Dynamics of solid structures: methods using integrodifferential relations
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2018]
|
| Schlagworte: | |
| Online-Zugang: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110516234&searchTitles=true Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XVII, 288 Seiten Illustrationen 24 cm |
| ISBN: | 9783110516234 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804178184975941632 |
|---|---|
| adam_text | CONTENTS
PREFACE* VII
BASIC NOTATION * XI
1 INTRODUCTION * 1
2 GENERALIZED FORMULATIONS OF PARABOLIC AND HYPERBOLIC PROBLEMS -
2.1 FINITE-DIMENSIONAL MECHANICAL SYSTEMS * 9
2.1.1 FORCED MOTIONS OF A MECHANICAL SYSTEM WITH ELASTIC ELEMENTS
2.1.2 VARIATIONAL STATEMENT OF MECHANICAL PROBLEMS * 11
2.1.3 RELATION WITH CONVENTIONAL VARIATIONAL PRINCIPLES *
13
2.2 LONGITUDINAL MOTIONS OF ELASTIC RODS * 15
2.2.1 EQUATIONS OF ROD DYNAMICS * 16
2.2.2 VARIATIONAL STATEMENT OF THE IBVP * 17
2.3 MEMBRANE VIBRATIONS AND ACOUSTIC WAVES * 20
2.3.1 CLASSICAL STATEMENT * 21
2.3.2 WEAKENED FORMULATION RELYING ON THE MIDR * 23
2.3.3 CONDITIONS OFSTATIONARITY * 24
2.4 HEAT TRANSFER IN SOLIDS * 25
2.4.1 EQUATIONS IN LINEAR THERMODYNAMICS * 26
2.4.2 GENERALIZED FORMULATION BASED ON THE MIDR * 26
2.4.3 VARIATIONAL PROPERTIES OF THE MINIMIZATION PROBLEM * 28
3 VARIATIONAL PRINCIPLES IN LINEAR ELASTICITY * 31
3.1 DYNAMICS OF ELASTIC BODIES * 31
3.1.1 PROBLEMS OF ELASTODYNAMICS * 31
3.1.2 HAMILTON PRINCIPLES *
33
3.1.3 INTEGRODIFFERENTIAL STATEMENT IN ELASTICITY * 35
3.1.4 A FAMILY OF CONSTITUTIVE FUNCTIONALS * 36
3.1.5 COMPARATIVE ANALYSIS OF VARIATIONAL PROBLEMS * 38
3.1.6 DYNAMIC VARIATIONAL PRINCIPLE IN DISPLACEMENTS AND STRESSES -
3.2 SPECTRAL PROBLEMS IN ELASTICITY * 43
3.2.1 HARMONIC VIBRATIONS OF ELASTIC BODIES * 43
3.2.2 NATURAL VIBRATIONS OF SOLIDS * 45
3.2.3 VARIATIONAL STATEMENTS OF HARMONIC PROBLEMS * 45
3.3 VARIATIONAL FORMULATIONS IN ELASTOSTATICS * 47
3.3.1 STATIC PROBLEMS IN LINEAR ELASTICITY * 47
3.3.2 RELATIONSHIP OF STATIC VARIATIONAL PRINCIPLES * 48
3.3.3 BILATERAL ENERGY ESTIMATES * 50
4 VARIATIONAL STATEMENTS IN STRUCTURAL MECHANICS * 53
4.1 LATERAL MOTIONS OF ELASTIC BEAMS * 53
4.1.1 DYNAMIC EQUATIONS FOR BEAM BENDING* 53
4.1.2 COMPLEMENTARY HAMILTON PRINCIPLES * 55
4.1.3 METHOD OF INTEGRODIFFERENTIAL RELATIONS IN BEAM THEORY * 57
4.1.4 ENERGY ESTIMATES OF SOLUTION QUALITY * 58
4.1.5 A FAMILY OF VARIATIONAL PROBLEMS * 59
4.1.6 COMPARISON OF VARIATIONAL FORMULATIONS * 62
4.2 LONGITUDINAL MOTIONS OF VISCOELASTIC RODS * 64
4.2.1 MODELS OF DEFORMATION WITH VISCOSITY AND RHEOLOGY * 64
4.2.2 MINIMIZATION WITH INTEGRAL CONSTITUTIVE RELATIONS * 65
