Inequality problems in mechanics and applications: convex and nonconvex energy functions
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston u.a.
Birkhäuser
1985
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 412 S. graph. Darst. |
| ISBN: | 3764330945 0817630945 |
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MARC
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| 100 | 1 | |a Panagiōtopulos, Panagiōtēs D. |d 1950-1998 |e Verfasser |0 (DE-588)128484446 |4 aut | |
| 245 | 1 | 0 | |a Inequality problems in mechanics and applications |b convex and nonconvex energy functions |c P. D. Panagiotopoulos |
| 264 | 1 | |a Boston u.a. |b Birkhäuser |c 1985 | |
| 300 | |a XVII, 412 S. |b graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
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|---|---|
| adam_text |
P. D. PANAGIOTOPOULOS INEQUALITY PROBLEMS IN MECHANICS AND APPLICATIONS
CONVEX AND NONCONVEX ENERGY FUNCTIONS 1985 BIRKHAUSER BOSTON * BASEL *
STUTTGART CONTENTS PREFACE XIII INTRODUCTION XV GUIDELINES FOR THE
READER XIX PART 1. INTRODUCTORY TOPICS 1 CHAPTER 1. ESSENTIAL NOTIONS
AND PROPOSITIONS OF FUNCTIONAL ANALYSIS 3 1.1 TOPOLOGICAL VECTOR SPACES
AND RELATED SUBJECTS 3 1.1.1 TOPOLOGICAL SPACES AND CONTINUOUS MAPPINGS
3 1.1.2 LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES, NORMED SPACES AND
LINEAR MAPPINGS 6 1.2 DUALITY IN TOPOLOGICAL VECTOR SPACES 8 1.2.1
DUALITY. WEAK AND STRONG TOPOLOGIES 8 1.2.2 TOPOLOGICALLY DUAL PAIRS OF
VECTOR SPACES 11 1.2.3 DUALITY IN NORMED AND HILBERT SPACES 12 1.2.4
TRANSPOSE OF A CONTINUOUS LINEAR MAPPING SCALES OF HILBERT SPACES. THE
LAX-MILGRAM THEOREM 14 1.3 CERTAIN FUNCTION SPACES AND THEIR PROPERTIES
15 1.3.1 THE SPACES C M (Q), C M (Q), D(Q), D(Q) AND IF(Q) 15 1.3.2
SPACES OF DISTRIBUTIONS 18 1.3.3 SOBOLEV SPACES 20 1.3.4 TRACE THEOREM.
IMBEDDING PROPERTIES OF SOBOLEV SPACES. 23 1.3.5 THE SPACE OF FUNCTIONS
OF BOUNDED DEFORMATION 25 1.4 ADDITIONAL TOPICS 26 1.4.1 ELEMENTS OF THE
THEORY OF VECTOR-VALUED FUNCTIONS AND DISTRIBUTIONS 26 1.4.2 ELEMENTS OF
DIFFERENTIAL CALCULUS 28 1.4.3 SUPPLEMENTARY NOTIONS AND PROPOSITIONS 29
VIII CONTENTS CHAPTER 2. ELEMENTS OF CONVEX ANALYSIS 35 2.1 CONVEX SETS
AND FUNCTIONAL 35 2.1.1 DEFINITIONS 35 2.1.2 LOWER SEMICONTINUOUS CONVEX
FUNCTIONALS 37 2.2 - MINIMIZATION OF CONVEX FUNCTIONALS 39 2.2.1
EXISTENCE OF A MINIMUM 39 2.2.2 VARIATIONAL INEQUALITIES 40 2.3
SUBDIFFERENTIABILITY 41 2.3.1 DEFINITIONS AND RELATED PROPOSITIONS 41
2.3.2 ONE-SIDED DIRECTIONAL GATEAUX-DIFFERENTIAL 43 2.4 SUBDIFFERENTIAL
CALCULUS 48 2.4.1 THE SUBDIFFERENTIAL OF A SUM OF FUNCTIONALS AND OF A
COMPOSITE FUNCTIONAL 48 2.4.2 THE RELATIVE INTERIOR OF R{DF) 50 2.5
CONJUGATES OF CONVEX FUNCTIONALS 51 2.5.1 THE CLASSES T(X) AND T 0 (X)
