Continuum mechanics using Mathematica: fundamentals, applications and scientific computing
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
2006
|
| Series: | Modeling and simulation in science, engineering and technology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 388 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9780817632403 0817632409 |
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| adam_text | ANTONIO ROMANO RENATO LANCELLOTTA ADDOLORATA MARASCO CONTINUUM MECHANICS
USING MATHEMATICA FUNDAMENTALS, APPLICATIONS AND SCIENTIFIC COMPUTING
BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE IX 1 ELEMENTS OF
LINEAR ALGEBRA 1 1.1 MOTIVATION TO STUDY LINEAR ALGEBRA 1 1.2 VECTOR
SPACES AND BASES 2 1.3 EUCLIDEAN VECTOR SPACE 5 1.4 BASE CHANGES 9 1.5
VECTOR PRODUCT 11 1.6 MIXED PRODUCT 13 1.7 ELEMENTS OF TENSOR ALGEBRA 14
1.8 EIGENVALUES AND EIGENVECTORS OF A EUCLIDEAN SECOND-ORDER TENSOR 20
1.9 ORTHOGONAL TENSORS 24 1.10 CAUCHY S POLAR DECOMPOSITION THEOREM 28
1.11 HIGHER ORDER TENSORS 29 1.12 EUCLIDEAN POINT SPACE 30 1.13
EXERCISES 32 1.14 THE PROGRAM VECTORSYS 36 1.15 THE PROGRAM
EIGENSYSTEMAG 41 2 VECTOR ANALYSIS 45 2.1 CURVILINEAR COORDINATES 45 2.2
EXAMPLES OF CURVILINEAR COORDINATES 48 2.3 DIFFERENTIATION OF VECTOR
FIELDS 50 2.4 THE STOKES AND GAUSS THEOREMS 55 2.5 SINGULAR SURFACES 56
2.6 USEFUL FORMULAE 60 2.7 SOME CURVILINEAR COORDINATES 62 2.7.1
GENERALIZED POLAR COORDINATES 63 2.7.2 CYLINDRICAL COORDINATES 64 2.7.3
SPHERICAL COORDINATES 65 2.7.4 ELLIPTIC COORDINATES 66 VI CONTENTS 2.7.5
PARABOLIC COORDINATES 67 2.7.6 BIPOLAR COORDINATES 68 2.7.7 PROLATE AND
OBLATE SPHEROIDAL COORDINATES 68 2.7.8 PARABOLOIDAL COORDINATES 69 2.8
EXERCISES 69 2.9 THE PROGRAM OPERATOR 70 3 FINITE AND INFINITESIMAL
DEFORMATIONS 77 3.1 DEFORMATION GRADIENT 77 3.2 STRETCH RATIO AND
ANGULAR DISTORTION 80 3.3 INVARIANTS OF C AND B 83 3.4 DISPLACEMENT AND
DISPLACEMENT GRADIENT 84 3.5 INFINITESIMAL DEFORMATION THEORY 86 3.6
TRANSFORMATION RULES FOR DEFORMATION TENSORS 88 3.7 SOME RELEVANT
FORMULAE 89 3.8 COMPATIBILITY CONDITIONS 92 3.9 CURVILINEAR COORDINATES
95 3.10 EXERCISES 96 3.11 THE PROGRAM DEFORMATION 101 4 KINEMATICS 109
4.1 VELOCITY AND ACCELERATION 109 4.2 VELOCITY GRADIENT 112 4.3 RIGID,
IRROTATIONAL, AND ISOCHORIC MOTIONS 113 4.4 TRANSFORMATION RULES FOR A
CHANGE OF FRAME 115 4.5 SINGULAR MOVING SURFACES 116 4.6 TIME DERIVATIVE
OF A MOVING VOLUME 119 4.7 WORKED EXERCISES 123 4.8 THE PROGRAM VELOCITY
126 5 BALANCE EQUATIONS 131 5.1 GENERAL FORMULATION OF A BALANCE
EQUATION 131 5.2 MASS CONSERVATION . . . 136 5.3 MOMENTUM BALANCE
EQUATION 137 5.4 BALANCE OF ANGULAR MOMENTUM 140 5.5 ENERGY BALANCE 141
