Continuum mechanics: with 279 figures and 4 tables
Gespeichert in:
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| Format: | Buch |
| Sprache: | English Norwegian |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2008]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xviii, 661 Seiten Illustrationen, Diagramme |
| ISBN: | 9783540742975 |
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| 245 | 1 | 0 | |a Continuum mechanics |b with 279 figures and 4 tables |c Fridtjov Irgens |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c [2008] | |
| 300 | |a xviii, 661 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Continuum mechanics |v Textbooks | |
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Datensatz im Suchindex
| _version_ | 1804137254278397952 |
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| adam_text | IMAGE 1
FRIDTJOV IRGENS
CONTINUUM MECHANICS
WITH 279 FIGURES AND 4 TABLES
4Y SPRI RINGER
IMAGE 2
CONTENTS
1 INTRODUCTION 1
1.1 THE CONTINUUM HYPOTHESIS 1
1.2 ELASTICITY, PLASTICITY, AND FRACTURE 2
1.3 FLUIDS 8
1.4 VISCOELASTICITY 12
1.5 AN OUTLINE FOR THE PRESENT BOOK 16
2 MATHEMATICAL FOUNDATION 19
2.1 MATRICES AND DETERMINANTS 19
2.2 COORDINATE SYSTEMS AND VECTORS 23
2.3 COORDINATE TRANSFORMATIONS 28
2.4 SCALAR FIELDS AND VECTOR FIELDS 30
PROBLEMS 34
3 DYNAMICS 37
3.1 KINEMATICS 37
3.1.1 LAGRANGIAN COORDINATES AND EULERIAN COORDINATES 37
3.1.2 MATERIAL DERIVATIVE OF AN INTENSIVE QUANTITY 40
3.1.3 MATERIAL DERIVATIVE OF AN EXTENSIVE QUANTITY 41
3.2 EQUATIONS OF MOTION 42
3.2.1 EULER S AXIOMS 42
3.2.2 NEWTON S 3. LAW 46
3.2.3 COORDINATE STRESSES 47
3.2.4 CAUCHY S STRESS THEOREM AND CAUCHY S STRESS TENSOR . .. 50 3.2.5
CAUCHY EQUATIONS OF MOTION 54
3.2.6 ALTERNATIVE DERIVATION OF THE CAUCHY EQUATIONS 58
3.3 STRESS ANALYSIS 60
3.3.1 PRINCIPAL STRESSES 60
3.3.2 STRESS DEVIATOR AND STRESS ISOTROP 65
3.3.3 EXTREMAL VALUES FOR NORMAL STRESS 68
3.3.4 MAXIMUM SHEAR STRESS 69
XI
IMAGE 3
XII CONTENTS
3.3.5 PLANE STRESS 70
3.3.6 MOHR DIAGRAM FOR PLANE STRESS 73
3.3.7 MOHR DIAGRAM FOR GENERAL STATES OF STRESS 77
PROBLEMS 79
4 TENSORS 83
4.1 DEFINITION OF TENSORS 83
4.2 TENSOR ALGEBRA 89
4.2.1 ISOTROPIE TENSORS OF 4. ORDER 94
4.2.2 TENSORS AS POLYADICS 96
4.3 TENSORS OF 2. ORDER. PART ONE 97
4.3.1 SYMMETRIE TENSORS OF 2. ORDER 100
4.3.2 ALTERNATIVE INVARIANTS 103
4.3.3 DEVIATOR AND ISOTROP 104
4.4 TENSOR FIELDS 105
4.4.1 GRADIENT, DIVERGENCE, AND ROTATION 105
4.4.2 DEL-OPERATOR 107
4.4.3 ORTHOGONAL COORDINATES 108
4.4.4 MATERIAL DERIVATIVE OF A TENSOR FIELD 110
4.5 RIGID-BODY DYNAMICS 111
4.5.1 KINEMATICS 112
4.5.2 RELATIVE MOTION 117
4.5.3 KINETICS 119
4.6 TENSORS OF 2. ORDER. PART TWO 122
4.6.1 ROTATION OF VECTORS AND TENSORS 123
4.6.2 POLAR DECOMPOSITION 124
4.6.3 ISOTROPIE FUNCTIONS OF TENSORS 125
PROBLEMS 129
5 DEFORMATION ANALYSIS 133
5.1 STRAIN MEASURES 133
5.2 THE GREEN STRAIN TENSOR 134
5.3 SMALL STRAINS AND SMALL DEFORMATIONS 139
5.3.1 SMALL STRAINS 140
5.3.2 SMALL DEFORMATIONS 141
5.3.3 COORDINATE STRAMS IN CYLINDRICAL COORDINATES AND SPHERICAL
COORDINATES 142
