Introduction to continuum mechanics:
Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors in introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Pergamon Press
1993
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors in introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples and problems, many with solutions Through the addition of more advanced material, this popular introduction to modern continuum mechanics has been fully revised to serve a dual purpose for introductory courses in undergraduate engineering curriculum, and for beginning graduate courses |
| Physical Description: | XIV, 556 S. graph. Darst. |
| ISBN: | 0080417000 0080417019 |
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| 100 | 1 | |a Lai, Wei M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to continuum mechanics |c Wei Michael Lai ; David Rubin ; Erhard Krempl |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1993 | |
| 300 | |a XIV, 556 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 520 | 3 | |a Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors in introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples and problems, many with solutions | |
| 520 | |a Through the addition of more advanced material, this popular introduction to modern continuum mechanics has been fully revised to serve a dual purpose for introductory courses in undergraduate engineering curriculum, and for beginning graduate courses | ||
| 650 | 4 | |a Continuum mechanics | |
| 650 | 0 | 7 | |a Kontinuumsmechanik |0 (DE-588)4032296-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143389-0 |a Aufgabensammlung |2 gnd-content | |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rubin, David |e Verfasser |4 aut | |
| 700 | 1 | |a Krempl, Erhard |e Verfasser |0 (DE-588)105990884 |4 aut | |
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Record in the Search Index
| _version_ | 1804135871228674048 |
|---|---|
| adam_text | CONTENTS PREFACE TO THE THIRD EDITION XII PREFACE TO THE FIRST EDITION
XIII THE AUTHORS XIV CHAPTER 1 INTRODUCTION 1 1.1 CONTINUUM THEORY 1 1.2
CONTENTS OF CONTINUUM MECHANICS 1 CHAPTER 2 TENSORS 3 PART A THE
INDICIAL NOTATION 3 2A1 SUMMATION CONVENTION, DUMMY INDICES 3 2A2 FREE
INDICES 5 2A3 KRONECKER DELTA 6 2A4 PERMUTATION SYMBOL 7 2A5
MANIPULATIONS WITH THE INDICIAL NOTATION 8 PARTB TENSORS 11 2B1 TENSOR:
A LINEAR TRANSFORMATION 11 2B2 COMPONENTS OF A TENSOR 13 2B3 COMPONENTS
OF A TRANSFORMED VECTOR 16 2B4 SUM OF TENSORS 17 2B5 PRODUCT OF TWO
TENSORS 18 2B6 TRANSPOSE OF A TENSOR 20 2B7 DYADIC PRODUCT OF TWO
VECTORS 21 2B8 TRACE OF A TENSOR 22 2B9 IDENTITY TENSOR AND TENSOR
INVERSE 23 2B10 ORTHOGONAL TENSOR 24 2B11 TRANSFORMATION MATRIX BETWEEN
TWO RECTANGULAR CARTESIAN COORDINATE SYSTEMS 26 2B12 TRANSFORMATION LAWS
FOR CARTESIAN COMPONENTS OF VECTORS 28 2B13 TRANSFORMATION LAW FOR
CARTESIAN COMPONENTS OF A TENSOR 30 2B14 DEFINING TENSORS BY