5.6 ENTROPY INEQUALITY 143 5.7 LAGRANGIAN FORMULATION OF BALANCE
EQUATIONS 146 5.8 THE PRINCIPLE OF VIRTUAL DISPLACEMENTS 150 5.9
EXERCISES 151 CONTENTS VII CONSTITUTIVE EQUATIONS 155 6.1 CONSTITUTIVE
AXIOMS 155 6.2 THERMOVISCOELASTIC BEHAVIOR 160 6.3 LINEAR
THERMOELASTICITY 165 6.4 EXERCISES 169 SYMMETRY GROUPS: SOLIDS AND
FLUIDS 171 7.1 SYMMETRY 171 7.2 ISOTROPIC SOLIDS 174 7.3 PERFECT AND
VISCOUS FLUIDS 177 7.4 ANISOTROPIC SOLIDS 181 7.5 EXERCISES 183 7.6 THE
PROGRAM LINELASTICITYTENSOR 185 WAVE PROPAGATION 189 8.1 INTRODUCTION
189 8.2 CAUCHY S PROBLEM FOR SECOND-ORDER PDES 190 8.3 CHARACTERISTICS
AND CLASSIFICATION OF PDES 194 8.4 EXAMPLES 196 8.5 CAUCHY S PROBLEM FOR
A QUASI-LINEAR FIRST-ORDER SYSTEM . 199 8.6 CLASSIFICATION OF
FIRST-ORDER SYSTEMS 201 8.7 EXAMPLES 202 8.8 SECOND-ORDER SYSTEMS 206
8.9 ORDINARY WAVES 207 8.10 LINEARIZED THEORY AND WAVES 211 8.11
SHOCKWAVES 215 8.12 EXERCISES 218 8.13 THE PROGRAM PDEEQCLASS 221 8.14
THE PROGRAM PDESYSCLASS 227 8.15 THE PROGRAM WAVESI 233 8.16 THE PROGRAM
WAVESII 239 FLUID MECHANICS 245 9.1 PERFECT FLUID 245 9.2 STEVINO S LAW
AND ARCHIMEDES PRINCIPLE 246 9.3 FUNDAMENTAL THEOREMS OF FLUID DYNAMICS
250 9.4 BOUNDARY VALUE PROBLEMS FOR A PERFECT FLUID 254 9.5 2D STEADY
FLOW OF A PERFECT FLUID 256 9.6 D ALEMBERT S PARADOX AND THE
KUTTA-JOUKOWSKY THEOREM 264 9.7 LIFT AND AIRFOILS 267 9.8 NEWTONIAN
FLUIDS 272 9.9 APPLICATIONS OF THE NAVIER-STOKES EQUATION 273 9.10
DIMENSIONAL ANALYSIS AND THE NAVIER-STOKES EQUATION . . . 274 9.11
BOUNDARY LAYER 276 CONTENTS 9.12 MOTION OF A VISCOUS LIQUID AROUND AN
OBSTACLE 281 9.13 ORDINARY WAVES IN PERFECT FLUIDS 287 9.14 SHOCK WAVES
IN FLUIDS 290 9.15 SHOCK WAVES IN A PERFECT GAS 293 9.16 EXERCISES 296
9.17 THE PROGRAM POTENTIAL 298 9.18 THE PROGRAM WING 306 9.19 THE
PROGRAM JOUKOWSKY 309 9.20 THE PROGRAM JOUKOWSKYMAP 312 10 LINEAR
ELASTICITY 317 10.1 BASIC EQUATIONS OF LINEAR ELASTICITY 317 10.2
UNIQUENESS THEOREMS 321 10.3 EXISTENCE AND UNIQUENESS OF EQUILIBRIUM
SOLUTIONS 323 10.4 EXAMPLES OF DEFORMATIONS 327 10.5 THE
BOUSSINESQ-PAPKOVICH-NEUBER SOLUTION 329 10.6 SAINT-VENANT S CONJECTURE
330 10.7 THE FUNDAMENTAL SAINT-VENANT SOLUTIONS 335 10.8 ORDINARY WAVES
IN ELASTIC SYSTEMS 339 10.9 PLANE WAVES 345 10.10 REFLECTION OF PLANE
WAVES IN A HALF-SPACE 350 10.11 RAYLEIGH WAVES 356 10.12 REFLECTION AND
REFRACTION OF SH WAVES 359 10.13 HARMONIC WAVES IN A LAYER 362 10.14
EXERCISES 365 11 OTHER APPROACHES TO THERMODYNAMICS 367 11.1 BASIC
THERMODYNAMICS 367 11.2 EXTENDED THERMODYNAMICS 370 11.3 SERRIN S
APPROACH 372 11.4 AN APPLICATION TO VISCOUS FLUIDS 375 REFERENCES 379
INDEX 383
|
| adam_txt |
ANTONIO ROMANO RENATO LANCELLOTTA ADDOLORATA MARASCO CONTINUUM MECHANICS