5.3.4 PRINCIPAL STRAINS AND PRINCIPAL DIRECTIONS OF STRAINS 144 5.3.5
STRAIN ISOTROP AND STRAIN DEVIATOR 145
5.3.6 ROTATION TENSOR FOR SMALL DEFORMATIONS 145
5.3.7 SMALL STRAINS IN A MATERIAL SURFACE 147
5.3.8 MOHR DIAGRAM FOR STRAIN 148
5.3.9 EQUATIONS OF COMPATIBILITY 148
5.3.10 COMPATIBILITY EQUATIONS AS SUFFICIENT CONDITIONS 150
5.4 RATES OF DEFORMATION, STRAIN, AND ROTATION 151
IMAGE 4
CONTENTS XIII
5.4.1 RATE OF DEFORMATION MATRIX AND RATE OF ROTATION MATRIX IN
CYLINDRICAL AND SPHERICAL COORDINATES 158
5.5 LARGE DEFORMATIONS 160
5.5.1 SPECIAL TYPES OF DEFORMATIONS AND FLOWS 166
5.5.2 THE CONTINUITY EQUATION IN A PARTICLE 172
5.5.3 REDUCTION TO SMALL DEFORMATIONS 172
5.5.4 DEFORMATION WITH RESPECT TO THE PRESENT CONFIGURATION .. 173 5.6
THE PIOLA-KIRCHHOFF STRESS TENSORS 175
PROBLEMS 178
6 WORK AND ENERGY 183
6.1 MECHANICAL ENERGY BALANCE 183
6.1.1 THE WORK-ENERGY EQUATION FOR RIGID BODIES 186
6.1.2 CONJUGATE STRESS TENSORS AND DEFORMATION TENSORS 189 6.2 THE
PRINCIPLE OF VIRTUAL POWER 190
6.3 THERMAL ENERGY BALANCE 192
6.3.1 THERMODYNAMIC INTRODUCTION 192
6.3.2 THERMAL ENERGY BALANCE 193
6.4 THE SECOND LAW OF THERMODYNAMICS 195
PROBLEMS 198
7 THEORY OF ELASTICITY 199
7.1 INTRODUCTION 199
7.2 THE HOOKEAN SOLID 200
7.2.1 AN ALTERNATIVE DEVELOPMENT OF THE GENERALIZED HOOKE S LAW 205
7.2.2 STRAIN ENERGY 206
7.3 TWO-DIMENSIONAL THEORY OF ELASTICITY 207
7.3.1 PLANE STRESS 207
7.3.2 PLANE DISPLACEMENTS 213
7.3.3 AIRY S STRESS FUNCTION 217
7.3.4 AIRY S STRESS FUNCTION IN POLAR COORDINATES 223
7.3.5 AXIAL SYMMETRY 229
7.4 TORSION OF CYLINDRICAL BARS 232
7.4.1 THE COULOMB THEORY OF TORSION 232
7.4.2 THE SAINT-VENANT THEORY OF TORSION 234
7.4.3 PRANDTL S STRESS FUNCTION 238
7.4.4 THE MEMBRANE ANALOGY 241
7.5 THERMOELASTICITY 244
7.5.1 CONSTITUTIVE EQUATIONS 244
7.5.2 PLANE STRESS 245
7.5.3 PLANE DISPLACEMENTS 248
7.6 HYPERELASTICITY 249
7.6.1 ELASTIC ENERGY 249
7.6.2 THE BASIC EQUATIONS OF HYPERELASTICITY 252
IMAGE 5
XIV CONTENTS
7.6.3 THE UNIQUENESS THEOREM 258
7.7 STRESS WAVES IN ELASTIC MATERIALS 260
7.7.1 LONGITUDINAL WAVES IN CYLINDRICAL BARS 260
7.7.2 THE HOPKINSON EXPERIMENT 266
7.7.3 PLANE ELASTIC WAVES 268
7.7.4 ELASTIC WAVES IN AN INFINITE MEDIUM 270
7.7.5 SEISMIC WAVES 270
7.7.6 REFLECTION OF ELASTIC WAVES 271
7.7.7 TENSILE FRACTURE DUE TO COMPRESSION WAVE 272
7.7.8 SURFACE WAVES. RAYLEIGH WAVES 273
7.8 ANISOTROPIE MATERIALS 274
7.8.1 HYPERELASTICITY 276
7.8.2 MATERIALS WITH ONE PLANE OF SYMMETRY 277
7.8.3 THREE ORTHOGONAL SYMMETRY PLANES. ORTHOTROPY 279
7.8.4 TRANSVERSE ISOTROPY 281
7.8.5 ISOTROPY 283
7.9 COMPOSITE MATERIALS 284
7.9.1 LAMINA 285
7.9.2 FROM LAMINA AXES TO LAMINATE AXES 288
7.9.3 ENGINEERING PARAMETERS RELATED TO LAMINATE AXES 290
7.9.4 PLATE LAMINATE OF UNIDIRECTIONAL LAMINAS 290
7.10 LARGE DEFORMATIONS 292
7.10.1 ISOTROPIE ELASTICITY 293
7.10.2 HYPERELASTICITY 294
PROBLEMS 297
8 FLUID MECHANICS 303
8.1 INTRODUCTION 303
8.2 CONTROL VOLUME. REYNOLDS TRANSPORT THEOREM 306
8.2.1 ALTERNATIVE DERIVATION OF THE REYNOLDS TRANSPORT THEOREM 309
8.2.2 CONTROL VOLUME EQUATIONS 310