TRANSFORMATION LAWS 32 2B15 SYMMETRIC AND ANTISYMMETRIC TENSORS 35 2B16
THE DUAL VECTOR OF AN ANTISYMMETRIC TENSOR 36 2B17 EIGENVALUES AND
EIGENVECTORS OF A TENSOR 38 2B18 PRINCIPAL VALUES AND PRINCIPAL
DIRECTIONS OF REAL SYMMETRIC TENSORS 43 2B19 MATRIX OF A TENSOR WITH
RESPECT TO PRINCIPAL DIRECTIONS 44 2B20 PRINCIPAL SCALAR INVARIANTS OF A
TENSOR 45 PART C TENSOR CALCULUS 47 2C1 TENSOR-VALUED FUNCTIONS OF A
SCALAR 47 2C2 SCALAR FIELD, GRADIENT OF A SCALAR FUNCTION 49 2C3 VECTOR
FIELD, GRADIENT OF A VECTOR FIELD 53 2C4 DIVERGENCE OF A VECTOR FIELD
AND DIVERGENCE OF A TENSOR FIELD 54 2C5 CURL OF A VECTOR FIELD 55 PART D
CURVILINEAR COORDINATES 57 2D1 POLAR COORDINATES 57 2D2 CYLINDRICAL
COORDINATES 61 2D3 SPHERICAL COORDINATES 63 PROBLEMS 68 CHAPTER 3
KINEMATICS OF A CONTINUUM 79 3.1 DESCRIPTION OF MOTIONS OF A CONTINUUM
79 3.2 MATERIAL DESCRIPTION AND SPATIAL DESCRIPTION 83 3.3 MATERIAL
DERIVATIVE 85 3.4 ACCELERATION OF A PARTICLE IN A CONTINUUM 87 3.5
DISPLACEMENT FIELD 92 3.6 KINEMATIC EQUATIONS FOR RIGID BODY MOTION 93
3.7 INFINITESIMAL DEFORMATIONS 94 3.8 GEOMETRICAL MEANING OF THE
COMPONENTS OF THE INFINITESIMAL STRAIN TENSOR 99 3.9 PRINCIPAL STRAIN
105 3.10 DILATATION 105 3.11 THE INFINITESIMAL ROTATION TENSOR 106 3.12
TIME RATE OF CHANGE OF A MATERIAL ELEMENT 106 3.13 THE RATE OF
DEFORMATION TENSOR 108 3.14 THE SPIN TENSOR AND THE ANGULAR VELOCITY
VECTOR 111 3.15 EQUATION OF CONSERVATION OF MASS 112 3.16 COMPATIBILITY
CONDITIONS FOR INFINITESIMAL STRAIN COMPONENTS 114 3.17 COMPATIBILITY
CONDITIONS FOR THE RATE OF DEFORMATION COMPONENTS 119 3.18 DEFORMATION
GRADIENT 120 3.19 LOCAL RIGID BODY DISPLACEMENTS 121 3.20 FINITE
DEFORMATION 121 3.21 POLAR DECOMPOSITION THEOREM 124 3.22 CALCULATION OF
THE STRETCH TENSOR FROM THE DEFORMATION GRADIENT 126 3.23 RIGHT
CAUCHY-GREEN DEFORMATION TENSOR 128 3.24 LAGRANGIAN STRAIN TENSOR 134
3.25 LEFT CAUCHY-GREEN DEFORMATION TENSOR 138 3.26 EULERIAN STRAIN
TENSOR 141 3.27 COMPATIBILITY CONDITIONS FOR COMPONENTS OF FINITE
DEFORMATION TENSOR 144 3.28 CHANGE OF AREA DUE TO DEFORMATION 145 3.29
CHANGE OF VOLUME DUE TO DEFORMATION 146 3.30 COMPONENTS OF DEFORMATION
TENSORS IN OTHER COORDINATES 149 3.31 CURRENT CONFIGURATION AS THE
REFERENCE CONFIGURATION 158 PROBLEMS 160 CHAPTER 4 STRESS 173 4.1 STRESS
VECTOR 173 4.2 STRESS TENSOR 174 4.3 COMPONENTS OF STRESS TENSOR 176 4.4
SYMMETRY OF STRESS TENSOR - PRINCIPLE OF MOMENT OF MOMENTUM 178 4.5
PRINCIPAL STRESSES 182 4.6 MAXIMUM SHEARING STRESS 182 4.7 EQUATIONS OF
MOTION - PRINCIPLE OF LINEAR MOMENTUM 187 4.8 EQUATIONS OF MOTION IN
CYLINDRICAL AND SPHERICAL COORDINATES 190 4.9 BOUNDARY CONDITION FOR THE
STRESS TENSOR 192 4.10 PIOLA KIRCHHOFF STRESS TENSORS 195 4.11 EQUATIONS
OF MOTION WRITTEN WITH RESPECT TO THE REFERENCE CONFIGURATION 201 4.12
STRESS POWER 203 4.13 RATE OF HEAT FLOW INTO AN ELEMENT BY CONDUCTION
207 4.14 ENERGY EQUATION 208 4.15 ENTROPY INEQUALITY 209 PROBLEMS 210
CHAPTER 5 THE ELASTIC SOLID 217 5.1 MECHANICAL PROPERTIES 217 5.2 LINEAR