51 2.5.2 THE CONJUGACY OPERATION 54 2.6 * MAXIMAL MONOTONE OPERATORS 55
2.6.1 DEFINITIONS AND FUNDAMENTAL RESULTS 55 2.6.2 MAXIMAL MONOTONE
GRAPHS IN IR 2 57 PART 2. INEQUALITY PROBLEMS 61 CHAPTER 3. VARIATIONAL
INEQUALITIES AND SUPERPOTENTIALS 6 3 3.1 MECHANICAL LAWS AND CONSTRAINTS
63 3.1.1 GENERALIZED FORCES AND THE PRINCIPLE OF VIRTUAL POWER. 63
3.1.2 MULTIVALUED LAWS AND CONSTRAINTS IN MECHANICS 67 3.1.3
MINIMIZATION PROBLEMS AND VARIATIONAL INEQUALITIES CHARACTERIZING THE
EQUILIBRIUM CONFIGURATIONS 70 3.1.4 DISSIPATIVE LAWS. A NOTE ON THE
EIGENVALUE PROBLEM FOR SUPERPOTENTIAL LAWS 72 3.2 SUPERPOTENTIALS AND
DUALITY 73 3.2.1 THE HYPOTHESIS OF NORMAL DISSIPATION 73 3.2.2 DUALITY
OF VARIATIONAL PRINCIPLES 75 3.3 SUBDIFFERENTIAL BOUNDARY CONDITIONS AND
CONSTITUTIVE LAWS 81 3.3.1 SUBDIFFERENTIAL BOUNDARY CONDITIONS 81 3.3.2
SUBDIFFERENTIAL CONSTITUTIVE LAWS I 92 3.3.3 SUBDIFFERENTIAL
CONSTITUTIVE LAWS II 99 3.3.4 EXTENSION OF SUBDIFFERENTIAL RELATIONS TO
FUNCTION SPACES 104 CONTENTS ** IX CHAPTER 4. VARIATIONAL INEQUALITIES
AND MULTIVALUED CONVEX AND NONCONVEX PROBLEMS IN MECHANICS 115 4.1 TWO
GENERAL VARIATIONAL INEQUALITIES AND THE DERIVATION OF VARIATIONAL
INEQUALITY "PRINCIPLES" IN MECHANICS 115 4.1.1 . VARIATIONAL
INEQUALITIES OF THE FICHERA TYPE ".:. 115 4.1.2 VARIATIONAL
INEQUALITIES OF OTHER TYPES 122 4.L3 THE DERIVATION OF VARIATIONAL
INEQUALITY "PRINCIPLES" IN MECHANICS 124 4.2 COEXISTENT PHASES. THE
MORPHOLOGY OF MATERIAL PHASES. 126 4.2.1 NEOCLASSICAL PROCESSES AND
GIBBSIAN STATES. RULES FOR COEXISTENT PHASES , 126 4.2.2 MINIMUM
PROBLEMS FOR GIBBSIAN STATES 132 4.2.3 COMPARISON OF GIBBSIAN STATES.
SOME RESULTS OF THE DYNAMIC PROBLEM 135 4.3 NONCONVEX SUPERPOTENTIALS
140 4.3.1 INTRODUCTION AND BRIEF SURVEY OF THE BASIC MATHEMATICAL
PROPERTIES 140 4.3.2- NONCONVEX SUPERPOTENTIALS. HEMIVARIATIONAL
INEQUALITIES AND SUBSTATIONARITY PRINCIPLES 146 4.3.3 GENERALIZATIONS OF
THE HYPOTHESIS OF NORMAL DISSIPATION 156 4.4 THE INTEGRAL INCLUSION
APPROACH TO INEQUALITY PROBLEMS 160 CHAPTER 5. FRICTION PROBLEMS IN THE
THEORY OF ELASTICITY 163 5.1 THE STATIC B.V.P 163 5.1.1 THE CLASSICAL
FORMULATION 163 5.1.2 THE VARIATIONAL FORMULATION * 165 5.2 EXISTENCE
AND UNIQUENESS PROPOSITIONS 167 5.2.1 , EQUIVALENT MINIMUM PROBLEM. THE
CASE MES F V 0 167 5.2.2 STUDY OF THE CASE T V = 0. 169 5.2.3 FURTHER
PROPERTIES OF THE SOLUTION 171 5.3 DUAL FORMULATION. COMPLEMENTARY
ENERGY 172 5.3.1 MINIMIZATION OF THE COMPLEMENTARY ENERGY 172 5.3.2
DUALITY .' 174 5.4 THE DYNAMIC B.V.P 177 5.4.1 CLASSICAL AND VARIATIONAL
FORMULATIONS OF THE PROBLEM . 177 5.4.2 EXISTENCE OF SOLUTION 179 5.4.3
THE REGULARIZED PROBLEM 185 5.4.4 THE UNIQUENESS OF THE SOLUTION 188 5.5
A NOTE ON OTHER TYPES OF FRICTION PROBLEMS 188 CONTENTS CHAPTER 6.