8.2.3 CONTINUITY EQUATION 312
8.3 PERFECT FLUID = EULERIAN FLUID 313
8.3.1 BERNOULLI S EQUATION 315
8.3.2 CIRCULATION AND VORTICITY 319
8.3.3 SOUND WAVES 322
8.4 LINEARLY VISCOUS FLUID = NEWTONIAN FLUID 323
8.4.1 CONSTITUTIVE EQUATIONS 323
8.4.2 THE NAVIER-STOKES EQUATIONS 330
8.4.3 DISSIPATION 333
8.4.4 THE ENERGY EQUATION 335
8.4.5 THE BERNOULLI EQUATION FOR PIPE FLOW 336
8.5 POTENTIAL FLOW 339
8.5.1 THE D ALEMBERT PARADOX 343
IMAGE 6
XV
8.6 NON-NEWTONIAN FLUIDS 343
8.6.1 INTRODUCTION 343
8.6.2 GENERALIZED NEWTONIAN FLUIDS 344
8.6.3 VISCOMETRIC FLOWS. KINEMATICS 347
8.6.4 MATERIAL FUNCTIONS FOR VISCOMETRIC FLOWS 353
8.6.5 EXTENSIONAL FLOWS 356
PROBLEMS 358
VISCOELASTICITY 361
9.1 INTRODUCTION 361
9.2 LINEARLY VISCOELASTIC MATERIALS 368
9.2.1 MECHANICAL MODELS 368
9.2.2 GENERAL RESPONSE EQUATION 376
9.2.3 THE BOLTZMANN SUPERPOSITION PRINCIPLE 377
9.2.4 LINEARLY VISCOELASTIC MATERIAL MODELS 380
9.2.5 BEAM THEORY 385
9.2.6 TORSION 388
9.3 THE CORRESPONDENCE PRINCIPLE 388
9.3.1 QUASI-STATIC PROBLEMS 391
9.4 DYNAMIC RESPONSE 394
9.4.1 COMPLEX NOTATION 398
9.4.2 VISCOELASTIC FOUNDATION 404
9.5 VISCOELASTIC WAVES 407
9.5.1 ACCELERATION WAVES IN A CYLINDRICAL BAR 407
9.5.2 PROGRESSIVE HARMONIE WAVE IN A CYLINDRICAL BAR 411
9.5.3 WAVES IN INFINITE VISCOELASTIC MEDIUM 414
9.6 NON-LINEAR VISCOELASTICITY 419
9.6.1 THE NORTON FLUID 422
9.6.2 STEADY BENDING OF NON-LINEARLY VISCOELASTIC BEAMS . . .. 423
PROBLEMS 425
THEORY OF PLASTICITY 433
10.1 INTRODUCTION 433
10.2 YIELD CRITERIA 435
10.2.1 THE MISES YIELD CRITERION 440
10.2.2 THE TRESCA YIELD CRITERION 444
10.2.3 YIELD CRITERIA FOR HARDENING MATERIALS 449
10.3 FLOW RULES 451
10.3.1 THE GENERAL FLOW RULE 451
10.3.2 ELASTIC-PERFECTLY PLASTIC TRESCA MATERIAL 452
10.3.3 ELASTIC-PERFECTLY PLASTIC MISES MATERIAL 457
10.4 ELASTIC-PLASTIC ANALYSIS 458
10.4.1 PLANE STRESS PROBLEMS 459
10.4.2 PLANE STRAIN PROBLEMS 463
10.4.3 GENERAL TWO-DIMENSIONAL PROBLEM 466
IMAGE 7
CONTENTS
10.5 LIMIT LOAD ANALYSIS FOR PLANE BEAMS AND FRAMES 471
10.5.1 INTRODUCTION 471
10.5.2 PLASTIC COLLAPSE 471
10.5.3 LIMIT LOAD THEOREM FOR PLANE BEAMS AND FRAMES 477
10.6 THE DRUCKER POSTULATE 479
10.7 LIMIT LOAD ANALYSIS 483
10.7.1 LOWER BOUND LIMIT LOAD THEOREM 485
10.7.2 UPPER BOUND LIMIT LOAD THEOREM 486
10.7.3 DISCONTINUITY IN STRESS AND VELOCITY 489
10.7.4 INDENTATION 491
10.8 YIELD LINE THEORY 495
10.9 MISES MATERIAL WITH ISOTROPIE HARDENING 503
10.10 YIELD CRITERIA DEPENDENT ON THE MEAN STRESS 507
10.10.1 THE MOHR-COULOMB CRITERION 507
10.10.2 THE DRUCKER-PRAGER CRITERION 510
10.11 VISCOPLASTICITY 511
10.11.1 INTRODUCTION 511
10.11.2 THE BINGHAM ELASTO-VISCOPLASTIC MODELS 511
PROBLEMS 515
CONSTITUTIVE EQUATIONS 517
11.1 INTRODUCTION 517
11.2 OBJECTIVE TENSOR FIELDS 519
11.2.1 TENSOR COMPONENTS IN TWO REFERENCES 521
11.2.2 MATERIAL DERIVATIVE OF OBJECTIVE TENSORS 522
11.2.3 DEFORMATIONS WITH RESPECT TO FIXED REFERENCE CONFIGURATION 524
11.2.4 DEFORMATION WITH RESPECT TO THE PRESENT CONFIGURATION .. 527 11.3
COROTATIONAL DERIVATIVE 530
11.4 CONVECTED DERIVATIVE 531
11.5 GENERAL PRINCIPLES OF CONSTITUTIVE THEORY 532