ELASTIC SOLID 220 PART A LINEAR ISOTROPIC ELASTIC SOLID 225 5.3 LINEAR
ISOTROPIC ELASTIC SOLID 225 5.4 YOUNG S MODULUS, POISSON S RATIO, SHEAR
MODULUS, AND BULK MODULUS 228 5.5 EQUATIONS OF THE INFINITESIMAL THEORY
OF ELASTICITY 232 5.6 NAVIER EQUATION IN CYLINDRICAL AND SPHERICAL
COORDINATES 236 5.7 PRINCIPLE OF SUPERPOSITION 238 5.8 PLANE
IRROTATIONAL WAVE 238 5.9 PLANE EQUIVOLUMINAL WAVE 242 5.10 REFLECTION
OF PLANE ELASTIC WAVES 248 5.11 VIBRATION OF AN INFINITE PLATE 251 5.12
SIMPLE EXTENSION 254 5.13 TORSION OF A CIRCULAR CYLINDER 258 5.14
TORSION OF A NONCIRCULAR CYLINDER 266 5.15 PURE BENDING OF A BEAM 269
5.16 PLANE STRAIN 275 5.17 PLANE STRAIN PROBLEM IN POLAR COORDINATES 281
5.18 THICK-WALLED CIRCULAR CYLINDER UNDER INTERNAL AND EXTERNAL PRESSURE
284 5.19 PURE BENDING OF A CURVED BEAM 285 5.20 STRESS CONCENTRATION DUE
TO A SMALL CIRCULAR HOLE IN A PLATE UNDER TENSION 287 5.21 HOLLOW SPHERE
SUBJECTED TO INTERNAL AND EXTERNAL PRESSURE 291 PART B LINEAR
ANISOTROPIC ELASTIC SOLID 293 5.22 CONSTITUTIVE EQUATIONS FOR
ANISOTROPIC ELASTIC SOLID 293 5.23 PLANE OF MATERIAL SYMMETRY 296 5.24
CONSTITUTIVE EQUATION FOR A MONOCLINIC ANISOTROPIC ELASTIC SOLID 299
5.25 CONSTITUTIVE EQUATIONS FOR AN ORTHOTROPIC ELASTIC SOLID 301 5.26
CONSTITUTIVE EQUATION FOR A TRANSVERSELY ISOTROPIC ELASTIC MATERIAL 303
5.27 CONSTITUTIVE EQUATION FOR ISOTROPIC ELASTIC SOLID 306 5.28
ENGINEERING CONSTANTS FOR ISOTROPIC ELASTIC SOLID. 307 5.29 ENGINEERING
CONSTANTS FOR TRANSVERSELY ISOTROPIC ELASTIC SOLID 308 5.30 ENGINEERING
CONSTANTS FOR ORTHOTROPIC ELASTIC SOLID 311 5.31 ENGINEERING CONSTANTS
FOR A MONOCLINIC ELASTIC SOLID. 312 PART C CONSTITUTIVE EQUATION FOR
ISOTROPIC ELASTIC SOLID UNDER LARGE DEFORMATION 314 5.32 CHANGE OF FRAME
314 5.33 CONSTITUTIVE EQUATION FOR AN ELASTIC MEDIUM UNDER LARGE
DEFORMATION. 319 5.34 CONSTITUTIVE EQUATION FOR AN ISOTROPIC ELASTIC
MEDIUM 322 5.35 SIMPLE EXTENSION OF AN INCOMPRESSIBLE ISOTROPIC ELASTIC
SOLID 324 5.36 SIMPLE SHEAR OF AN INCOMPRESSIBLE ISOTROPIC ELASTIC
RECTANGULAR BLOCK 325 5.37 BENDING OF A INCOMPRESSIBLE RECTANGULAR BAR.
327 5.38 TORSION AND TENSION OF AN INCOMPRESSIBLE SOLID CYLINDER 331
PROBLEMS 335 CHAPTER 6 NEWTONIAN VISCOUS FLUID 348 6.1 FLUIDS 348 6.2
COMPRESSIBLE AND INCOMPRESSIBLE FLUIDS 349 6.3 EQUATIONS OF HYDROSTATICS
350 6.4 NEWTONIAN FLUID 355 6.5 INTERPRETATION OF LAMBDA AND * 357 6.6
INCOMPRESSIBLE NEWTONIAN FLUID 359 6.7 NAVIER-STOKES EQUATION FOR
INCOMPRESSIBLE FLUIDS 360 6.8 NAVIER-STOKES EQUATIONS FOR IN
COMPRESSIBLE FLUIDS IN CYLINDRICAL AND SPHERICAL COORDINATES 364 6.9
BOUNDARY CONDITIONS 365 6.10 STREAMLINE, PATHLINE, STREAKLINE, STEADY,
UNSTEADY, LAMINAR AND TURBULENT FLOW 366 6.11 PLANE COUETTE FLOW 371
6.12 PLANE POISEUILLE FLOW 372 6.13 HAGEN POISEUILLE FLOW 374 6.14 PLANE
COUETTE FLOW OF TWO LAYERS OF INCOMPRESSIBLE FLUIDS 377 6.15 COUETTE
FLOW 380 6.16 FLOW NEAR AN OSCILLATING PLATE 381 6.17 DISSIPATION
