Boundary value problems in linear viscoelasticity:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1988
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 266 S. |
| ISBN: | 3540186158 0387186158 |
Internformat
MARC
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| 100 | 1 | |a Golden, John M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Boundary value problems in linear viscoelasticity |c J. M. Golden ; G. A. C. Graham |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1988 | |
| 300 | |a XIV, 266 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 4 | |a Viscoélasticité | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Viscoelasticity | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Elastizitätstheorie |0 (DE-588)4139506-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Viskoelastizität |0 (DE-588)4063621-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Viskoelastizität |0 (DE-588)4063621-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Lineare Elastizitätstheorie |0 (DE-588)4139506-2 |D s |
| 689 | 1 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Graham, George A. C. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804115332891148288 |
|---|---|
| adam_text | Contents
1. Fundamental Relationships 1
1.1 Stress and Strain 1
1.2 One dimensional Linear Viscoelasticity 4
1.2.1 Linear Hereditary Constitutive Laws 4
1.2.2 The Operator Algebra 6
1.2.3 Alternative Notation 8
1.2.4 Non aging Materials 9
1.3 Energy Considerations in the One dimensional Case 12
1.4 Creep and Relaxation 14
1.4.1 The Boltzmann Superposition Principle 17
1.5 The Frequency Representation 18
1.5.1 Dispersion Relations 20
1.5.2 Energy Considerations under Sinusoidal Deformation .. 22
1.5.3 Creep 23
1.6 Special Forms of the Viscoelastic Functions 25
1.6.1 Standard Linear Solid 25
1.6.2 Maxwell and Voigt Models 26
1.6.3 Spectrum Models 28
1.6.4 Continuous Spectra 31
1.6.5 Power Law Viscoelastic Functions 32
1.7 Temperature Dependence of the Viscoelastic Functions 34
1.7.1 Variable Temperature History 35
1.8 Three dimensional Constitutive and Dynamical Equations 37
1.8.1 Isothermal Theory 37
1.8.2 The Non inertial Approximation 39
1.8.3 Frequency Representation 40
1.8.4 Proportionality Assumption 40
1.8.5 Non isothermal Equations 41
1.8.6 Uniqueness and Other Theorems 42
1.9 Isotropic Media 43
1.9.1 Frequency Representation 45
1.9.2 Proportionality Assumption 45
1.9.3 Non isothermal Relations 46
1.9.4 Compatibility Equations 47
1.10 Causality : 48
1.11 Summary 50
XII Contents
2. General Theorems and Methods of Solution
of Boundary Value Problems 54
2.1 The Classical Correspondence Principle 54
2.1.1 Separation of Space and Time Variables 57
2.2 Time dependent Boundary Regions 57
2.3 Elastic Solutions in Terms of Green s Functions 59
2.4 Decomposition of Hereditary Integrals 63
2.5 The Integral Equation 67
2.6 Expanding and Contracting Boundary Regions 68
2.6.1 The Extended Correspondence Principle 68
2.6.2 The Generalized Partial Correspondence Principle 69
2.6.3 Repetitive Expansion and Contraction 70
2.7 Viscoelastic Papkovich Neuber Solution 73
2.8 Plane Strain in Linear Viscoelasticity 74
2.9 Contact between Viscoelastic Media 78
2.9.1 Inclusion of Inertial Affects 81
2.10 Receding Contact in Plane Viscoelasticity 81
2.11 Energy Loss in Moving Contact Problems 84
2.12 Solution of Problems Involving Aging Materials or
Non isothermal Conditions 87
2.12.1 Aging Materials 87
2.12.2 Non isothermal Problems 88
2.13 Summary 89
3. Plane Non inertial Contact Problems 91
3.1 Kolosov Muskhelishvili Equations Adapted to the Half Plane . 92
3.2 The First and Second Boundary Value Problems 95
3.3 The General Mixed Boundary Value Problem 99
3.3.1 Single Contact Interval 102
3.3.2 Frictionless Contact 103
3.4 The General Integral Equation 104
3.5 Moving Load Problems 105
3.5.1 Steady State Limit 106
3.6 Solution for a Single Load 109
3.6.1 Discrete Spectrum Model 112
3.7 Small Viscoelasticity Approximation 116
3.8 Hysteretic Friction 120
3.8.1 Small Viscoelasticity 122
3.9 Increasing and Decreasing Contact Area 123
3.10 The Plane Normal Contact Problem 126
3.11 The Steady State Limit of the Normal Problem 130
3.11.1 The Standard Linear Model 131
3.12 Summary 137
4. Plane Non inertial Crack Problems 140
4.1 Problem Formulation 140
4.2 Fully Open Cracks that are Stationary or Growing 143
Contents XIII
4.3 Monotonically Closing Cracks 146
4.4 Stationary Cracks 148
4.4.1 The Standard Linear Model 151
4.4.2 Steady State Solution 152
4.5 Growing Cracks under a General Loading History 155