11.5.1 PRESENT CONFIGURATION AS REFERENCE CONFIGURATION 536 11.6
MATERIAL SYMMETRY 539
11.6.1 SYMMETRY GROUPS 540
11.6.2 ISOTROPY 542
11.6.3 CHANGE OF REFERENCE CONFIGURATION 543
11.6.4 CLASSIFICATION OF SIMPLE MATERIALS 544
11.6.5 LIQUID CRYSTALS 548
11.7 THERMOELASTIC MATERIALS 548
11.8 THERMOVISCOUS FLUIDS 551
11.9 ADVANCED FLUID MODELS 552
11.9.1 INTRODUCTION 552
11.9.2 STOKESIAN FLUIDS OR REINER-RIVLIN FLUIDS 553
11.9.3 COROTATIONAL FLUID MODELS 554
IMAGE 8
XVII
11.9.4 QUASI-LINEAR COROTATIONAL FLUID MODELS 556
11.9.5 OLDROYDFLUIDS 557
TENSORS IN EUCLIDEAN SPACE E3 561
12.1 INTRODUCTION 561
12.2 GENERAL COORDINATES. BASE VECTORS 561
12.2.1 COVARIANT AND CONTRAVARIANT TRANSFORMATIONS 564
12.2.2 FUNDAMENTAL PARAMETERS OF A COORDINATE SYSTEM 567
12.2.3 ORTHOGONAL COORDINATES 568
12.3 VECTORFIELDS 569
12.4 TENSOR FIELDS 573
12.4.1 TENSOR COMPONENTS. TENSOR ALGEBRA 573
12.4.2 SYMMETRIE TENSORS OF 2. ORDER 575
12.4.3 TENSORS AS POLYADICS 576
12.5 DIFFERENTIATION OF TENSORS 577
12.5.1 CHRISTOFFEL SYMBOLS 577
12.5.2 ABSOLUTE AND COVARIANT DERIVATIVES OF VECTOR COMPONENTS 578
12.5.3 THE FRENET-SERRET FORMULAS OF SPACE CURVES 582
12.5.4 DIVERGENCE AND ROTATION OF A VECTOR FIELD 583
12.5.5 ORTHOGONAL COORDINATES 584
12.5.6 ABSOLUTE AND COVARIANT DERIVATIVES OF TENSOR COMPONENTS 586
12.6 INTEGRATION OF TENSOR FIELDS 591
12.7 TWO-POINT TENSOR COMPONENTS 592
12.8 RELATIVE TENSORS 595
PROBLEMS 596
CONTINUUM MECHANICS IN CURVILINEAR COORDINATES 599
13.1 INTRODUCTION 599
13.2 KINEMATICS 599
13.3 DEFORMATION ANALYSIS 601
13.3.1 STRAIN MEASURES 601
13.3.2 SMALL STRAINS AND SMALL DEFORMATIONS 603
13.3.3 RATES OF DEFORMATION, STRAIN, AND ROTATION 605
13.3.4 ORTHOGONAL COORDINATES 605
13.3.5 GENERAL ANALYSIS OF LARGE DEFORMATIONS 607
13.3.6 CONVECTED COORDINATES 608
13.4 CONVECTED DERIVATIVES OF TENSORS 611
13.5 STRESS TENSORS. EQUATIONS OF MOTION 615
13.5.1 PHYSICAL STRESS COMPONENTS 615
13.5.2 CAUCHY EQUATIONS OF MOTION 617
13.6 BASIC EQUATIONS IN ELASTICITY 618
13.7 BASIC EQUATIONS IN FLUID MECHANICS 619
13.7.1 PERFECT FLUIDS == EULERIAN FLUIDS 620
IMAGE 9
XVIII CONTENTS
13.7.2 LINEARLY VISCOUS FLUIDS = NEWTONIAN FLUIDS 620
13.7.3 ORTHOGONAL COORDINATES 621
PROBLEMS 623
APPENDICES 625
APPENDIX A DEL-OPERATOR 625
APPENDIX B THE NAVIER - STOKES EQUATIONS 626
APPENDIX C INTEGRAL THEOREMS 627
REFERENCES 643
SYMBOLS 645
INDEX 649
|
| adam_txt |
IMAGE 1
FRIDTJOV IRGENS
CONTINUUM MECHANICS
WITH 279 FIGURES AND 4 TABLES
4Y SPRI RINGER
IMAGE 2
CONTENTS
1 INTRODUCTION 1
1.1 THE CONTINUUM HYPOTHESIS 1
1.2 ELASTICITY, PLASTICITY, AND FRACTURE 2
1.3 FLUIDS 8
1.4 VISCOELASTICITY 12
1.5 AN OUTLINE FOR THE PRESENT BOOK 16
2 MATHEMATICAL FOUNDATION 19
2.1 MATRICES AND DETERMINANTS 19
2.2 COORDINATE SYSTEMS AND VECTORS 23
2.3 COORDINATE TRANSFORMATIONS 28
2.4 SCALAR FIELDS AND VECTOR FIELDS 30
PROBLEMS 34
3 DYNAMICS 37
3.1 KINEMATICS 37
3.1.1 LAGRANGIAN COORDINATES AND EULERIAN COORDINATES 37
3.1.2 MATERIAL DERIVATIVE OF AN INTENSIVE QUANTITY 40
3.1.3 MATERIAL DERIVATIVE OF AN EXTENSIVE QUANTITY 41
