CONTACT ELEMENT. ARBITRARY SURFACE
APPROXIMATION OF THE DEFORMABLE BODY 336
11.2.3 NODE-TO-SEGMENT APPROACH. DEFORMABLE ANISOTROPIC CONTACT SURFACE
337
11.3 NUMERICAL EXAMPLES ILLUSTRATING EFFECTS OF THE COUPLED ANISOTROPIC
ADHESION-FRICTION MODEL 339
11.3.1 LINEAR CONSTANT ORTHOTROPY ON THE PLANE 339
11.3.2 POLAR ORTHOTROPY ON A PLANE. LARGE DISPLACEMENT PROBLEM 347
11.3.3 SPIRAL ORTHOTROPY ON THE CYLINDER 351
11.3.4 DISCUSSION 355
11.4 SYMMETRIZATION OF VARIOUS FRICTION MODELS BASED ON A N AUGMENTED
LAGRANGIAN APPROACH 355
11.4.1 STRUCTURE OF MATRICES AFTER THE LINEARIZATION PROCESS 356
11.4.2 AUGMENTED LAGRANGIAN METHOD AND SYMMETRIC UZAWA ALGORITHM 358
11.5 NUMERICAL EXAMPLES FOR AUGMENTED LAGRANGIAN METHOD . . . 362 11.5.1
SMALL SLIDING PROBLEM. CONSTANT ORTHOTROPY 363
11.5.2 LARGE SLIDING PROBLEM. POLAR ORTHOTROPY 363
11.5.3 DISCUSSION 364
12 E X P E R I M E N T A L VALIDATIONS O F T H E C O U P L E D A N I S T
R O P I C ADHESION-FRICTION M O D E L 367
12.1 INTRODUCTION 367
12.2 EXPERIMENTAL INVESTIGATION 368
12.2.1 EXPERIMENTAL SETUP 369
12.2.2 EXPERIMENTAL RESULTS 370
12.3 CALIBRATION OF PARAMETERS FOR DIFFERENT MODELS 372
12.3.1 CASE 1 373
12.3.2 CASE 2 373
12.3.3 CASE 3 374
12.3.4 CASE 4 374
12.3.5 CASE 5 375
12.3.6 CALIBRATION OF THE THEORETICAL CURVE BY EXTREMAL VALUES 378
12.4 DISCUSSION 379
13 VARIOUS A S P E C T S O F I M P L E M E N T A T I O N O F T H E
CURVE-TO-CURVE C O N T A C T M O D E L 381
13.1 GENERAL STRUCTURE OF TANGENT MATRICES FOR C T C CONTACT . . . 381
13.1.1 TANGENT MATRIX FOR THE NORMAL FORCE N 382
13.1.2 TANGENT MATRICES FOR TANGENTIAL STICKING 383
13.1.3 TANGENT MATRICES FOR TANGENTIAL SLIDING 383
IMAGE 9
CONTENTS
X X I
13.1.4 TANGENT MATRICES FOR ROTATIONAL STICKING 383
13.1.5 TANGENT MATRICES FOR ROTATIONAL SLIDING 383
13.2 RESIDUAL VECTOR 384
13.2.1 P A R T FOR NORMAL INTERACTION 384
13.2.2 P A R T FOR TANGENTIAL INTERACTION 384
13.2.3 P A R T FOR MOMENT (ROTATIONAL) INTERACTION 385
13.3 COMBINATION WITH VARIOUS FINITE ELEMENT MODELS OF THE CONTINUUM FOR
CURVE-TO-CURVE CONTACT 385
13.3.1 IMPLEMENTATION OF CURVE-TO-CURVE CONTACT ALGORITHM - LINEAR
ELEMENT FOR EDGE-TO-EDGE CONTACT 385
13.3.2 COMBINATION OF FINITE BEAM ELEMENTS WITH THE CURVE-TO-CURVE
CONTACT ALGORITHM 389
13.3.3 DEVELOPMENT OF SPECIAL "SOLID-BEAM" ELEMENTS FOR BEAM-TO-BEAM
CONTACT 391
13.4 NUMERICAL EXAMPLES FOR CURVE-TO-CURVE CONTACT 393
13.4.1 BENDING OF A FLEXIBLE BEAM BY A RIGID BEAM. NON FRICTIONAL CASE
394
13.4.2 ANALYSIS OF CONTACT FOR INTERSECTING BEAMS 398
13.4.3 DISCUSSION 405
13.4.4 BENDING OF A FLEXIBLE BEAM BY A RIGID BEAM COMPARISON OF THREE
FINITE ELEMENT MODELS 405
13.4.5 CONTACT BETWEEN RINGS 408
13.4.6 TYING OF A KNOT 409
13.4.7 DISCUSSION 412
14 FRICTIONAL INTERACTION O F A SPIRAL R O P E A N D A C Y L I N D E R
- 3 D - G E N E R A L I Z A T I O N O F T H E E U L E R - E Y T E L W E
I N FORMULA CONSIDERING P I T C H 413
14.1 EQUILIBRIUM EQUATIONS FOR T H E ROPE IN SPACE 413
14.2 SOLUTION OF THE EQUILIBRIUM EQUATION FOR A SPIRAL LINE (HELIX) 416
14.3 CONCLUSIONS 422
R E F E R E N C E S 423
LIST O F LANGUAGES 437
I N D E X 439 |
| any_adam_object | 1 |
| author | Konyukhov, Alexander Schweizerhof, Karl |
| author_GND | (DE-588)143486306 |
| author_facet | Konyukhov, Alexander Schweizerhof, Karl |
| author_role | aut aut |
| author_sort | Konyukhov, Alexander |
| author_variant | a k ak k s ks |
| building | Verbundindex |
| bvnumber | BV040715887 |
| classification_rvk | UF 2000 |