USING MATHEMATICA FUNDAMENTALS, APPLICATIONS AND SCIENTIFIC COMPUTING
BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE IX 1 ELEMENTS OF
LINEAR ALGEBRA 1 1.1 MOTIVATION TO STUDY LINEAR ALGEBRA 1 1.2 VECTOR
SPACES AND BASES 2 1.3 EUCLIDEAN VECTOR SPACE 5 1.4 BASE CHANGES 9 1.5
VECTOR PRODUCT 11 1.6 MIXED PRODUCT 13 1.7 ELEMENTS OF TENSOR ALGEBRA 14
1.8 EIGENVALUES AND EIGENVECTORS OF A EUCLIDEAN SECOND-ORDER TENSOR 20
1.9 ORTHOGONAL TENSORS 24 1.10 CAUCHY'S POLAR DECOMPOSITION THEOREM 28
1.11 HIGHER ORDER TENSORS 29 1.12 EUCLIDEAN POINT SPACE 30 1.13
EXERCISES 32 1.14 THE PROGRAM VECTORSYS 36 1.15 THE PROGRAM
EIGENSYSTEMAG 41 2 VECTOR ANALYSIS 45 2.1 CURVILINEAR COORDINATES 45 2.2
EXAMPLES OF CURVILINEAR COORDINATES 48 2.3 DIFFERENTIATION OF VECTOR
FIELDS 50 2.4 THE STOKES AND GAUSS THEOREMS 55 2.5 SINGULAR SURFACES 56
2.6 USEFUL FORMULAE 60 2.7 SOME CURVILINEAR COORDINATES 62 2.7.1
GENERALIZED POLAR COORDINATES 63 2.7.2 CYLINDRICAL COORDINATES 64 2.7.3
SPHERICAL COORDINATES 65 2.7.4 ELLIPTIC COORDINATES 66 VI CONTENTS 2.7.5
PARABOLIC COORDINATES 67 2.7.6 BIPOLAR COORDINATES 68 2.7.7 PROLATE AND
OBLATE SPHEROIDAL COORDINATES 68 2.7.8 PARABOLOIDAL COORDINATES 69 2.8
EXERCISES 69 2.9 THE PROGRAM OPERATOR 70 3 FINITE AND'INFINITESIMAL
DEFORMATIONS 77 3.1 DEFORMATION GRADIENT 77 3.2 STRETCH RATIO AND
ANGULAR DISTORTION 80 3.3 INVARIANTS OF C AND B 83 3.4 DISPLACEMENT AND
DISPLACEMENT GRADIENT 84 3.5 INFINITESIMAL DEFORMATION THEORY 86 3.6
TRANSFORMATION RULES FOR DEFORMATION TENSORS 88 3.7 SOME RELEVANT
FORMULAE 89 3.8 COMPATIBILITY CONDITIONS 92 3.9 CURVILINEAR COORDINATES
95 3.10 EXERCISES 96 3.11 THE PROGRAM DEFORMATION 101 4 KINEMATICS 109
4.1 VELOCITY AND ACCELERATION 109 4.2 VELOCITY GRADIENT 112 4.3 RIGID,
IRROTATIONAL, AND ISOCHORIC MOTIONS 113 4.4 TRANSFORMATION RULES FOR A
CHANGE OF FRAME 115 4.5 SINGULAR MOVING SURFACES 116 4.6 TIME DERIVATIVE
OF A MOVING VOLUME 119 4.7 WORKED EXERCISES 123 4.8 THE PROGRAM VELOCITY
126 5 BALANCE EQUATIONS 131 5.1 GENERAL FORMULATION OF A BALANCE
EQUATION 131 5.2 MASS CONSERVATION . . . 136 5.3 MOMENTUM BALANCE
EQUATION 137 5.4 BALANCE OF ANGULAR MOMENTUM 140 5.5 ENERGY BALANCE 141
5.6 ENTROPY INEQUALITY 143 5.7 LAGRANGIAN FORMULATION OF BALANCE
EQUATIONS 146 5.8 THE PRINCIPLE OF VIRTUAL DISPLACEMENTS 150 5.9
EXERCISES 151 CONTENTS VII CONSTITUTIVE EQUATIONS 155 6.1 CONSTITUTIVE
AXIOMS 155 6.2 THERMOVISCOELASTIC BEHAVIOR 160 6.3 LINEAR
THERMOELASTICITY 165 6.4 EXERCISES 169 SYMMETRY GROUPS: SOLIDS AND
FLUIDS 171 7.1 SYMMETRY 171 7.2 ISOTROPIC SOLIDS 174 7.3 PERFECT AND
VISCOUS FLUIDS 177 7.4 ANISOTROPIC SOLIDS 181 7.5 EXERCISES 183 7.6 THE
PROGRAM LINELASTICITYTENSOR 185 WAVE PROPAGATION 189 8.1 INTRODUCTION