3.2 EQUATIONS OF MOTION 42
3.2.1 EULER'S AXIOMS 42
3.2.2 NEWTON'S 3. LAW 46
3.2.3 COORDINATE STRESSES 47
3.2.4 CAUCHY'S STRESS THEOREM AND CAUCHY'S STRESS TENSOR . . 50 3.2.5
CAUCHY EQUATIONS OF MOTION 54
3.2.6 ALTERNATIVE DERIVATION OF THE CAUCHY EQUATIONS 58
3.3 STRESS ANALYSIS 60
3.3.1 PRINCIPAL STRESSES 60
3.3.2 STRESS DEVIATOR AND STRESS ISOTROP 65
3.3.3 EXTREMAL VALUES FOR NORMAL STRESS 68
3.3.4 MAXIMUM SHEAR STRESS 69
XI
IMAGE 3
XII CONTENTS
3.3.5 PLANE STRESS 70
3.3.6 MOHR DIAGRAM FOR PLANE STRESS 73
3.3.7 MOHR DIAGRAM FOR GENERAL STATES OF STRESS 77
PROBLEMS 79
4 TENSORS 83
4.1 DEFINITION OF TENSORS 83
4.2 TENSOR ALGEBRA 89
4.2.1 ISOTROPIE TENSORS OF 4. ORDER 94
4.2.2 TENSORS AS POLYADICS 96
4.3 TENSORS OF 2. ORDER. PART ONE 97
4.3.1 SYMMETRIE TENSORS OF 2. ORDER 100
4.3.2 ALTERNATIVE INVARIANTS 103
4.3.3 DEVIATOR AND ISOTROP 104
4.4 TENSOR FIELDS 105
4.4.1 GRADIENT, DIVERGENCE, AND ROTATION 105
4.4.2 DEL-OPERATOR 107
4.4.3 ORTHOGONAL COORDINATES 108
4.4.4 MATERIAL DERIVATIVE OF A TENSOR FIELD 110
4.5 RIGID-BODY DYNAMICS 111
4.5.1 KINEMATICS 112
4.5.2 RELATIVE MOTION 117
4.5.3 KINETICS 119
4.6 TENSORS OF 2. ORDER. PART TWO 122
4.6.1 ROTATION OF VECTORS AND TENSORS 123
4.6.2 POLAR DECOMPOSITION 124
4.6.3 ISOTROPIE FUNCTIONS OF TENSORS 125
PROBLEMS 129
5 DEFORMATION ANALYSIS 133
5.1 STRAIN MEASURES 133
5.2 THE GREEN STRAIN TENSOR 134
5.3 SMALL STRAINS AND SMALL DEFORMATIONS 139
5.3.1 SMALL STRAINS 140
5.3.2 SMALL DEFORMATIONS 141
5.3.3 COORDINATE STRAMS IN CYLINDRICAL COORDINATES AND SPHERICAL
COORDINATES 142
5.3.4 PRINCIPAL STRAINS AND PRINCIPAL DIRECTIONS OF STRAINS 144 5.3.5
STRAIN ISOTROP AND STRAIN DEVIATOR 145
5.3.6 ROTATION TENSOR FOR SMALL DEFORMATIONS 145
5.3.7 SMALL STRAINS IN A MATERIAL SURFACE 147
5.3.8 MOHR DIAGRAM FOR STRAIN 148
5.3.9 EQUATIONS OF COMPATIBILITY 148
5.3.10 COMPATIBILITY EQUATIONS AS SUFFICIENT CONDITIONS 150
5.4 RATES OF DEFORMATION, STRAIN, AND ROTATION 151
IMAGE 4
CONTENTS XIII
5.4.1 RATE OF DEFORMATION MATRIX AND RATE OF ROTATION MATRIX IN
CYLINDRICAL AND SPHERICAL COORDINATES 158
5.5 LARGE DEFORMATIONS 160
5.5.1 SPECIAL TYPES OF DEFORMATIONS AND FLOWS 166
5.5.2 THE CONTINUITY EQUATION IN A PARTICLE 172
5.5.3 REDUCTION TO SMALL DEFORMATIONS 172
5.5.4 DEFORMATION WITH RESPECT TO THE PRESENT CONFIGURATION . 173 5.6
THE PIOLA-KIRCHHOFF STRESS TENSORS 175
PROBLEMS 178
6 WORK AND ENERGY 183
6.1 MECHANICAL ENERGY BALANCE 183
6.1.1 THE WORK-ENERGY EQUATION FOR RIGID BODIES 186
6.1.2 CONJUGATE STRESS TENSORS AND DEFORMATION TENSORS 189 6.2 THE
PRINCIPLE OF VIRTUAL POWER 190
6.3 THERMAL ENERGY BALANCE 192
6.3.1 THERMODYNAMIC INTRODUCTION 192
6.3.2 THERMAL ENERGY BALANCE 193
6.4 THE SECOND LAW OF THERMODYNAMICS 195
PROBLEMS 198
7 THEORY OF ELASTICITY 199
7.1 INTRODUCTION 199
7.2 THE HOOKEAN SOLID 200
7.2.1 AN ALTERNATIVE DEVELOPMENT OF THE GENERALIZED HOOKE'S LAW 205
7.2.2 STRAIN ENERGY 206
7.3 TWO-DIMENSIONAL THEORY OF ELASTICITY 207
7.3.1 PLANE STRESS 207
7.3.2 PLANE DISPLACEMENTS 213
7.3.3 AIRY'S STRESS FUNCTION 217
7.3.4 AIRY'S STRESS FUNCTION IN POLAR COORDINATES 223