4.6 The Griffith Criteria for Crack Extension in Viscoelasticity ... 157
4.7 Barenblatt s Theory of Brittle Cracks 162
4.8 Crack in a Field of Bending 164
4.8.1 A Standard Linear Solid 167
4.9 Summary 170
5. Three dimensional Contact Problems 172
5.1 Generalized Boussinesq Formula 173
5.2 The Normal Contact Problem under Varying Load 174
5.2.1 The Steady State Problem 180
5.3 Impact Problems 183
5.3.1 The First Phase 187
5.3.2 The Second Phase 188
5.3.3 The Short Time Approximation 191
5.4 Hysteretic Friction 193
5.4.1 Small Viscoelasticity Approximation 193
5.4.2 Small Velocity Approximation 196
5.5 Summary 198
6. Thermoviscoelastic Boundary Value Problems 199
6.1 A Sphere in a Specified Temperature Field 200
6.2 Summary 205
7. Plane Inertial Problems 206
7.1 Displacement Traction Relationships on the Boundary 206
7.1.1 Antiplane Strain 209
7.2 Contact Problems on a Slightly Viscoelastic Medium 210
7.3 Crack Problems 212
7.4 Summary 215
Appendix I Tables of Relevant Integrals and Other Formulae 217
Table Al.l Hilbert Transforms on [ 1, 1] 217
Table A1.2 Hilbert Transforms on [a, b] 219
Table A 1.3 Miscellaneous Integrals Associated with
Hilbert Transforms 220
Table A1.4 Other Miscellaneous Integrals and
Relationships 221
Appendix II Boundary Value Problems for Analytic Functions 224
A2.1 Some Properties of Analytic Functions 225
A2.1.1 The Principle Value of a Singular Integral . 225
A2.1.2 Analytic Continuation 226
XIV Contents
A2.1.3 Liouville s Theorem 227
A2.1.4 Singularities 227
A2.1.5 Branch Points 227
A2.2 Cauchy Integrals 228
A2.3 The Hilbert Problem with Constant Coefficient .. 231
A2.4 The Hilbert Transform 235
Appendix III Fourier Transforms 241
A3.1 Definition and Basic Properties 241
A3.2 Analytic Properties of Fourier Integrals 244
Appendix IV Non singular Integral Equations 247
A4.1 Fredholm Equations 247
A4.2 Volterra Equations 249
References 251
Subject Index 261
|
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| id | DE-604.BV000879691 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:20:56Z |
| institution | BVB |
| isbn | 3540186158 0387186158 |
| language | English |
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| physical | XIV, 266 S. |
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| spelling | Golden, John M. Verfasser aut Boundary value problems in linear viscoelasticity J. M. Golden ; G. A. C. Graham Berlin u.a. Springer 1988 XIV, 266 S. txt rdacontent n rdamedia nc rdacarrier Problèmes aux limites Viscoélasticité Boundary value problems Viscoelasticity Randwertproblem (DE-588)4048395-2 gnd rswk-swf Lineare Elastizitätstheorie (DE-588)4139506-2 gnd rswk-swf Viskoelastizität (DE-588)4063621-5 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s Viskoelastizität (DE-588)4063621-5 s DE-604 Lineare Elastizitätstheorie (DE-588)4139506-2 s Graham, George A. C. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000552230&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Golden, John M. Graham, George A. C. Boundary value problems in linear viscoelasticity Problèmes aux limites Viscoélasticité Boundary value problems Viscoelasticity Randwertproblem (DE-588)4048395-2 gnd Lineare Elastizitätstheorie (DE-588)4139506-2 gnd Viskoelastizität (DE-588)4063621-5 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4139506-2 (DE-588)4063621-5 |
| title | Boundary value problems in linear viscoelasticity |
| title_auth | Boundary value problems in linear viscoelasticity |
| title_exact_search | Boundary value problems in linear viscoelasticity |
| title_full | Boundary value problems in linear viscoelasticity J. M. Golden ; G. A. C. Graham |
| title_fullStr | Boundary value problems in linear viscoelasticity J. M. Golden ; G. A. C. Graham |
| title_full_unstemmed | Boundary value problems in linear viscoelasticity J. M. Golden ; G. A. C. Graham |
| title_short | Boundary value problems in linear viscoelasticity |
| title_sort | boundary value problems in linear viscoelasticity |
| topic | Problèmes aux limites Viscoélasticité Boundary value problems Viscoelasticity Randwertproblem (DE-588)4048395-2 gnd Lineare Elastizitätstheorie (DE-588)4139506-2 gnd Viskoelastizität (DE-588)4063621-5 gnd |
| topic_facet | Problèmes aux limites Viscoélasticité Boundary value problems Viscoelasticity Randwertproblem Lineare Elastizitätstheorie Viskoelastizität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000552230&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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