FUNCTIONS FOR NEWTONIAN FLUIDS 383 6.18 ENERGY EQUATION FOR A NEWTONIAN
FLUID 384 6.19 VORTICITY VECTOR 387 6.20 IRROTATIONAL FLOW 390 6.21
IRROTATIONAL FLOW OF AN INVISCID, INCOMPRESSIBLE FLUID OF HOMOGENEOUS
DENSITY 391 6.22 IRROTATIONAL FLOWS AS SOLUTIONS OF NAVIER-STOKES
EQUATION 394 6.23 VORTICITY TRANSPORT EQUATION FOR INCOMPRESSIBLE
VISCOUS FLUID WITH A CONSTANT DENSITY 396 6.24 CONCEPT OF A BOUNDARY
LAYER 399 6.25 COMPRESSIBLE NEWTONIAN FLUID 401 6.26 ENERGY EQUATION IN
TERMS OF ENTHALPY 402 6.27 ACOUSTIC WAVE 404 6.28 IRROTATIONAL,
BAROTROPIC FLOWS OF INVISCID COMPRESSIBLE FLUID 408 6.29 ONE-DIMENSIONAL
FLOW OF A COMPRESSIBLE FLUID 412 PROBLEMS 419 CHAPTER 7 INTEGRAL
FORMULATION OF GENERAL PRINCIPLES 427 7.1 GREEN S THEOREM 427 7.2
DIVERGENCE THEOREM 430 7.3 INTEGRALS OVER A CONTROL VOLUME AND INTEGRALS
OVER A MATERIAL VOLUME 433 7.4 REYNOLDS TRANSPORT THEOREM 435 7.5
PRINCIPLE OF CONSERVATION OF MASS 437 7.6 PRINCIPLE OF LINEAR MOMENTUM
440 7.7 MOVING FRAMES 447 7.8 CONTROL VOLUME FIXED WITH RESPECT TO A
MOVING FRAME 449 7.9 PRINCIPLE OF MOMENT OF MOMENTUM 451 7.10 PRINCIPLE
OF CONSERVATION OF ENERGY 454 PROBLEMS 458 CHAPTER 8 NON-NEWTONIAN
FLUIDS 462 PART A LINEAR VISCOELASTIC FLUID 464 8.1 LINEAR MAXWELL FLUID
464 8.2 GENERALIZED LINEAR MAXWELL FLUID WITH DISCRETE RELAXATION
SPECTRA 471 8.3 INTEGRAL FORM OF THE LINEAR MAXWELL FLUID AND OF THE
GENERALIZED LINEAR MAXWELL FLUID WITH DISCRETE RELAXATION SPECTRA 473
8.4 GENERALIZED LINEAR MAXWELL FLUID WITH A CONTINUOUS RELAXATION
SPECTRUM 474 PARTB NONLINEAR VISCOELASTIC FLUID 476 8.5 CURRENT
CONFIGURATION AS REFERENCE CONFIGURATION 476 8.6 RELATIVE DEFORMATION
GRADIENT 477 8.7 RELATIVE DEFORMATION TENSORS 478 8.8 CALCULATIONS OF
THE RELATIVE DEFORMATION TENSOR 480 8.9 HISTORY OF DEFORMATION TENSOR.
RIVLIN-ERICKSEN TENSORS 486 8.10 RIVLIN-ERICKSEN TENSOR IN TERMS OF
VELOCITY GRADIENTS - THE RECURSIVE FORMULAS 491 8.11 RELATION BETWEEN
VELOCITY GRADIENT AND DEFORMATION GRADIENT 493 8.12 TRANSFORMATION LAWS
FOR THE RELATIVE DEFORMATION TENSORS UNDER A CHANGE OF FRAME 494 8.13
TRANSFORMATION LAW FOR THE RIVLIN-ERICKSEN TENSORS UNDER A CHANGE OF
FRAME 496 8.14 INCOMPRESSIBLE SIMPLE FLUID 497 8.15 SPECIAL SINGLE
INTEGRAL TYPE NONLINEAR CONSTITUTIVE EQUATIONS 498 8.16 GENERAL SINGLE
INTEGRAL TYPE NONLINEAR CONSTITUTIVE EQUATIONS 503 8.17 DIFFERENTIAL
TYPE CONSTITUTIVE EQUATIONS 503 8.18 OBJECTIVE RATE OF STRESS 506 8.19
THE RATE TYPE CONSTITUTIVE EQUATIONS 511 PART C VISCOMETRIC FLOW OF
SIMPLE FLUID 516 8.20 VISCOMETRIC FLOW 516 8.21 STRESSES IN VISCOMETRIC
FLOW OF AN INCOMPRESSIBLE SIMPLE FLUID 520 8.22 CHANNEL FLOW 523 8.23
COUETTE FLOW 526 PROBLEMS 532 APPENDIX: MATRICES 537 ANSWER TO PROBLEMS
543 REFERENCES 550 INDEX 552
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| adam_txt |
CONTENTS PREFACE TO THE THIRD EDITION XII PREFACE TO THE FIRST EDITION
XIII THE AUTHORS XIV CHAPTER 1 INTRODUCTION 1 1.1 CONTINUUM THEORY 1 1.2