189 8.2 CAUCHY'S PROBLEM FOR SECOND-ORDER PDES 190 8.3 CHARACTERISTICS
AND CLASSIFICATION OF PDES 194 8.4 EXAMPLES 196 8.5 CAUCHY'S PROBLEM FOR
A QUASI-LINEAR FIRST-ORDER SYSTEM . 199 8.6 CLASSIFICATION OF
FIRST-ORDER SYSTEMS 201 8.7 EXAMPLES 202 8.8 SECOND-ORDER SYSTEMS 206
8.9 ORDINARY WAVES 207 8.10 LINEARIZED THEORY AND WAVES 211 8.11
SHOCKWAVES 215 8.12 EXERCISES 218 8.13 THE PROGRAM PDEEQCLASS 221 8.14
THE PROGRAM PDESYSCLASS 227 8.15 THE PROGRAM WAVESI 233 8.16 THE PROGRAM
WAVESII 239 FLUID MECHANICS 245 9.1 PERFECT FLUID 245 9.2 STEVINO'S LAW
AND ARCHIMEDES' PRINCIPLE 246 9.3 FUNDAMENTAL THEOREMS OF FLUID DYNAMICS
250 9.4 BOUNDARY VALUE PROBLEMS FOR A PERFECT FLUID 254 9.5 2D STEADY
FLOW OF A PERFECT FLUID 256 9.6 D'ALEMBERT'S PARADOX AND THE
KUTTA-JOUKOWSKY THEOREM 264 9.7 LIFT AND AIRFOILS 267 9.8 NEWTONIAN
FLUIDS 272 9.9 APPLICATIONS OF THE NAVIER-STOKES EQUATION 273 9.10
DIMENSIONAL ANALYSIS AND THE NAVIER-STOKES EQUATION . . . 274 9.11
BOUNDARY LAYER 276 CONTENTS 9.12 MOTION OF A VISCOUS LIQUID AROUND AN
OBSTACLE 281 9.13 ORDINARY WAVES IN PERFECT FLUIDS 287 9.14 SHOCK WAVES
IN FLUIDS 290 9.15 SHOCK WAVES IN A PERFECT GAS 293 9.16 EXERCISES 296
9.17 THE PROGRAM POTENTIAL 298 9.18 THE PROGRAM WING 306 9.19 THE
PROGRAM JOUKOWSKY 309 9.20 THE PROGRAM JOUKOWSKYMAP 312 10 LINEAR
ELASTICITY 317 10.1 BASIC EQUATIONS OF LINEAR ELASTICITY 317 10.2
UNIQUENESS THEOREMS 321 10.3 EXISTENCE AND UNIQUENESS OF EQUILIBRIUM
SOLUTIONS 323 10.4 EXAMPLES OF DEFORMATIONS 327 10.5 THE
BOUSSINESQ-PAPKOVICH-NEUBER SOLUTION 329 10.6 SAINT-VENANT'S CONJECTURE
330 10.7 THE FUNDAMENTAL SAINT-VENANT SOLUTIONS 335 10.8 ORDINARY WAVES
IN ELASTIC SYSTEMS 339 10.9 PLANE WAVES 345 10.10 REFLECTION OF PLANE
WAVES IN A HALF-SPACE 350 10.11 RAYLEIGH WAVES 356 10.12 REFLECTION AND
REFRACTION OF SH WAVES 359 10.13 HARMONIC WAVES IN A LAYER 362 10.14
EXERCISES 365 11 OTHER APPROACHES TO THERMODYNAMICS 367 11.1 BASIC
THERMODYNAMICS 367 11.2 EXTENDED THERMODYNAMICS 370 11.3 SERRIN'S
APPROACH 372 11.4 AN APPLICATION TO VISCOUS FLUIDS 375 REFERENCES 379
INDEX 383 |
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| id | DE-604.BV021525413 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:23:45Z |
| indexdate | 2024-07-09T20:37:49Z |
| institution | BVB |
| isbn | 9780817632403 0817632409 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014741852 |
| oclc_num | 64163728 |
| open_access_boolean | |
| owner | DE-703 DE-634 DE-91G DE-BY-TUM DE-83 DE-11 |
| owner_facet | DE-703 DE-634 DE-91G DE-BY-TUM DE-83 DE-11 |
| physical | XII, 388 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Modeling and simulation in science, engineering and technology |
