Unilateral contact problems: variational methods and existence theorems
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC Press
2005
|
| Series: | Pure and applied mathematics
270 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 398 S. |
| ISBN: | 1574446290 |
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Record in the Search Index
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| adam_text | UNILATERAL CONTACT PROBLEMS VARIATIONAL METHODS AND EXISTENCE THEOREMS
CHRISTOFECK UNIVERSITDT ERLANGEN ERLANGEN, GERMANY JIH JARUSEK ACADEMY
OF SCIENCES OF THE CZECH REPUBLIC PRAGUE, CZECH REPUBLIC MIROSLAV KRBEC
ACADEMY OF SCIENCES OF THE CZECH REPUBLIC PRAGUE, CZECH REPUBLIC CHAPMAN
& HALL/CRC TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK SINGAPORE
CONTENTS 1 INTRODUCTION 1 1.1 NOTATIONS 6 1.2 LINEAR ELASTICITY 9 1.2.1
DEFORMATION OF BODIES, THE STRAIN TENSOR 9 1.2.2 THE STRESS TENSOR 11
1.2.3 THE EQUATIONS OF LINEAR ELASTICITY 13 1.2.4 THE KORN INEQUALITY 14
1.2.5 SPECIAL CASES 19 1.3 FORMULATION OF CONTACT PROBLEMS 19 1.3.1
CONTACT AND FRICTION MODELS 19 1.3.2 THE DYNAMIC CONTACT PROBLEM 21 1.4
VARIATIONAL PRINCIPLES IN MECHANICS 22 1.5 THE STATIC CONTACT PROBLEM 26
1.6 GEOMETRY OF DOMAINS 35 1.7 THE METHOD OF TANGENTIAL TRANSLATIONS 38
1.7.1 PRELIMINARIES 38 1.7.2 SHIFT TECHNIQUE FOR A HALFSPACE 40 1.7.3
SHIFT TECHNIQUE WITH LOCAL RECTIFICATION 45 2 BACKGROUND 61 2.1 FIXED
POINT THEOREMS 61 2.1.1 COVERING THEOREMS 62 2.1.2 FIXED POINT
PRINCIPLES 65 2.2 SOME GENERAL REMARKS .A 76 2.3 CRASH COURSE IN
INTERPOLATION 85 2.3.1 CLASSICAL THEOREMS 86 2.3.2 THE COMPLEX
INTERPOLATION METHOD 87 2.3.3 FOURIER MULTIPLIERS 89 2.3.4 THE REAL
INTERPOLATION METHOD 93 2.4 BESOV AND LIZORKIN-TRIEBEL SPACES 99 2.4.1
THE CLASSICAL DEFINITION 99 2.4.2 THE FOURIER ANALYSIS APPROACH 106
2.4.3 IMBEDDINGS AND INTERPOLATION 108 2.4.4 EQUIVALENCE OF DEFINITIONS
112 2.5 THE POTENTIAL SPACES 119 2.5.1 INTERPOLATION IN POTENTIAL SPACES
127 2.6 VECTOR-VALUED SOBOLEV AND BESOV SPACES 130 2.6.1 SOME SPECIAL
TYPES OF ANISOTROPIC SPACES . 136 2.7 EXTENSIONS AND TRACES 138 2.7.1
GEOMETRICAL PROPERTIES OF BOUNDARIES OF DOMAINS . . 138 2.7.2 ESTIMATES
OF GAGLIARDO-NIRENBERG TYPE 141 2.7.3 EXTENSION OPERATORS 144 2.8 SPACES
ON DOMAINS 146 2.8.1 TRACES 146 2.8.2 THE PROBLEM OF NORMS AND
INTERPOLATION ON DOMAINS 149 2.8.3 COMPACT IMBEDDINGS 156 3 STATIC AND
QUASISTATIC CONTACT PROBLEMS 159 3.1 COERCIVE STATIC CASE 159 3.1.1
APPROXIMATE PROBLEMS AND LIMIT PROCEDURES 160 3.1.2 CALCULATION OF THE
ADMISSIBLE COEFFICIENT OF FRICTION . 178 3.2 SEMICOERCIVE CONTACT
PROBLEM 185 3.3 CONTACT PROBLEMS FOR TWO BODIES 194 3.3.1 COERCIVE CASE
196 3.3.2 SEMICOERCIVE PROBLEMS 202 3.4 QUASISTATIC CONTACT PROBLEM 203
4 DYNAMIC CONTACT PROBLEMS 219 4.1 A SHORT SURVEY ABOUT RESULTS FOR
ELASTIC MATERIALS 220 4.1.1 A DOMAIN CONSTRAINT FOR STRINGS 221 4.1.2
OBSTACLE AT A FINITE NUMBER OF POINTS 223 4.1.3 BOUNDARY CONTACT OF A
HALFSPACE 225 4.1.4 A RESULT BASED ON COMPENSATED COMPACTNESS . . . .