SUBDIFFERENTIAL CONSTITUTIVE LAWS AND BOUNDARY CONDITIONS 191 6.1
SUBDIFFERENTIAL MATERIAL LAWS AND CLASSICAL BOUNDARY CONDITIONS 191
6.1.1 FORMULATION OF THE PROBLEM 191 6.1.2 THE EXISTENCE AND UNIQUENESS
OF THE SOLUTION 194 6.1.3. DUALITY ! 196 6.2 LINEAR ELASTIC MATERIAL LAW
AND SUBDIFFERENTIAL BOUNDARY CONDITIONS 198 6.2.1 FORMULATION OF THE
BOUNDARY CONDITIONS 198 6.2.2 EXISTENCE AND UNIQUENESS PROPOSITIONS 201
6.2.3 DUALITY 204 6.3 SUBDIFFERENTIAL MATERIAL LAWS AND SUBDIFFERENTIAL
BOUNDARY CONDITIONS. MINIMUM PROPOSITIONS FOR NONMONOTONE LAWS 206 6.3.1
FORMULATION AND STUDY OF THE PROBLEM 206 6.3.2 NONMONOTONE LAWS 209 6.4
THE CORRESPONDING DYNAMIC AND INCREMENTAL PROBLEMS. 211 CHAPTER 7.
INEQUALITY PROBLEMS IN THE THEORY OF THIN ELASTIC PLATES . 215 7.1
STATIC UNILATERAL PROBLEMS OF VON KARMAN PLATES 215 7.1.1 GENERALITIES
215 7.1.2 BOUNDARY CONDITIONS AND CORRESPONDING VARIATIONAL FORMULATIONS
217 7.1.3 THE EXISTENCE OF THE SOLUTION 220 7.1.4 IN-PLANE UNILATERAL
BOUNDARY CONDITIONS 225 7.2 THE UNILATERAL BUCKLING PROBLEM. EIGENVALUE
PROBLEMS FOR VARIATIONAL INEQUALITIES 226 7.2.1 FORMULATION OF THE
PROBLEM 226 7.2.2 A GENERAL PROPOSITION ON THE EXISTENCE OF THE SOLUTION
. 229 7.2.3 APPLICATION TO THE BUCKLING PROBLEM 233 7.2.4 EXTENSION OF
THE RAYLEIGH-QUOTIENT RULE TO UNILATERAL PROBLEMS 235 7.3 DYNAMIC
UNILATERAL PROBLEMS OF VON KARMAN PLATES . 237 7.3.1 BOUNDARY
CONDITIONS AND VARIATIONAL INEQUALITIES 237 7.3.2 EXISTENCE PROPOSITION
240 7.3.3 UNIQUENESS PROPOSITION 247 CONTENTS . XI CHAPTER 8.