4.3 STRUCTURES WITH LUMPED AND DISTRIBUTED PARAMETERS * 67
4.3.1 M OTIONSOFA ROD WEIGHTED AT THE ENDS * 67
4.3.2 VARIATIONAL STATEMENT FOR HYBRID SYSTEM DYNAMICS * 69
5 RITZ METHOD FOR INITIAL-BOUNDARY VALUE PROBLEMS * 71
5.1 FINITE-DIMENSIONAL DYNAMIC PROBLEMS * 71
5.1.1 CHAIN OF LINEAR OSCILLATORS * 71
5.1.2 POLYNOMIAL APPROXIMATION OF TIME FUNCTIONS * 72
5.2 BIVARIATE POLYNOMIALS IN ROD AND BEAM MODELING * 74
5.2.1 LONGITUDINAL MOTIONS OF AN ELASTIC HOMOGENEOUS ROD * 74
5.2.2 CONVENTIONAL GALERKIN METHOD * 77
5.2.3 RITZ METHOD AND THE MIDR * 78
5.2.4 LATERAL ELASTIC DISPLACEMENTS * 83
5.2.5 NUMERICAL SIMULATION OF BEAM BENDING * 85
5.3 FEM MODELING OF ELASTIC ROD DYNAMICS * 88
5.3.1 MODIFIED MINIMIZATION PROBLEM * 88
5.3.2 PIECEWISE POLYNOMIAL APPROXIMATIONS * 89
5.3.3 CONTINUITY OF KINEMATIC AND DYNAMIC FIELDS * 93
5.3.4 CONSTITUTIVE RELATIONS IN THE FEM * 97
5.4 SPLINE REPRESENTATION OF ELASTIC BODY MOTIONS * 101
5.4.1 APPROXIMATION TO A PROBLEM OF ELASTODYNAMICS * 101
5.4.2 FORCED MOTIONS OF AN ELASTIC BODY * 104
5.4.3 APPROXIMATIONS OF DISPLACEMENT AND STRESS FIELDS * 105
5.4.4 NUMERICAL EXAMPLE * 107
6 VARIATIONAL AND PROJECTION TECHNIQUES WITH SEMI-DISCRETIZATION * 113
6.1 VARIATIONAL APPROACH TO ELASTIC STRUCTURE DYNAMICS * 113
6.1.1 VARIATIONAL STATEMENTS OF A DYNAMIC PROBLEM * 113
6.1.2 APPROXIMATING SYSTEM OFODES * 114
6.1.3 NUMERICAL ANALYSIS OF ELASTIC BEAM MOTIONS * 118
6.2 PROJECTION APPROACH TO DYNAMIC PROBLEMS * 122
6.2.1 PROJECTION STATEMENT FOR ELASTIC BEAM MOTIONS * 122
6.2.2 MODIFICATION OF THE PETROV-GALERKIN METHOD * 123
6.3 FEM REALIZATION OF THE PETROV-GALERKIN METHOD * 125
7 INTEGRODIFFERENTIAL APPROACH TO EIGENVALUE PROBLEMS
* 129
7.1 MODIFICATION OF THE GALERKIN METHOD FOR ELASTIC STRUCTURES * 129
7.1.1 LONGITUDINAL MOTIONS OF AN ELASTIC ROD * 129
7.1.2 COMPARISON OF GALERKIN AND VARIATIONAL APPROACHES * 131
7.1.3 PROJECTION APPROACH BASED ON THE MIDR * 136
7.2 SEMI-DISCRETIZATION IN PROBLEMS OF NATURAL BEAM VIBRATIONS * 139
7.2.1 NATURAL VIBRATIONS OF ELASTIC PLATES * 139
7.2.2 VARIATIONAL APPROACH TO THE EIGENVALUE PROBLEM * 142
7.2.3 PROJECTION APPROACH TO THE EIGENVALUE PROBLEM * 144
7.2.4 VARIATIONAL VERSUS PROJECTION APPROACHES * 146
7.2.5 LONGITUDINAL PLATE VIBRATIONS * 147
7.2.6 LATERAL IN-PLANE VIBRATIONS * 150
7.3 SPECIAL MODELS FOR PLATE MOTIONS * 152
7.3.1 STATEMENT OF THE EIGENVALUE PROBLEM * 152
7.3.2 SIMPLIFIED MODEL OF LONGITUDINAL VIBRATIONS * 156
7.3.3 REFINED MODEL OF 2D ROD VIBRATIONS * 159
7.3.4 LATERAL VIBRATIONS OF A FREE 2D BEAM * 161
8 SPATIAL VIBRATIONS OF ELASTIC BEAMS WITH CONVEX CROSS-SECTIONS
* 165
8.1 NATURAL MOTIONS OF A CUBOID BEAM * 165
