Mathematical models in contact mechanics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2012
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society lecture note series
398 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 280 S. graph. Darst. 23 cm |
| ISBN: | 9781107606654 1107606659 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Titel: Mathematical models in contact mechanics
Autor: Sofonea, Mircea
Jahr: 2012
Contents Preface pag ; xi I Introduction to variational inequalities 1 1 Preliminaries on functional analysis 3 1.1 Norrued spaces 3 1.1.1 Basic definitions 3 1.1.2 Linear continuous operators 6 1.1.3 Fixed point theorems 8 1.2 Hilbert spaces 11 1.2.1 Projection operators 11 1.2.2 Orthogonality 15 1.2.3 Duality and weak convergence 17 1.3 Elements of nonlinear analysis 19 1.3.1 Monotone operators 19 1.3.2 Convex lower semicontinuous functions 24 1.3.3 Minimization problems 29 2 Elliptic variational inequalities 33 2.1 Variational inequalities of the first kind 33 2.1.1 Existence and uniqueness 34 2.1.2 Penalization 35
Contents viii 2.2 Variational inequalities of the second kind 40 2.2.1 Existence and uniqueness 40 2.2.2 A convergence result 42 2.2.3 Regularization 43 2.3 Quasi variational inequalities 49 2.3.1 The Banach fixed point argument 49 2.3.2 The Schauder fixed point argument 51 2.3.3 A convergence result 54 3 History-dependent variational inequalities 57 3.1 Nonlinear equations with history-dependent operators 57 3.1.1 Spaces of vector-valued functions 58 3.1.2 Two examples 61 3.1.3 The general case 65 3.2 History-dependent quasivariational inequalities 67 3.2.1 A basic existence and uniqueness result 67 3.2.2 A convergence result — 73 3.3 Evolutionary variational inequalities 75 3.3.1 Existence and uniqueness 75 3.3.2 Convergence results 78 II Modelling and analysis of contact problems 81 4 Modelling of contact problems 83 4.1 Function spaces in contact mechanics 84 4.1.1 Preliminaries 84 4.1.2 Spaces for the displacement field 85 4.1.3 Spaces for the stress field 88 4.1.4 Spaces for piezoelectric contact problems 89 4.2 Physical setting and constitutive laws 91 4.2.1 Physical setting 91 4.2.2 Elastic constitutive laws 92 4.2.3 Viscoelastic constitutive laws 95 4.2.4 Viscoplastic constitutive laws 98 4.2.5 The von Mises convex 100 4.3 Modelling of elastic contact problems 103 4.3.1 Preliminaries 104 4.3.2 Contact conditions 104 4.3.3 Friction laws 107 4.4 Modelling of elastic-viscoplastic contact problems 111 4.4.1 Preliminaries 111 4.4.2 Contact conditions and friction laws 112
Contents ix 4.5 Modelling of piezoelectric contact problems 114 4.5.1 Physical setting and preliminaries 114 4.5.2 Constitutive laws 117 4.5.3 Contact conditions 119 5 Analysis of elastic contact problems 123 5.1 The Signorini contact problem 123 5.1.1 Problem statement 123 5.1.2 Existence and uniqueness 126 5.1.3 Penalization 128 5.1.4 Dual variational formulation 131 5.1.5 Minimization 137 5.1.6 One-dimensional example 139 5.2 Frictional contact problems 143 5.2.1 Statement of the problems 144 5.2.2 Existence and uniqueness 147 5.2.3 A convergence result 148 5.2.4 Regularization 149 5.2.5 Dual variational formulation 155 5.2.6 Minimization 160 5.3 A frictional contact problem with normal compliance 162 5.3.1 Problem statement 162 5.3.2 The Banach fixed point argument 164 5.3.3 The Schauder fixed point argument 166 5.3.4 Convergence results 167 6 Analysis of elastic-visco plastic contact problems 173 6.1 Bilateral frictionless contact problems 173 6.1.1 Contact of materials with short memory 174 6.1.2 Contact of materials with long memory 176 6.2 Viscoelastic contact problems with long memory 178 6.2.1 Frictionless contact with unilateral constraint 178 6.2.2 Frictional contact with normal compliance 181 6.2.3 A convergence result 183 6.3 Viscoelastic contact problems with short memory 185 6.3.1 Contact with normal compliance 186 6.3.2 Contact with normal damped response 189 6.3.3 Other frictional contact problems 192 6.3.4 Convergence results 196 6.4 Viscoplastic frictionless contact problems 200 6.4.1 Contact with normal compliance 200 6.4.2 Contact with unilateral constraint 205 6.4.3 A convergence result 208