CONTENTS OF CONTINUUM MECHANICS 1 CHAPTER 2 TENSORS 3 PART A THE
INDICIAL NOTATION 3 2A1 SUMMATION CONVENTION, DUMMY INDICES 3 2A2 FREE
INDICES 5 2A3 KRONECKER DELTA 6 2A4 PERMUTATION SYMBOL 7 2A5
MANIPULATIONS WITH THE INDICIAL NOTATION 8 PARTB TENSORS 11 2B1 TENSOR:
A LINEAR TRANSFORMATION 11 2B2 COMPONENTS OF A TENSOR 13 2B3 COMPONENTS
OF A TRANSFORMED VECTOR 16 2B4 SUM OF TENSORS 17 2B5 PRODUCT OF TWO
TENSORS 18 2B6 TRANSPOSE OF A TENSOR 20 2B7 DYADIC PRODUCT OF TWO
VECTORS 21 2B8 TRACE OF A TENSOR 22 2B9 IDENTITY TENSOR AND TENSOR
INVERSE 23 2B10 ORTHOGONAL TENSOR 24 2B11 TRANSFORMATION MATRIX BETWEEN
TWO RECTANGULAR CARTESIAN COORDINATE SYSTEMS 26 2B12 TRANSFORMATION LAWS
FOR CARTESIAN COMPONENTS OF VECTORS 28 2B13 TRANSFORMATION LAW FOR
CARTESIAN COMPONENTS OF A TENSOR 30 2B14 DEFINING TENSORS BY
TRANSFORMATION LAWS 32 2B15 SYMMETRIC AND ANTISYMMETRIC TENSORS 35 2B16
THE DUAL VECTOR OF AN ANTISYMMETRIC TENSOR 36 2B17 EIGENVALUES AND
EIGENVECTORS OF A TENSOR 38 2B18 PRINCIPAL VALUES AND PRINCIPAL
DIRECTIONS OF REAL SYMMETRIC TENSORS 43 2B19 MATRIX OF A TENSOR WITH
RESPECT TO PRINCIPAL DIRECTIONS 44 2B20 PRINCIPAL SCALAR INVARIANTS OF A
TENSOR 45 PART C TENSOR CALCULUS 47 2C1 TENSOR-VALUED FUNCTIONS OF A
SCALAR 47 2C2 SCALAR FIELD, GRADIENT OF A SCALAR FUNCTION 49 2C3 VECTOR
FIELD, GRADIENT OF A VECTOR FIELD 53 2C4 DIVERGENCE OF A VECTOR FIELD
AND DIVERGENCE OF A TENSOR FIELD 54 2C5 CURL OF A VECTOR FIELD 55 PART D
CURVILINEAR COORDINATES 57 2D1 POLAR COORDINATES 57 2D2 CYLINDRICAL
COORDINATES 61 2D3 SPHERICAL COORDINATES 63 PROBLEMS 68 CHAPTER 3
KINEMATICS OF A CONTINUUM 79 3.1 DESCRIPTION OF MOTIONS OF A CONTINUUM
79 3.2 MATERIAL DESCRIPTION AND SPATIAL DESCRIPTION 83 3.3 MATERIAL
DERIVATIVE 85 3.4 ACCELERATION OF A PARTICLE IN A CONTINUUM 87 3.5
DISPLACEMENT FIELD 92 3.6 KINEMATIC EQUATIONS FOR RIGID BODY MOTION 93
3.7 INFINITESIMAL DEFORMATIONS 94 3.8 GEOMETRICAL MEANING OF THE
COMPONENTS OF THE INFINITESIMAL STRAIN TENSOR 99 3.9 PRINCIPAL STRAIN
105 3.10 DILATATION 105 3.11 THE INFINITESIMAL ROTATION TENSOR 106 3.12
TIME RATE OF CHANGE OF A MATERIAL ELEMENT 106 3.13 THE RATE OF
DEFORMATION TENSOR 108 3.14 THE SPIN TENSOR AND THE ANGULAR VELOCITY
VECTOR 111 3.15 EQUATION OF CONSERVATION OF MASS 112 3.16 COMPATIBILITY
CONDITIONS FOR INFINITESIMAL STRAIN COMPONENTS 114 3.17 COMPATIBILITY
CONDITIONS FOR THE RATE OF DEFORMATION COMPONENTS 119 3.18 DEFORMATION
GRADIENT 120 3.19 LOCAL RIGID BODY DISPLACEMENTS 121 3.20 FINITE
DEFORMATION 121 3.21 POLAR DECOMPOSITION THEOREM 124 3.22 CALCULATION OF
THE STRETCH TENSOR FROM THE DEFORMATION GRADIENT 126 3.23 RIGHT
CAUCHY-GREEN DEFORMATION TENSOR 128 3.24 LAGRANGIAN STRAIN TENSOR 134
3.25 LEFT CAUCHY-GREEN DEFORMATION TENSOR 138 3.26 EULERIAN STRAIN
TENSOR 141 3.27 COMPATIBILITY CONDITIONS FOR COMPONENTS OF FINITE
DEFORMATION TENSOR 144 3.28 CHANGE OF AREA DUE TO DEFORMATION 145 3.29
CHANGE OF VOLUME DUE TO DEFORMATION 146 3.30 COMPONENTS OF DEFORMATION