8.1.1 PROJECTION APPROACH TO A 3D EIGENVALUE PROBLEM IN ELASTICITY * 165
8.1.2 SYSTEM OF DAES APPROXIMATING THE BEAM VIBRATIONS * 167
8.1.3 DECOMPOSITION OF VIBRATION EQUATIONS FOR A HOMOGENEOUS BEAM * 168
8.1.4 BREATHING OF A BODY WITH THE SQUARE CROSS SECTION * 170
8.1.5 TORSION OF THE BODY * 173
8.1.6 LONGITUDINAL VIBRATIONS * 174
8.1.7 LATERAL VIBRATIONS * 177
8.2 NATURAL VIBRATIONS OF BEAMS WITH TRIANGULAR CROSS SECTIONS * 180
8.2.1 DYNAMICS OF AN ELASTIC TRIANGULAR PRISM * 180
8.2.2 SEMI-DISCRETIZATION OF DISPLACEMENT AND STRESS FIELDS * 181
8.2.3 INTEGRAL PROJECTIONS FOR THE TRIANGULAR CROSS SECTION * 184
8.2.4 NATURAL VIBRATIONS OF A BEAM WITH THE ISOSCELES CROSS SECTION *
189
9 DOUBLE MINIMIZATION IN OPTIMAL CONTROL PROBLEMS
* 197
9.1 OPTIMIZATION OF BEAM MOTIONS WITH POLYNOMIALS * 197
9.1.1 STATEMENT OF AN OPTIMAL CONTROL PROBLEM * 197
9.1.2 DISCRETIZATION BASED ON THE MIDR * 198
9.1.3 PARAMETRIC OPTIMIZATION OF THE BEAM MOTIONS * 199
9.1.4 NUMERICAL EXAMPLES OF CONTROLLED MOTIONS * 200
9.2 POLYNOMIAL CONTROL IN DYNAMIC PROBLEMS OF LINEAR ELASTICITY * 206
9.2.1 STATEMENT OF AN INVERSE DYNAMIC PROBLEM * 206
9.2.2 TIME-SPACE DISCRETIZATION BASED ON THE MIDR * 208
9.2.3 OPTIMIZATION OF MOTION PARAMETERS * 208
9.2.4 STRUCTURE OF POLYNOMIAL APPROXIMATIONS * 209
9.2.5 LONGITUDINAL MOTIONS OF A CONTROLLED ELASTIC ROD * 210
9.2.6 CONTROLLED MOTIONS OF A CUBOID BODY WITH THE SQUARE BASES * 212
9.2.7 COMPARISON OF 2D AND 4D MODELS * 215
9.3 FEM IN CONTROL PROBLEMS OF ELASTIC ROD DISPLACEMENTS * 220
9.3.1 STATEMENT OF AN OPTIMAL CONTROL PROBLEM * 220
9.3.2 PARAMETERIZATION OF STATE AND CONTROL FUNCTIONS * 221
9.3.3 CONTROL OPTIMIZATION FOR APPROXIMATE SYSTEMS * 223
9.3.4 REGULARIZATION OF INTEGRAL ERROR* 224
9.3.5 EXACT SOLUTION OF THE CONTROL PROBLEM * 226
10 SEMI-DISCRETE APPROXIMATIONS IN INVERSE DYNAMIC PROBLEMS * 229
10.1 PROJECTION APPROACH TO OPTIMIZATION IN ELASTODYNAMICS * 229
10.1.1 SEMI-DISCRETIZATION AND FEM IN CONTROLLED BEAM DYNAMICS *
229
10.1.2 OPTIMIZATION AND REGULARIZATION OF APPROXIMATE SOLUTIONS * 231
10.1.3 SOLUTION QUALITY IN PARAMETRIC OPTIMIZATION * 232
10.2 OPTIMAL CONTROL OF ELASTIC BODY MOTIONS * 235
10.2.1 VARIATIONAL FORMULATION OF A DIRECT DYNAMIC PROBLEM * 235
10.2.2 PROJECTION FORMULATION OF THE PROBLEM ON BODY MOTIONS * 237
10.2.3 STATEMENT OF AN OPTIMAL CONTROL PROBLEM * 238
10.2.4 ALGORITHM OF DISCRETIZATION * 239
10.2.5 SPECTRAL BOUNDARY VALUE PROBLEM * 242
10.2.6 SYSTEM OF ODES WITH RESPECT TO TIME * 244
10.2.7 FINITE-DIMENSIONAL CONTROL PROBLEM * 245
10.3 VARIATIONAL APPROACH TO OPTIMIZATION OF PARABOLIC SYSTEMS * 248
10.3.1 STATEMENT OF A CONTROL PROBLEM * 248