x Contents 7 Analysis of piezoelectric contact problems 217 7.1 An electro-elastic frictional contact problem 217 7.1.1 Problem statement 218 7.1.2 Existence and uniqueness 220 7.1.3 Dual variational formulation 223 7.2 An electro-viscoelastic frictional contact problem 227 7.2.1 Problem statement 227 7.2.2 Existence and uniqueness 231 7.3 An electro-viscoplastic frictionless contact problem 237 7.3.1 Problem statement 237 7.3.2 Existence and uniqueness 241 Bibliographical notes 251 List of symbols 257 References 262 Index 275
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| any_adam_object | 1 |
| author | Sofonea, Mircea 1957- Matei, Andaluzia |
| author_GND | (DE-588)1028214723 (DE-588)1026794765 |
| author_facet | Sofonea, Mircea 1957- Matei, Andaluzia |
| author_role | aut aut |
| author_sort | Sofonea, Mircea 1957- |
| author_variant | m s ms a m am |
| building | Verbundindex |
| bvnumber | BV040482606 |
| classification_rvk | SI 320 |
| classification_tum | MTA 010f PHY 200f MAT 490f |
| ctrlnum | (OCoLC)810268575 (DE-599)BSZ371448352 |
| dewey-full | 620.105 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.105 |
| dewey-search | 620.105 |
| dewey-sort | 3620.105 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040482606 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:24:41Z |
| institution | BVB |
| isbn | 9781107606654 1107606659 |
| language | English |
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| oclc_num | 810268575 |
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| owner_facet | DE-91G DE-BY-TUM DE-706 |
| physical | XIV, 280 S. graph. Darst. 23 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Sofonea, Mircea 1957- Verfasser (DE-588)1028214723 aut Mathematical models in contact mechanics M. Sofonea ; A. Matei 1. publ. Cambridge Cambridge Univ. Press 2012 XIV, 280 S. graph. Darst. 23 cm txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 398 Mathematisches Modell Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Kontaktmechanik (DE-588)4798356-5 gnd rswk-swf Contact mechanics / Mathematical models Kontaktmechanik (DE-588)4798356-5 s Variationsrechnung (DE-588)4062355-5 s DE-604 Matei, Andaluzia Verfasser (DE-588)1026794765 aut London Mathematical Society lecture note series 398 (DE-604)BV000000130 398 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025329792&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sofonea, Mircea 1957- Matei, Andaluzia Mathematical models in contact mechanics London Mathematical Society lecture note series Mathematisches Modell Variationsrechnung (DE-588)4062355-5 gnd Kontaktmechanik (DE-588)4798356-5 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4798356-5 |
| title | Mathematical models in contact mechanics |
| title_auth | Mathematical models in contact mechanics |
| title_exact_search | Mathematical models in contact mechanics |
| title_full | Mathematical models in contact mechanics M. Sofonea ; A. Matei |
| title_fullStr | Mathematical models in contact mechanics M. Sofonea ; A. Matei |
| title_full_unstemmed | Mathematical models in contact mechanics M. Sofonea ; A. Matei |
| title_short | Mathematical models in contact mechanics |
| title_sort | mathematical models in contact mechanics |
| topic | Mathematisches Modell Variationsrechnung (DE-588)4062355-5 gnd Kontaktmechanik (DE-588)4798356-5 gnd |
| topic_facet | Mathematisches Modell Variationsrechnung Kontaktmechanik |
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