Integrodifferential relations in linear elasticity:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2012
|
| Series: | De Gruyter studies in mathematical physics
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 280 S. |
| ISBN: | 9783110270303 |
Staff View
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| 245 | 1 | 0 | |a Integrodifferential relations in linear elasticity |c Georgy V. Kostin, Vasily V. Saurin |
| 264 | 1 | |a Berlin [u.a.] |b De Gruyter |c 2012 | |
| 300 | |a XI, 280 S. | ||
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PREFACE V
1 INTRODUCTION 1
2 BASIC CONCEPTS O F THE LINEAR THEORY O F ELASTICITY 6
2.1 STRESSES 6
2.2 LINEAR STRAINS 13
2.3 CONSTITUTIVE RELATIONS 19
2.4 BOUNDARY VALUE PROBLEMS 26
2.4.1 STATIC STATEMENTS 26
2.4.2 DYNAMIC PROBLEMS 30
2.5 SIMPLIFIED MODELS 31
2.5.1 ELASTIC RODS AND STRINGS 31
2.5.2 BEAM MODELS 35
2.5.3 MEMBRANES 38
2.5.4 PLANE STRESS AND STRAIN STATES 40
3 CONVENTIONAL VARIATIONAL PRINCIPLES 43
3.1 CLASSICAL VARIATIONAL APPROACHES 43
3.1.1 ENERGY RELATIONS 43
3.1.2 DIRECT PRINCIPLES 44
3.1.3 COMPLEMENTARY PRINCIPLES 47
3.2 VARIATIONAL PRINCIPLES IN DYNAMICS 49
3.3 GENERALIZED VARIATIONAL PRINCIPLES 55
3.3.1 RELATIONS AMONG VARIATIONAL PRINCIPLES 55
3.3.2 SEMI-INVERSE APPROACH 60
3.4 FINITE DIMENSIONAL DISCRETIZATION 61
3.4.1 RITZ METHOD 62
3.4.2 GALERKIN METHOD 64
3.4.3 FINITE ELEMENT METHOD 66
3.4.4 BOUNDARY ELEMENT METHOD 72
HTTP://D-NB.INFO/1027213499
IMAGE 2
X CONTENTS
4 THE METHOD O F INTEGRODIFFERENTIAL RELATIONS 73
4.1 BASIC IDEAS 73
4.1.1 ANALYTICAL SOLUTIONS IN LINEAR ELASTICITY 73
4.1.2 INTEGRAL FORMULATION O F HOOKE S LAW 78
4.2 FAMILY O F QUADRATIC FUNCTIONALS 81
4.3 RITZ METHOD IN THE MIDR 83
4.3.1 ALGORITHM O F POLYNOMIAL APPROXIMATIONS 83
4.3.2 2D CLAMPED PLATE - STATIC CASE 85
4.4 2D NATURAL VIBRATIONS 90
4.4.1 EIGENVALUE PROBLEM 90
4.4.2 FREE VIBRATIONS O F CIRCULAR AND ELLIPTIC MEMBRANES 93
5 VARIATIONAL PROPERTIES O F THE INTEGRODIFFERENTIAL STATEMENTS 101
5.1 VARIATIONAL PRINCIPLES FOR QUADRATIC FUNCTIONALS 101
5.2 RELATIONS WITH THE CONVENTIONAL PRINCIPLES 103
5.3 BILATERAL ENERGY ESTIMATES 106
5.4 BODY ON AN ELASTIC FOUNDATION 114
5.4.1 VARIATIONAL PRINCIPLE FOR THE ENERGY ERROR FUNCTIONAL 114
5.4.2 BILATERAL ESTIMATES 118
6 ADVANCE FINITE ELEMENT TECHNIQUE 124
6.1 PIECEWISE POLYNOMIAL APPROXIMATIONS 124
6.2 SMOOTH POLYNOMIAL SPLAINS 127
6.2.1 ARGYRIS TRIANGLE 127
6.2.2 STIFFNESS MATRIX FOR THE ARGYRIS TRIANGLE 132
6.2.3 ~* 2 APPROXIMATIONS FOR A TRIANGLE ELEMENT 133
6.3 FINITE ELEMENT TECHNIQUE IN LINEAR ELASTICITY PROBLEMS 136
6.4 MESH ADAPTATION AND MESH REFINEMENT 145
7 SEMI-DISCRETIZATION AND VARIATIONAL TECHNIQUE 158
7.1 REDUCTION O F PDE SYSTEM TO ODES 158
7.1.1 BEAM-ORIENTED NOTATION 158
7.1.2 SEMI-DISCRETIZATION IN THE DISPLACEMENTS 160
7.1.3 SEMI-DISCRETIZATION IN THE STRESSES 162
7.2 ANALYSIS O F BEAM STRESS-STRAIN STATE 166
7.3 2D ELASTIC BEAM VIBRATIONS 170
IMAGE 3
CONTENTS XI
8 AN ASYMPTOTIC APPROACH 177
8.1 CLASSICAL VARIATIONAL APPROACH 177
8.2 INTEGRODIFFERENTIAL APPROACH 182
8.2.1 BASIC IDEAS O F ASYMPTOTIC APPROXIMATIONS 182
8.2.2 BEAM EQUATIONS - GENERAL CASE O F LOADING 187
8.3 ELASTIC BEAM VIBRATIONS 190
8.3.1 STATEMENT O F AN EIGENVALUE PROBLEM 190
8.3.2 LONGITUDINAL VIBRATIONS 194
8.3.3 LATERAL VIBRATIONS 199
8.4 3D STATIC PROBLEM 204
9 A PROJECTION APPROACH 218
9.1 PROJECTION FORMULATION O F LINEAR ELASTICITY PROBLEMS 218
9.2 PROJECTIONS VS. VARIATIONS AND ASYMPTOTICS 222
10 3D STATIC BEAM MODELING 227
10.1 PROJECTION ALGORITHMS 227