7.3.5 AXIAL SYMMETRY 229
7.4 TORSION OF CYLINDRICAL BARS 232
7.4.1 THE COULOMB THEORY OF TORSION 232
7.4.2 THE SAINT-VENANT THEORY OF TORSION 234
7.4.3 PRANDTL'S STRESS FUNCTION 238
7.4.4 THE MEMBRANE ANALOGY 241
7.5 THERMOELASTICITY 244
7.5.1 CONSTITUTIVE EQUATIONS 244
7.5.2 PLANE STRESS 245
7.5.3 PLANE DISPLACEMENTS 248
7.6 HYPERELASTICITY 249
7.6.1 ELASTIC ENERGY 249
7.6.2 THE BASIC EQUATIONS OF HYPERELASTICITY 252
IMAGE 5
XIV CONTENTS
7.6.3 THE UNIQUENESS THEOREM 258
7.7 STRESS WAVES IN ELASTIC MATERIALS 260
7.7.1 LONGITUDINAL WAVES IN CYLINDRICAL BARS 260
7.7.2 THE HOPKINSON EXPERIMENT 266
7.7.3 PLANE ELASTIC WAVES 268
7.7.4 ELASTIC WAVES IN AN INFINITE MEDIUM 270
7.7.5 SEISMIC WAVES 270
7.7.6 REFLECTION OF ELASTIC WAVES 271
7.7.7 TENSILE FRACTURE DUE TO COMPRESSION WAVE 272
7.7.8 SURFACE WAVES. RAYLEIGH WAVES 273
7.8 ANISOTROPIE MATERIALS 274
7.8.1 HYPERELASTICITY 276
7.8.2 MATERIALS WITH ONE PLANE OF SYMMETRY 277
7.8.3 THREE ORTHOGONAL SYMMETRY PLANES. ORTHOTROPY 279
7.8.4 TRANSVERSE ISOTROPY 281
7.8.5 ISOTROPY 283
7.9 COMPOSITE MATERIALS 284
7.9.1 LAMINA 285
7.9.2 FROM LAMINA AXES TO LAMINATE AXES 288
7.9.3 ENGINEERING PARAMETERS RELATED TO LAMINATE AXES 290
7.9.4 PLATE LAMINATE OF UNIDIRECTIONAL LAMINAS 290
7.10 LARGE DEFORMATIONS 292
7.10.1 ISOTROPIE ELASTICITY 293
7.10.2 HYPERELASTICITY 294
PROBLEMS 297
8 FLUID MECHANICS 303
8.1 INTRODUCTION 303
8.2 CONTROL VOLUME. REYNOLDS' TRANSPORT THEOREM 306
8.2.1 ALTERNATIVE DERIVATION OF THE REYNOLDS' TRANSPORT THEOREM 309
8.2.2 CONTROL VOLUME EQUATIONS 310
8.2.3 CONTINUITY EQUATION 312
8.3 PERFECT FLUID = EULERIAN FLUID 313
8.3.1 BERNOULLI'S EQUATION 315
8.3.2 CIRCULATION AND VORTICITY 319
8.3.3 SOUND WAVES 322
8.4 LINEARLY VISCOUS FLUID = NEWTONIAN FLUID 323
8.4.1 CONSTITUTIVE EQUATIONS 323
8.4.2 THE NAVIER-STOKES EQUATIONS 330
8.4.3 DISSIPATION 333
8.4.4 THE ENERGY EQUATION 335
8.4.5 THE BERNOULLI EQUATION FOR PIPE FLOW 336
8.5 POTENTIAL FLOW 339
8.5.1 THE D'ALEMBERT PARADOX 343
IMAGE 6
XV
8.6 NON-NEWTONIAN FLUIDS 343
8.6.1 INTRODUCTION 343
8.6.2 GENERALIZED NEWTONIAN FLUIDS 344
8.6.3 VISCOMETRIC FLOWS. KINEMATICS 347
8.6.4 MATERIAL FUNCTIONS FOR VISCOMETRIC FLOWS 353
8.6.5 EXTENSIONAL FLOWS 356
PROBLEMS 358
VISCOELASTICITY 361
9.1 INTRODUCTION 361
9.2 LINEARLY VISCOELASTIC MATERIALS 368
9.2.1 MECHANICAL MODELS 368
9.2.2 GENERAL RESPONSE EQUATION 376
9.2.3 THE BOLTZMANN SUPERPOSITION PRINCIPLE 377
9.2.4 LINEARLY VISCOELASTIC MATERIAL MODELS 380
9.2.5 BEAM THEORY 385
9.2.6 TORSION 388
9.3 THE CORRESPONDENCE PRINCIPLE 388
9.3.1 QUASI-STATIC PROBLEMS 391
9.4 DYNAMIC RESPONSE 394
9.4.1 COMPLEX NOTATION 398
9.4.2 VISCOELASTIC FOUNDATION 404
9.5 VISCOELASTIC WAVES 407
9.5.1 ACCELERATION WAVES IN A CYLINDRICAL BAR 407
9.5.2 PROGRESSIVE HARMONIE WAVE IN A CYLINDRICAL BAR 411
9.5.3 WAVES IN INFINITE VISCOELASTIC MEDIUM 414
9.6 NON-LINEAR VISCOELASTICITY 419
9.6.1 THE NORTON FLUID 422
9.6.2 STEADY BENDING OF NON-LINEARLY VISCOELASTIC BEAMS . . . 423
PROBLEMS 425
THEORY OF PLASTICITY 433
10.1 INTRODUCTION 433
10.2 YIELD CRITERIA 435
10.2.1 THE MISES YIELD CRITERION 440