227 4.1.5 A RESULT APPLICABLE TO POLYHARMONIC PROBLEMS . . . . 228
4.1.5.1 EXISTENCE OF SOLUTIONS 229 4.1.5.2 APPLICATIONS 233 4.2 RESULTS
FOR MATERIALS WITH SINGULAR MEMORY 234 4.2.1 DOMAIN CONTACT 235 4.2.2
BOUNDARY CONTACT 244 4.3 VISCOELASTIC MEMBRANES 250 4.4 PROBLEMS WITH
GIVEN FRICTION 255 4.4.1 CONTACT CONDITION IN DISPLACEMENTS 256 4.4.1.1
EXISTENCE OF SOLUTIONS 257 4.4.1.2 CONSERVATION OF ENERGY IN
VISCOELASTIC CON- TACT PROBLEMS 264 4.4.2 CONTACT CONDITION IN
VELOCITIES 264 5 DYNAMIC CONTACT PROBLEMS WITH COULOMB FRICTION 269 5.1
SOLVABILITY OF FRICTIONAL CONTACT PROBLEMS 270 5.2 ANISOTROPIC MATERIAL
299 5.3 ISOTROPIC MATERIAL 306 5.3.1 THE CASE OF TWO SPACE DIMENSIONS
307 5.3.2 THE CASE OF THREE SPACE DIMENSIONS 317 5.3.3 THE CASE OF A
GENERAL DIMENSION 322 5.3.4 THE NON-HOMOGENEOUS CASE 326 5.4
THERMO-VISCOELASTIC PROBLEMS 326 5.4.1 FIXED-POINT APPROACH 332 5.4.1.1
APPROXIMATE PROBLEM 333 5.4.1.2 EXISTENCE OF THE SOLUTION OF THE
THERMO-VISCO- ELASTIC CONTACT PROBLEM 341 5.4.2 ENERGETIC APPROACH 346
5.4.2.1 A MODEL WITH HEAT CONDUCTIVITY DEPENDING ON THE TEMPERATURE 349
5.4.2.2 A PROBLEM WITH HEAT CONDUCTIVITY DEPEN- DENT ON THE TEMPERATURE
GRADIENT 368 BIBLIOGRAPHY 385 LIST OF NOTATIONS 393 SUBJECT INDEX 397
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| spelling | Eck, Christof 1968-2011 Verfasser (DE-588)135641497 aut Unilateral contact problems variational methods and existence theorems by Christof Eck ; Jiří Janušek ; Miroslav Krbec Boca Raton [u.a.] Chapman & Hall/CRC Press 2005 398 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 270 Mathematisches Modell Differential equations, Partial Contact mechanics Mathematical models Friction Mathematical models Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Reibung (DE-588)4049098-1 gnd rswk-swf Kontaktmechanik (DE-588)4798356-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Kontaktmechanik (DE-588)4798356-5 s Reibung (DE-588)4049098-1 s Mathematisches Modell (DE-588)4114528-8 s Jarušek, Jiři Verfasser aut Krbec, Miroslav 1950-2012 Verfasser (DE-588)1145946542 aut Pure and applied mathematics 270 (DE-604)BV000001885 270 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013327249&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eck, Christof 1968-2011 Jarušek, Jiři Krbec, Miroslav 1950-2012 Unilateral contact problems variational methods and existence theorems Pure and applied mathematics Mathematisches Modell Differential equations, Partial Contact mechanics Mathematical models Friction Mathematical models Partielle Differentialgleichung (DE-588)4044779-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd Reibung (DE-588)4049098-1 gnd Kontaktmechanik (DE-588)4798356-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4114528-8 (DE-588)4049098-1 (DE-588)4798356-5 |
| title | Unilateral contact problems variational methods and existence theorems |
| title_auth | Unilateral contact problems variational methods and existence theorems |
| title_exact_search | Unilateral contact problems variational methods and existence theorems |
| title_full | Unilateral contact problems variational methods and existence theorems by Christof Eck ; Jiří Janušek ; Miroslav Krbec |
| title_fullStr | Unilateral contact problems variational methods and existence theorems by Christof Eck ; Jiří Janušek ; Miroslav Krbec |
| title_full_unstemmed | Unilateral contact problems variational methods and existence theorems by Christof Eck ; Jiří Janušek ; Miroslav Krbec |
| title_short | Unilateral contact problems |
| title_sort | unilateral contact problems variational methods and existence theorems |
| title_sub | variational methods and existence theorems |
| topic | Mathematisches Modell Differential equations, Partial Contact mechanics Mathematical models Friction Mathematical models Partielle Differentialgleichung (DE-588)4044779-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd Reibung (DE-588)4049098-1 gnd Kontaktmechanik (DE-588)4798356-5 gnd |
| topic_facet | Mathematisches Modell Differential equations, Partial Contact mechanics Mathematical models Friction Mathematical models Partielle Differentialgleichung Reibung Kontaktmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013327249&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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