VARIATIONAL AND HEMIVARIATIONAL INEQUALITIES IN LINEAR THERMOELASTICITY
251 8.1 B.V.P.S AND THEIR VARIATIONAL FORMULATIONS 251 8.1.1 * CLASSICAL
FORMULATIONS 251 8.1.2 VARIATIONAL FORMULATIONS 254 8.2 EXISTENCE AND
UNIQUENESS PROPOSITIONS 256 8.2.1 STUDY OF PROBLEM 1 256 8.2.2 STUDY OF
PROBLEM 2. SOME REMARKS ON RELATED PROBLEMS 264 8.3 GENERALIZATIONS AND
RELATED VARIATIONALTNEQUALITIES 267 8.4 HEMIVARIATIONAL INEQUALITIES IN
LINEAR THERMOELASTICITY. 269 8.4.1 FORMULATION OF CERTAIN GENERAL
PROBLEMS 269 8.4.2 AN EXISTENCE RESULT FOR A HEMIVARIATIONAL INEQUALITY.
* A MODEL PROBLEM 272 CHAPTER 9. VARIATIONAL INEQUALITIES IN THE THEORY
OF PLASTICITY AND VISCOPLASTICITY 277 9.1 ELASTIC VISCOPLASTIC MATERIALS
277 9.1.1 FORMULATION OF THE DYNAMIC PROBLEM, EXISTENCE AND UNIQUENESS
OF THE SOLUTION 277 9.1.2 THE QUASI-STATIC PROBLEM 287 9.2 ELASTIC
PERFECTLY PLASTIC MATERIALS 291 9.2.1 FORMULATION OF THE QUASI-STATIC
PROBLEM 291 9.2.2 EXISTENCE AND UNIQUENESS PROPOSITIONS 293 9.3 RIGID
VISCOPLASTIC FLOW PROBLEMS 299 9.3.1 CLASSICAL FORMULATION OF THE
GENERAL DYNAMIC PROBLEM . 299 9.3.2 THE FUNCTIONAL FRAMEWORK AND
EXISTENCE PROPOSITIONS. 300 9.3.3 THE RELATION BETWEEN VELOCITY AND
STRESS FIELDS 311 9.4 OTHER PROBLEMS ON BINGHAM FLUIDS 314 9.4.1 LAMINAR
FLOW IN A CYLINDRICAL PIPE 314 9.4.2 HEAT TRANSFER IN RIGID VISCOPLASTIC
FLOWS 317 9.4.3 VARIATIONAL INEQUALITIES IN THE CASE OF THE GENERAL LAW
A E DW(D) 319 PART 3. NUMERICAL APPLICATIONS 321 CHAPTER 10. THE
NUMERICAL TREATMENT OF STATIC INEQUALITY PROBLEMS . 323 10.1 UNILATERAL
CONTACT AND FRICTION PROBLEMS 324 10.1.1 DISCRETE FORMS OF THE PROBLEMS
OF MINIMUM POTENTIAL AND COMPLEMENTARY ENERGY 324 10.1.2 APPLICATIONS
329 10.2 TORSION OF CYLINDRICAL OR PRISMATIC BARS WITH CONVEX
STRAIN-ENERGY DENSITY 331 XLL CONTENTS 10.2.1 FORMULATION OF THE PROBLEM
331 10.2.2 DISCRETIZATION AND NUMERICAL APPLICATION 334 10.3 A LINEAR
ANALYSIS APPROACH TO CERTAIN CLASSES OF INEQUALITY PROBLEMS 341 10.3.1
DESCRIPTION OF THE METHOD 341 10.3.2 APPLICATIONS 343 CHAPTER 11.
INCREMENTAL AND DYNAMIC INEQUALITY PROBLEMS 349 11.1 THE ELASTOPLASTIC
CALCULATION OF CABLE STRUCTURES 349 11.1.1 FORMULATION OF THE PROBLEM AS
A LINEAR COMPLEMENTARITY PROBLEM AND RELATED EXPRESSIONS 349 11.1.2
MULTILEVEL DECOMPOSITION TECHNIQUES 355 11.1.3 APPLICATION 357 11.2
INCREMENTAL ELASTOPLASTIC ANALYSIS.L.C.P.S, VARIATIONAL INEQUALITIES AND
MINIMUM PROPOSITIONS 360 11.3 DYNAMIC UNILATERAL CONTACT PROBLEMS 366
EPILOGUE 373 APPENDICES 375 APPENDIX I. SOME BASIC NOTIONS [20] [112]
[321] [322] 375 APPENDIX II. RIGIDIFYING VELOCITY FIELDS. OBJECTIVITY
[112] [197] [322] 377 APPENDIX III. DISSIPATION [112] 378 APPENDIX IV.