10.2.2 THE TRESCA YIELD CRITERION 444
10.2.3 YIELD CRITERIA FOR HARDENING MATERIALS 449
10.3 FLOW RULES 451
10.3.1 THE GENERAL FLOW RULE 451
10.3.2 ELASTIC-PERFECTLY PLASTIC TRESCA MATERIAL 452
10.3.3 ELASTIC-PERFECTLY PLASTIC MISES MATERIAL 457
10.4 ELASTIC-PLASTIC ANALYSIS 458
10.4.1 PLANE STRESS PROBLEMS 459
10.4.2 PLANE STRAIN PROBLEMS 463
10.4.3 GENERAL TWO-DIMENSIONAL PROBLEM 466
IMAGE 7
CONTENTS
10.5 LIMIT LOAD ANALYSIS FOR PLANE BEAMS AND FRAMES 471
10.5.1 INTRODUCTION 471
10.5.2 PLASTIC COLLAPSE 471
10.5.3 LIMIT LOAD THEOREM FOR PLANE BEAMS AND FRAMES 477
10.6 THE DRUCKER POSTULATE 479
10.7 LIMIT LOAD ANALYSIS 483
10.7.1 LOWER BOUND LIMIT LOAD THEOREM 485
10.7.2 UPPER BOUND LIMIT LOAD THEOREM 486
10.7.3 DISCONTINUITY IN STRESS AND VELOCITY 489
10.7.4 INDENTATION 491
10.8 YIELD LINE THEORY 495
10.9 MISES MATERIAL WITH ISOTROPIE HARDENING 503
10.10 YIELD CRITERIA DEPENDENT ON THE MEAN STRESS 507
10.10.1 THE MOHR-COULOMB CRITERION 507
10.10.2 THE DRUCKER-PRAGER CRITERION 510
10.11 VISCOPLASTICITY 511
10.11.1 INTRODUCTION 511
10.11.2 THE BINGHAM ELASTO-VISCOPLASTIC MODELS 511
PROBLEMS 515
CONSTITUTIVE EQUATIONS 517
11.1 INTRODUCTION 517
11.2 OBJECTIVE TENSOR FIELDS 519
11.2.1 TENSOR COMPONENTS IN TWO REFERENCES 521
11.2.2 MATERIAL DERIVATIVE OF OBJECTIVE TENSORS 522
11.2.3 DEFORMATIONS WITH RESPECT TO FIXED REFERENCE CONFIGURATION 524
11.2.4 DEFORMATION WITH RESPECT TO THE PRESENT CONFIGURATION . 527 11.3
COROTATIONAL DERIVATIVE 530
11.4 CONVECTED DERIVATIVE 531
11.5 GENERAL PRINCIPLES OF CONSTITUTIVE THEORY 532
11.5.1 PRESENT CONFIGURATION AS REFERENCE CONFIGURATION 536 11.6
MATERIAL SYMMETRY 539
11.6.1 SYMMETRY GROUPS 540
11.6.2 ISOTROPY 542
11.6.3 CHANGE OF REFERENCE CONFIGURATION 543
11.6.4 CLASSIFICATION OF SIMPLE MATERIALS 544
11.6.5 LIQUID CRYSTALS 548
11.7 THERMOELASTIC MATERIALS 548
11.8 THERMOVISCOUS FLUIDS 551
11.9 ADVANCED FLUID MODELS 552
11.9.1 INTRODUCTION 552
11.9.2 STOKESIAN FLUIDS OR REINER-RIVLIN FLUIDS 553
11.9.3 COROTATIONAL FLUID MODELS 554
IMAGE 8
XVII
11.9.4 QUASI-LINEAR COROTATIONAL FLUID MODELS 556
11.9.5 OLDROYDFLUIDS 557
TENSORS IN EUCLIDEAN SPACE E3 561
12.1 INTRODUCTION 561
12.2 GENERAL COORDINATES. BASE VECTORS 561
12.2.1 COVARIANT AND CONTRAVARIANT TRANSFORMATIONS 564
12.2.2 FUNDAMENTAL PARAMETERS OF A COORDINATE SYSTEM 567
12.2.3 ORTHOGONAL COORDINATES 568
12.3 VECTORFIELDS 569
12.4 TENSOR FIELDS 573
12.4.1 TENSOR COMPONENTS. TENSOR ALGEBRA 573
12.4.2 SYMMETRIE TENSORS OF 2. ORDER 575
12.4.3 TENSORS AS POLYADICS 576
12.5 DIFFERENTIATION OF TENSORS 577
12.5.1 CHRISTOFFEL SYMBOLS 577
12.5.2 ABSOLUTE AND COVARIANT DERIVATIVES OF VECTOR COMPONENTS 578
12.5.3 THE FRENET-SERRET FORMULAS OF SPACE CURVES 582
12.5.4 DIVERGENCE AND ROTATION OF A VECTOR FIELD 583
12.5.5 ORTHOGONAL COORDINATES 584
12.5.6 ABSOLUTE AND COVARIANT DERIVATIVES OF TENSOR COMPONENTS 586
12.6 INTEGRATION OF TENSOR FIELDS 591
12.7 TWO-POINT TENSOR COMPONENTS 592
12.8 RELATIVE TENSORS 595
PROBLEMS 596
CONTINUUM MECHANICS IN CURVILINEAR COORDINATES 599
13.1 INTRODUCTION 599