TENSORS IN OTHER COORDINATES 149 3.31 CURRENT CONFIGURATION AS THE
REFERENCE CONFIGURATION 158 PROBLEMS 160 CHAPTER 4 STRESS 173 4.1 STRESS
VECTOR 173 4.2 STRESS TENSOR 174 4.3 COMPONENTS OF STRESS TENSOR 176 4.4
SYMMETRY OF STRESS TENSOR - PRINCIPLE OF MOMENT OF MOMENTUM 178 4.5
PRINCIPAL STRESSES 182 4.6 MAXIMUM SHEARING STRESS 182 4.7 EQUATIONS OF
MOTION - PRINCIPLE OF LINEAR MOMENTUM 187 4.8 EQUATIONS OF MOTION IN
CYLINDRICAL AND SPHERICAL COORDINATES 190 4.9 BOUNDARY CONDITION FOR THE
STRESS TENSOR 192 4.10 PIOLA KIRCHHOFF STRESS TENSORS 195 4.11 EQUATIONS
OF MOTION WRITTEN WITH RESPECT TO THE REFERENCE CONFIGURATION 201 4.12
STRESS POWER 203 4.13 RATE OF HEAT FLOW INTO AN ELEMENT BY CONDUCTION
207 4.14 ENERGY EQUATION 208 4.15 ENTROPY INEQUALITY 209 PROBLEMS 210
CHAPTER 5 THE ELASTIC SOLID 217 5.1 MECHANICAL PROPERTIES 217 5.2 LINEAR
ELASTIC SOLID 220 PART A LINEAR ISOTROPIC ELASTIC SOLID 225 5.3 LINEAR
ISOTROPIC ELASTIC SOLID 225 5.4 YOUNG'S MODULUS, POISSON'S RATIO, SHEAR
MODULUS, AND BULK MODULUS 228 5.5 EQUATIONS OF THE INFINITESIMAL THEORY
OF ELASTICITY 232 5.6 NAVIER EQUATION IN CYLINDRICAL AND SPHERICAL
COORDINATES 236 5.7 PRINCIPLE OF SUPERPOSITION 238 5.8 PLANE
IRROTATIONAL WAVE 238 5.9 PLANE EQUIVOLUMINAL WAVE 242 5.10 REFLECTION
OF PLANE ELASTIC WAVES 248 5.11 VIBRATION OF AN INFINITE PLATE 251 5.12
SIMPLE EXTENSION 254 5.13 TORSION OF A CIRCULAR CYLINDER 258 5.14
TORSION OF A NONCIRCULAR CYLINDER 266 5.15 PURE BENDING OF A BEAM 269
5.16 PLANE STRAIN 275 5.17 PLANE STRAIN PROBLEM IN POLAR COORDINATES 281
5.18 THICK-WALLED CIRCULAR CYLINDER UNDER INTERNAL AND EXTERNAL PRESSURE
284 5.19 PURE BENDING OF A CURVED BEAM 285 5.20 STRESS CONCENTRATION DUE
TO A SMALL CIRCULAR HOLE IN A PLATE UNDER TENSION 287 5.21 HOLLOW SPHERE
SUBJECTED TO INTERNAL AND EXTERNAL PRESSURE 291 PART B LINEAR
ANISOTROPIC ELASTIC SOLID 293 5.22 CONSTITUTIVE EQUATIONS FOR
ANISOTROPIC ELASTIC SOLID 293 5.23 PLANE OF MATERIAL SYMMETRY 296 5.24
CONSTITUTIVE EQUATION FOR A MONOCLINIC ANISOTROPIC ELASTIC SOLID 299
5.25 CONSTITUTIVE EQUATIONS FOR AN ORTHOTROPIC ELASTIC SOLID 301 5.26
CONSTITUTIVE EQUATION FOR A TRANSVERSELY ISOTROPIC ELASTIC MATERIAL 303
5.27 CONSTITUTIVE EQUATION FOR ISOTROPIC ELASTIC SOLID 306 5.28
ENGINEERING CONSTANTS FOR ISOTROPIC ELASTIC SOLID. 307 5.29 ENGINEERING
CONSTANTS FOR TRANSVERSELY ISOTROPIC ELASTIC SOLID 308 5.30 ENGINEERING
CONSTANTS FOR ORTHOTROPIC ELASTIC SOLID 311 5.31 ENGINEERING CONSTANTS
FOR A MONOCLINIC ELASTIC SOLID. 312 PART C CONSTITUTIVE EQUATION FOR
ISOTROPIC ELASTIC SOLID UNDER LARGE DEFORMATION 314 5.32 CHANGE OF FRAME
314 5.33 CONSTITUTIVE EQUATION FOR AN ELASTIC MEDIUM UNDER LARGE
DEFORMATION. 319 5.34 CONSTITUTIVE EQUATION FOR AN ISOTROPIC ELASTIC
MEDIUM 322 5.35 SIMPLE EXTENSION OF AN INCOMPRESSIBLE ISOTROPIC ELASTIC
SOLID 324 5.36 SIMPLE SHEAR OF AN INCOMPRESSIBLE ISOTROPIC ELASTIC
RECTANGULAR BLOCK 325 5.37 BENDING OF A INCOMPRESSIBLE RECTANGULAR BAR.