| spelling | Romano, Antonio Verfasser aut Continuum mechanics using Mathematica fundamentals, applications and scientific computing Antonio Romano ; Renato Lancellotta ; Addolorata Marasco Boston ; Basel ; Berlin Birkhäuser 2006 XII, 388 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Modeling and simulation in science, engineering and technology Mathematica (Computer file) Datenverarbeitung Continuum mechanics Data processing Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s Mathematica Programm (DE-588)4268208-3 s DE-604 Lancellotta, Renato Verfasser aut Marasco, Addolorata 1972- Verfasser (DE-588)123267722 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014741852&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Romano, Antonio Lancellotta, Renato Marasco, Addolorata 1972- Continuum mechanics using Mathematica fundamentals, applications and scientific computing Mathematica (Computer file) Datenverarbeitung Continuum mechanics Data processing Mathematica Programm (DE-588)4268208-3 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4268208-3 (DE-588)4032296-8 |
| title | Continuum mechanics using Mathematica fundamentals, applications and scientific computing |
| title_auth | Continuum mechanics using Mathematica fundamentals, applications and scientific computing |
| title_exact_search | Continuum mechanics using Mathematica fundamentals, applications and scientific computing |
| title_exact_search_txtP | Continuum mechanics using Mathematica fundamentals, applications and scientific computing |
| title_full | Continuum mechanics using Mathematica fundamentals, applications and scientific computing Antonio Romano ; Renato Lancellotta ; Addolorata Marasco |
| title_fullStr | Continuum mechanics using Mathematica fundamentals, applications and scientific computing Antonio Romano ; Renato Lancellotta ; Addolorata Marasco |
| title_full_unstemmed | Continuum mechanics using Mathematica fundamentals, applications and scientific computing Antonio Romano ; Renato Lancellotta ; Addolorata Marasco |
| title_short | Continuum mechanics using Mathematica |
| title_sort | continuum mechanics using mathematica fundamentals applications and scientific computing |
| title_sub | fundamentals, applications and scientific computing |
| topic | Mathematica (Computer file) Datenverarbeitung Continuum mechanics Data processing Mathematica Programm (DE-588)4268208-3 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Mathematica (Computer file) Datenverarbeitung Continuum mechanics Data processing Mathematica Programm Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014741852&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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