10.3.2 FOURIER METHOD IN HEAT TRANSFER PROBLEMS * 250
10.3.3 OPTIMAL CONTROL PROBLEM OF ROD HEATING * 252
10.3.4 VARIATIONAL FORMULATION OF THE IBVP * 253
10.3.5 SPATIAL DISCRETIZATION WITH POLYNOMIALS * 253
10.3.6 DISCRETIZATION ERROR IN THE VARIATIONAL APPROACH * 255
10.3.7 NUMERICAL RESULTS OF HEAT CONTROL * 255
11 MODELING AND CONTROL IN MECHATRONICS * 259
11.1 OPTIMAL ROTATIONS OF AN ELECTROMECHANICAL MANIPULATOR * 259
11.1.1 MOTION OF A FLEXIBLE LINK BY A DRIVE * 259
11.1.2 OPTIMAL ANGULAR ROTATION OF THE LINK * 261
11.1.3 PROJECTION APPROACH TO THE PROBLEM ON LINK MOTIONS -
11.2 CONTROL OF A FLEXIBLE STRUCTURE WITH VISCOELASTIC LINKS -
11.2.1 CONTROLLED MECHANISM WITH FLEXIBLE LINKS * 268
11.2.2 OPTIMAL CONTROL PROBLEM OF STRUCTURE MOTION * 269
11.2.3 FINITE ELEMENT ALGORITHM * 270
11.2.4 NUMERICAL SIMULATION OF STRUCTURE DYNAMICS * 271
A VECTORS AND TENSORS * 275
B SOBOLEV SPACES * 279
BIBLIOGRAPHY * 281
INDEX * 287
263
268
|
| any_adam_object | 1 |
| author | Kostin, Georgij V. Saurin, Vasilij V. |
| author_GND | (DE-588)1028782063 (DE-588)1028335547 |
| author_facet | Kostin, Georgij V. Saurin, Vasilij V. |
| author_role | aut aut |
| author_sort | Kostin, Georgij V. |
| author_variant | g v k gv gvk v v s vv vvs |
| building | Verbundindex |
| bvnumber | BV044707908 |
| ctrlnum | (OCoLC)1015859842 (DE-599)DNB1135495386 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
| format | Book |
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| id | DE-604.BV044707908 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:59:57Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110516234 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030104495 |
| oclc_num | 1015859842 |
| open_access_boolean | |
| owner | DE-29 DE-83 |
| owner_facet | DE-29 DE-83 |
| physical | XVII, 288 Seiten Illustrationen 24 cm |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | De Gruyter |
| record_format | marc |
| spelling | Kostin, Georgij V. (DE-588)1028782063 aut Dynamics of solid structures methods using integrodifferential relations Georgy V. Kostin, Vasily V. Saurin Berlin ; Boston De Gruyter [2018] © 2018 XVII, 288 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Elastomechanik (DE-588)4014161-5 gnd rswk-swf Integrodifferentialgleichung (DE-588)4161939-0 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Strukturmechanik (DE-588)4126904-4 gnd rswk-swf Variationsproblem (DE-588)4187419-5 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s Strukturmechanik (DE-588)4126904-4 s Elastomechanik (DE-588)4014161-5 s Variationsproblem (DE-588)4187419-5 s