327 5.38 TORSION AND TENSION OF AN INCOMPRESSIBLE SOLID CYLINDER 331
PROBLEMS 335 CHAPTER 6 NEWTONIAN VISCOUS FLUID 348 6.1 FLUIDS 348 6.2
COMPRESSIBLE AND INCOMPRESSIBLE FLUIDS 349 6.3 EQUATIONS OF HYDROSTATICS
350 6.4 NEWTONIAN FLUID 355 6.5 INTERPRETATION OF LAMBDA AND * 357 6.6
INCOMPRESSIBLE NEWTONIAN FLUID 359 6.7 NAVIER-STOKES EQUATION FOR
INCOMPRESSIBLE FLUIDS 360 6.8 NAVIER-STOKES EQUATIONS FOR IN
COMPRESSIBLE FLUIDS IN CYLINDRICAL AND SPHERICAL COORDINATES 364 6.9
BOUNDARY CONDITIONS 365 6.10 STREAMLINE, PATHLINE, STREAKLINE, STEADY,
UNSTEADY, LAMINAR AND TURBULENT FLOW 366 6.11 PLANE COUETTE FLOW 371
6.12 PLANE POISEUILLE FLOW 372 6.13 HAGEN POISEUILLE FLOW 374 6.14 PLANE
COUETTE FLOW OF TWO LAYERS OF INCOMPRESSIBLE FLUIDS 377 6.15 COUETTE
FLOW 380 6.16 FLOW NEAR AN OSCILLATING PLATE 381 6.17 DISSIPATION
FUNCTIONS FOR NEWTONIAN FLUIDS 383 6.18 ENERGY EQUATION FOR A NEWTONIAN
FLUID 384 6.19 VORTICITY VECTOR 387 6.20 IRROTATIONAL FLOW 390 6.21
IRROTATIONAL FLOW OF AN INVISCID, INCOMPRESSIBLE FLUID OF HOMOGENEOUS
DENSITY 391 6.22 IRROTATIONAL FLOWS AS SOLUTIONS OF NAVIER-STOKES
EQUATION 394 6.23 VORTICITY TRANSPORT EQUATION FOR INCOMPRESSIBLE
VISCOUS FLUID WITH A CONSTANT DENSITY 396 6.24 CONCEPT OF A BOUNDARY
LAYER 399 6.25 COMPRESSIBLE NEWTONIAN FLUID 401 6.26 ENERGY EQUATION IN
TERMS OF ENTHALPY 402 6.27 ACOUSTIC WAVE 404 6.28 IRROTATIONAL,
BAROTROPIC FLOWS OF INVISCID COMPRESSIBLE FLUID 408 6.29 ONE-DIMENSIONAL
FLOW OF A COMPRESSIBLE FLUID 412 PROBLEMS 419 CHAPTER 7 INTEGRAL
FORMULATION OF GENERAL PRINCIPLES 427 7.1 GREEN'S THEOREM 427 7.2
DIVERGENCE THEOREM 430 7.3 INTEGRALS OVER A CONTROL VOLUME AND INTEGRALS
OVER A MATERIAL VOLUME 433 7.4 REYNOLDS TRANSPORT THEOREM 435 7.5
PRINCIPLE OF CONSERVATION OF MASS 437 7.6 PRINCIPLE OF LINEAR MOMENTUM
440 7.7 MOVING FRAMES 447 7.8 CONTROL VOLUME FIXED WITH RESPECT TO A
MOVING FRAME 449 7.9 PRINCIPLE OF MOMENT OF MOMENTUM 451 7.10 PRINCIPLE
OF CONSERVATION OF ENERGY 454 PROBLEMS 458 CHAPTER 8 NON-NEWTONIAN
FLUIDS 462 PART A LINEAR VISCOELASTIC FLUID 464 8.1 LINEAR MAXWELL FLUID
464 8.2 GENERALIZED LINEAR MAXWELL FLUID WITH DISCRETE RELAXATION
SPECTRA 471 8.3 INTEGRAL FORM OF THE LINEAR MAXWELL FLUID AND OF THE
GENERALIZED LINEAR MAXWELL FLUID WITH DISCRETE RELAXATION SPECTRA 473
8.4 GENERALIZED LINEAR MAXWELL FLUID WITH A CONTINUOUS RELAXATION
SPECTRUM 474 PARTB NONLINEAR VISCOELASTIC FLUID 476 8.5 CURRENT
CONFIGURATION AS REFERENCE CONFIGURATION 476 8.6 RELATIVE DEFORMATION
GRADIENT 477 8.7 RELATIVE DEFORMATION TENSORS 478 8.8 CALCULATIONS OF
THE RELATIVE DEFORMATION TENSOR 480 8.9 HISTORY OF DEFORMATION TENSOR.