| ctrlnum | (OCoLC)812569634 (DE-599)DNB102301646X |
| dewey-full | 620.10501518 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.10501518 |
| dewey-search | 620.10501518 |
| dewey-sort | 3620.10501518 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen Physik |
| format | Book |
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| id | DE-604.BV040715887 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:30:56Z |
| institution | BVB |
| isbn | 9783642315305 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025696200 |
| oclc_num | 812569634 |
| open_access_boolean | |
| owner | DE-703 DE-83 DE-706 |
| owner_facet | DE-703 DE-83 DE-706 |
| physical | XXI, 443 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in applied and computational mechanics |
| series2 | Lecture notes in applied and computational mechanics |
| spelling | Konyukhov, Alexander Verfasser (DE-588)143486306 aut Computational contact mechanics geometrically exact theory for arbitrary shaped bodies Alexander Konyukhov and Karl Schweizerhof Berlin [u.a.] Springer 2013 XXI, 443 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in applied and computational mechanics 67 Kontaktmechanik (DE-588)4798356-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Kontaktmechanik (DE-588)4798356-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Schweizerhof, Karl Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-31531-2 Lecture notes in applied and computational mechanics 67 (DE-604)BV017110729 67 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4052433&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=025696200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Konyukhov, Alexander Schweizerhof, Karl Computational contact mechanics geometrically exact theory for arbitrary shaped bodies Lecture notes in applied and computational mechanics Kontaktmechanik (DE-588)4798356-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4798356-5 (DE-588)4128130-5 |
| title | Computational contact mechanics geometrically exact theory for arbitrary shaped bodies |
| title_auth | Computational contact mechanics geometrically exact theory for arbitrary shaped bodies |
| title_exact_search | Computational contact mechanics geometrically exact theory for arbitrary shaped bodies |
| title_full | Computational contact mechanics geometrically exact theory for arbitrary shaped bodies Alexander Konyukhov and Karl Schweizerhof |
| title_fullStr | Computational contact mechanics geometrically exact theory for arbitrary shaped bodies Alexander Konyukhov and Karl Schweizerhof |
| title_full_unstemmed | Computational contact mechanics geometrically exact theory for arbitrary shaped bodies Alexander Konyukhov and Karl Schweizerhof |
| title_short | Computational contact mechanics |
| title_sort | computational contact mechanics geometrically exact theory for arbitrary shaped bodies |
| title_sub | geometrically exact theory for arbitrary shaped bodies |
| topic | Kontaktmechanik (DE-588)4798356-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Kontaktmechanik Numerisches Verfahren |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4052433&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025696200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV017110729 |
| work_keys_str_mv | AT konyukhovalexander computationalcontactmechanicsgeometricallyexacttheoryforarbitraryshapedbodies AT schweizerhofkarl computationalcontactmechanicsgeometricallyexacttheoryforarbitraryshapedbodies |