10.2 CANTILEVER BEAM WITH THE TRIANGULAR CROSS SECTION 241
10.3 PROJECTION BEAM MODEL 246
10.4 CHARACTERISTICS O F A BEAM WITH THE TRIANGULAR CROSS SECTION 248
11 3D BEAM VIBRATIONS 252
11.1 INTEGRAL PROJECTIONS IN EIGENVALUE PROBLEMS 252
11.2 NATURAL VIBRATIONS OF A BEAM WITH THE TRIANGULAR CROSS SECTION 255
11.3 FORCED VIBRATIONS O F A BEAM WITH THE TRIANGULAR CROSS SECTION 266
A VECTORS AND TENSORS 269
B SOBOLEV SPACES 271
BIBLIOGRAPHY 274
INDEX 278
|
| any_adam_object | 1 |
| author | Kostin, Georgij V. 1936- Saurin, Vasilij V. |
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| dewey-full | 531/.382 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531/.382 |
| dewey-search | 531/.382 |
| dewey-sort | 3531 3382 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:24:16Z |
| institution | BVB |
| isbn | 9783110270303 |
| language | English |
| lccn | 2012024559 |
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| physical | XI, 280 S. |
| publishDate | 2012 |
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| publisher | De Gruyter |
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| series | De Gruyter studies in mathematical physics |
| series2 | De Gruyter studies in mathematical physics |
| spelling | Kostin, Georgij V. 1936- Verfasser (DE-588)171625641 aut Integrodifferential relations in linear elasticity Georgy V. Kostin, Vasily V. Saurin Berlin [u.a.] De Gruyter 2012 XI, 280 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics 10 Elasticity Plasticity Integro-differential equations Lineare Elastizitätstheorie (DE-588)4139506-2 gnd rswk-swf Integrodifferentialgleichung (DE-588)4161939-0 gnd rswk-swf Lineare Elastizitätstheorie (DE-588)4139506-2 s Integrodifferentialgleichung (DE-588)4161939-0 s DE-604 Saurin, Vasilij V. Verfasser (DE-588)1028335547 aut Erscheint auch als Online-Ausgabe 978-3-11-027100-3 De Gruyter studies in mathematical physics 10 (DE-604)BV040141722 10 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025301386&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kostin, Georgij V. 1936- Saurin, Vasilij V. Integrodifferential relations in linear elasticity De Gruyter studies in mathematical physics Elasticity Plasticity Integro-differential equations Lineare Elastizitätstheorie (DE-588)4139506-2 gnd Integrodifferentialgleichung (DE-588)4161939-0 gnd |
| subject_GND | (DE-588)4139506-2 (DE-588)4161939-0 |
| title | Integrodifferential relations in linear elasticity |
| title_auth | Integrodifferential relations in linear elasticity |
| title_exact_search | Integrodifferential relations in linear elasticity |
| title_full | Integrodifferential relations in linear elasticity Georgy V. Kostin, Vasily V. Saurin |
| title_fullStr | Integrodifferential relations in linear elasticity Georgy V. Kostin, Vasily V. Saurin |
| title_full_unstemmed | Integrodifferential relations in linear elasticity Georgy V. Kostin, Vasily V. Saurin |
| title_short | Integrodifferential relations in linear elasticity |
| title_sort | integrodifferential relations in linear elasticity |
| topic | Elasticity Plasticity Integro-differential equations Lineare Elastizitätstheorie (DE-588)4139506-2 gnd Integrodifferentialgleichung (DE-588)4161939-0 gnd |
| topic_facet | Elasticity Plasticity Integro-differential equations Lineare Elastizitätstheorie Integrodifferentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025301386&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040141722 |
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