PLASTICITY AND THERMODYNAMICS [75] [196] 378 LIST OF NOTATIONS 381
REFERENCES 387 SUBJECT INDEX 407 |
| any_adam_object | 1 |
| author | Panagiōtopulos, Panagiōtēs D. 1950-1998 |
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| classification_rvk | SK 950 |
| classification_tum | MAT 342f PHY 013f MAT 499f |
| ctrlnum | (OCoLC)8493436 (DE-599)BVBBV002042562 |
| dewey-full | 531/.01/51526 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531/.01/51526 |
| dewey-search | 531/.01/51526 |
| dewey-sort | 3531 11 551526 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| oclc_num | 8493436 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-703 DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-706 DE-634 DE-188 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-706 DE-634 DE-188 DE-83 |
| physical | XVII, 412 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Panagiōtopulos, Panagiōtēs D. 1950-1998 Verfasser (DE-588)128484446 aut Inequality problems in mechanics and applications convex and nonconvex energy functions P. D. Panagiotopoulos Boston u.a. Birkhäuser 1985 XVII, 412 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Calcul des variations ram Inégalités (mathématiques) ram Mécanique analytique ram analyse convexe inriac analyse fonctionnelle inriac calcul variation inriac condition aux limites inriac frottement inriac inéquation variationnelle inriac mécanique inriac méthode numérique inriac plaque mince inriac plasticité inriac thermoélasticité inriac viscoplasticité inriac élasticité inriac Calculus of variations Inequalities (Mathematics) Mechanics, Analytic Variationsungleichung (DE-588)4187420-1 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 s Mechanik (DE-588)4038168-7 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001335767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Panagiōtopulos, Panagiōtēs D. 1950-1998 Inequality problems in mechanics and applications convex and nonconvex energy functions Calcul des variations ram Inégalités (mathématiques) ram Mécanique analytique ram analyse convexe inriac analyse fonctionnelle inriac calcul variation inriac condition aux limites inriac frottement inriac inéquation variationnelle inriac mécanique inriac méthode numérique inriac plaque mince inriac plasticité inriac thermoélasticité inriac viscoplasticité inriac élasticité inriac Calculus of variations Inequalities (Mathematics) Mechanics, Analytic Variationsungleichung (DE-588)4187420-1 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4187420-1 (DE-588)4038168-7 |
| title | Inequality problems in mechanics and applications convex and nonconvex energy functions |
| title_auth | Inequality problems in mechanics and applications convex and nonconvex energy functions |
| title_exact_search | Inequality problems in mechanics and applications convex and nonconvex energy functions |
| title_full | Inequality problems in mechanics and applications convex and nonconvex energy functions P. D. Panagiotopoulos |
| title_fullStr | Inequality problems in mechanics and applications convex and nonconvex energy functions P. D. Panagiotopoulos |
| title_full_unstemmed | Inequality problems in mechanics and applications convex and nonconvex energy functions P. D. Panagiotopoulos |
| title_short | Inequality problems in mechanics and applications |
| title_sort | inequality problems in mechanics and applications convex and nonconvex energy functions |
| title_sub | convex and nonconvex energy functions |
| topic | Calcul des variations ram Inégalités (mathématiques) ram Mécanique analytique ram analyse convexe inriac analyse fonctionnelle inriac calcul variation inriac condition aux limites inriac frottement inriac inéquation variationnelle inriac mécanique inriac méthode numérique inriac plaque mince inriac plasticité inriac thermoélasticité inriac viscoplasticité inriac élasticité inriac Calculus of variations Inequalities (Mathematics) Mechanics, Analytic Variationsungleichung (DE-588)4187420-1 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Calcul des variations Inégalités (mathématiques) Mécanique analytique analyse convexe analyse fonctionnelle calcul variation condition aux limites frottement inéquation variationnelle mécanique méthode numérique plaque mince plasticité thermoélasticité viscoplasticité élasticité Calculus of variations Inequalities (Mathematics) Mechanics, Analytic Variationsungleichung Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001335767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT panagiotopulospanagiotesd inequalityproblemsinmechanicsandapplicationsconvexandnonconvexenergyfunctions |