13.2 KINEMATICS 599
13.3 DEFORMATION ANALYSIS 601
13.3.1 STRAIN MEASURES 601
13.3.2 SMALL STRAINS AND SMALL DEFORMATIONS 603
13.3.3 RATES OF DEFORMATION, STRAIN, AND ROTATION 605
13.3.4 ORTHOGONAL COORDINATES 605
13.3.5 GENERAL ANALYSIS OF LARGE DEFORMATIONS 607
13.3.6 CONVECTED COORDINATES 608
13.4 CONVECTED DERIVATIVES OF TENSORS 611
13.5 STRESS TENSORS. EQUATIONS OF MOTION 615
13.5.1 PHYSICAL STRESS COMPONENTS 615
13.5.2 CAUCHY EQUATIONS OF MOTION 617
13.6 BASIC EQUATIONS IN ELASTICITY 618
13.7 BASIC EQUATIONS IN FLUID MECHANICS 619
13.7.1 PERFECT FLUIDS == EULERIAN FLUIDS 620
IMAGE 9
XVIII CONTENTS
13.7.2 LINEARLY VISCOUS FLUIDS = NEWTONIAN FLUIDS 620
13.7.3 ORTHOGONAL COORDINATES 621
PROBLEMS 623
APPENDICES 625
APPENDIX A DEL-OPERATOR 625
APPENDIX B THE NAVIER - STOKES EQUATIONS 626
APPENDIX C INTEGRAL THEOREMS 627
REFERENCES 643
SYMBOLS 645
INDEX 649 |
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| id | DE-604.BV023030164 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:16:39Z |
| indexdate | 2024-07-09T21:09:22Z |
| institution | BVB |
| isbn | 9783540742975 |
| language | English Norwegian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016234065 |
| oclc_num | 214305708 |
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| owner_facet | DE-706 DE-29T DE-20 DE-703 DE-634 DE-83 DE-91 DE-BY-TUM |
| physical | xviii, 661 Seiten Illustrationen, Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Springer |
| record_format | marc |
| spelling | Irgens, Fridtjov Verfasser (DE-588)1179843053 aut Continuum mechanics with 279 figures and 4 tables Fridtjov Irgens Berlin ; Heidelberg Springer [2008] xviii, 661 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Continuum mechanics Textbooks Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-74298-2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016234065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Irgens, Fridtjov Continuum mechanics with 279 figures and 4 tables Continuum mechanics Textbooks Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4032296-8 |
| title | Continuum mechanics with 279 figures and 4 tables |
| title_auth | Continuum mechanics with 279 figures and 4 tables |
| title_exact_search | Continuum mechanics with 279 figures and 4 tables |
| title_exact_search_txtP | Continuum mechanics with 279 figures and 4 tables |
| title_full | Continuum mechanics with 279 figures and 4 tables Fridtjov Irgens |
| title_fullStr | Continuum mechanics with 279 figures and 4 tables Fridtjov Irgens |
| title_full_unstemmed | Continuum mechanics with 279 figures and 4 tables Fridtjov Irgens |
| title_short | Continuum mechanics |
| title_sort | continuum mechanics with 279 figures and 4 tables |
| title_sub | with 279 figures and 4 tables |
| topic | Continuum mechanics Textbooks Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Continuum mechanics Textbooks Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016234065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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