Integrodifferentialgleichung (DE-588)4161939-0 s DE-604 Saurin, Vasilij V. Verfasser (DE-588)1028335547 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, ePDF 978-3-11-051644-9 Erscheint auch als Online-Ausgabe, ePub 978-3-11-051625-8 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110516234&searchTitles=true B:DE-101 application/pdf http://d-nb.info/1135495386/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030104495&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kostin, Georgij V. Saurin, Vasilij V. Dynamics of solid structures methods using integrodifferential relations Elastomechanik (DE-588)4014161-5 gnd Integrodifferentialgleichung (DE-588)4161939-0 gnd Festkörpermechanik (DE-588)4129367-8 gnd Strukturmechanik (DE-588)4126904-4 gnd Variationsproblem (DE-588)4187419-5 gnd |
| subject_GND | (DE-588)4014161-5 (DE-588)4161939-0 (DE-588)4129367-8 (DE-588)4126904-4 (DE-588)4187419-5 |
| title | Dynamics of solid structures methods using integrodifferential relations |
| title_auth | Dynamics of solid structures methods using integrodifferential relations |
| title_exact_search | Dynamics of solid structures methods using integrodifferential relations |
| title_full | Dynamics of solid structures methods using integrodifferential relations Georgy V. Kostin, Vasily V. Saurin |
| title_fullStr | Dynamics of solid structures methods using integrodifferential relations Georgy V. Kostin, Vasily V. Saurin |
| title_full_unstemmed | Dynamics of solid structures methods using integrodifferential relations Georgy V. Kostin, Vasily V. Saurin |
| title_short | Dynamics of solid structures |
| title_sort | dynamics of solid structures methods using integrodifferential relations |
| title_sub | methods using integrodifferential relations |
| topic | Elastomechanik (DE-588)4014161-5 gnd Integrodifferentialgleichung (DE-588)4161939-0 gnd Festkörpermechanik (DE-588)4129367-8 gnd Strukturmechanik (DE-588)4126904-4 gnd Variationsproblem (DE-588)4187419-5 gnd |
| topic_facet | Elastomechanik Integrodifferentialgleichung Festkörpermechanik Strukturmechanik Variationsproblem |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110516234&searchTitles=true http://d-nb.info/1135495386/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030104495&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kostingeorgijv dynamicsofsolidstructuresmethodsusingintegrodifferentialrelations AT saurinvasilijv dynamicsofsolidstructuresmethodsusingintegrodifferentialrelations AT walterdegruytergmbhcokg dynamicsofsolidstructuresmethodsusingintegrodifferentialrelations |
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