RIVLIN-ERICKSEN TENSORS 486 8.10 RIVLIN-ERICKSEN TENSOR IN TERMS OF
VELOCITY GRADIENTS - THE RECURSIVE FORMULAS 491 8.11 RELATION BETWEEN
VELOCITY GRADIENT AND DEFORMATION GRADIENT 493 8.12 TRANSFORMATION LAWS
FOR THE RELATIVE DEFORMATION TENSORS UNDER A CHANGE OF FRAME 494 8.13
TRANSFORMATION LAW FOR THE RIVLIN-ERICKSEN TENSORS UNDER A CHANGE OF
FRAME 496 8.14 INCOMPRESSIBLE SIMPLE FLUID 497 8.15 SPECIAL SINGLE
INTEGRAL TYPE NONLINEAR CONSTITUTIVE EQUATIONS 498 8.16 GENERAL SINGLE
INTEGRAL TYPE NONLINEAR CONSTITUTIVE EQUATIONS 503 8.17 DIFFERENTIAL
TYPE CONSTITUTIVE EQUATIONS 503 8.18 OBJECTIVE RATE OF STRESS 506 8.19
THE RATE TYPE CONSTITUTIVE EQUATIONS 511 PART C VISCOMETRIC FLOW OF
SIMPLE FLUID 516 8.20 VISCOMETRIC FLOW 516 8.21 STRESSES IN VISCOMETRIC
FLOW OF AN INCOMPRESSIBLE SIMPLE FLUID 520 8.22 CHANNEL FLOW 523 8.23
COUETTE FLOW 526 PROBLEMS 532 APPENDIX: MATRICES 537 ANSWER TO PROBLEMS
543 REFERENCES 550 INDEX 552 |
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| author | Lai, Wei M. Rubin, David Krempl, Erhard |
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| ctrlnum | (OCoLC)28633506 (DE-599)BVBBV021918798 |
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| dewey-ones | 531 - Classical mechanics |
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| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:05:39Z |
| indexdate | 2024-07-09T20:47:23Z |
| institution | BVB |
| isbn | 0080417000 0080417019 |
| language | English |
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| physical | XIV, 556 S. graph. Darst. |
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| spelling | Lai, Wei M. Verfasser aut Introduction to continuum mechanics Wei Michael Lai ; David Rubin ; Erhard Krempl 3. ed. Oxford [u.a.] Pergamon Press 1993 XIV, 556 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors in introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples and problems, many with solutions Through the addition of more advanced material, this popular introduction to modern continuum mechanics has been fully revised to serve a dual purpose for introductory courses in undergraduate engineering curriculum, and for beginning graduate courses Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Rubin, David Verfasser aut Krempl, Erhard Verfasser (DE-588)105990884 aut OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015133966&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lai, Wei M. Rubin, David Krempl, Erhard Introduction to continuum mechanics Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4032296-8 (DE-588)4143389-0 (DE-588)4123623-3 |
| title | Introduction to continuum mechanics |
| title_auth | Introduction to continuum mechanics |
| title_exact_search | Introduction to continuum mechanics |
| title_exact_search_txtP | Introduction to continuum mechanics |
| title_full | Introduction to continuum mechanics Wei Michael Lai ; David Rubin ; Erhard Krempl |
| title_fullStr | Introduction to continuum mechanics Wei Michael Lai ; David Rubin ; Erhard Krempl |
| title_full_unstemmed | Introduction to continuum mechanics Wei Michael Lai ; David Rubin ; Erhard Krempl |
| title_short | Introduction to continuum mechanics |
| title_sort | introduction to continuum mechanics |
| topic | Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Continuum mechanics Kontinuumsmechanik Aufgabensammlung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015133966&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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