Classical and computational solid mechanics:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific
[2017]
|
| Edition: | Second edition |
| Series: | Advanced series in engineering science
Volume 2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxi, 838 Seiten Diagramme |
| ISBN: | 9789814713658 9789814713641 |
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| 100 | 1 | |a Fung, Yuan-cheng |d 1919-2019 |e Verfasser |0 (DE-588)124296920 |4 aut | |
| 245 | 1 | 0 | |a Classical and computational solid mechanics |c Y.C. Fung, University of California, San Diego, USA; Pin Tong, University of California, San Diego, USA & Hong Kong University of Science and Technology, Hong Kong, China; Xiaohong Chen, UTC Aerospace Systems, USA |
| 250 | |a Second edition | ||
| 264 | 1 | |a New Jersey |b World Scientific |c [2017] | |
| 264 | 4 | |c © 2017 | |
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| 700 | 1 | |a Tong, Pin |e Verfasser |4 aut | |
| 700 | 1 | |a Chen, Xiaohong |e Verfasser |4 aut | |
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| adam_text | Titel: Classical and computational solid mechanics
Autor: Fung, Yuan-cheng
Jahr: 2017
CONTENTS
PREFACE TO THE SECOND EDITION vii
1 INTRODUCTION 1
1.1. Hooke s Law 2
1.2. Plasticity and Viscoelasticity 8
1.3. Vibrations 8
1.4. Prototype of Wave Dynamics 11
1.5. Biomechanics 14
1.6. Historical Remarks 17
2 TENSOR ANALYSIS 22
2.1. Notation and Summation Convention 22
2.2. Coordinate Transformation 24
2.3. Euclidean Metric Tensor 26
2.4. Scalars, Contravariant Vectors, Covariant Vectors 29
2.5. Tensor Fields of Higher Rank 30
2.6. Some Important Special Tensors 31
2.7. The Significance of Tensor Characteristics 32
2.8. Rectangular Cartesian Tensors 33
2.9. Contraction 34
2.10. Quotient Rule 35
2.11. Partial Derivatives in Cartesian Coordinates 36
2.12. Covariant Differentiation of Vector Fields 37
2.13. Tensor Equations 39
2.14. Geometric Interpretation of Tensor Components 41
2.15. Geometric Interpretation of Covariant Derivatives 47
2.16. Physical Components of a Vector 48
3 STRESS TENSOR 53
3.1. Stresses 53
3.2. Laws of Motion 56
3.3. Cauchy s Formula 57
3.4. Equations of Equilibrium 60
xii CONTENTS
3.5. Transformation of Coordinates 64
3.6. Plane State of Stress 66
3.7. Principal Stresses 68
3.8. Shearing Stresses 71
3.9. Mohr s Circles 72
3.10. Stress Deviations 72
3.11. Octahedral Shearing Stress 73
3.12. Stress Tensor in General Coordinates 75
3.13. Physical Components of a Stress Tensor in General
Coordinates 7»
3.14. Equations of Equilibrium in Curvilinear Coordinates 80
82
82
85
ANALYSIS OF STRAIN
4.1. Deformation
4.2. Strain Tensors in Rectangular Cartesian Coordinates
4.3. Geometric Interpretation of Infinitesimal Strain
Components °
4.4. Rotation 88
4.5. Finite Strain Components
90
96
99
4.6. Compatibility of Strain Components ^2
4.7. Multiply Connected Regions
4.8. Multivalued Displacements
4.9. Properties of the Strain Tensor ^
4.10. Physical Components l^fô
4.11. Example - Spherical Coordinates 105
4.12. Example - Cylindrical Polar Coordinates ^
5 CONSERVATION LAWS 108
5.1. Gauss Theorem 108
5.2. Material and Spatial Description of Changing
Configurations 109
5.3. Material Derivative of Volume Integral 112
5.4. The Equation of Continuity 113
5.5. The Equations of Motion 114
5.6. Moment of Momentum 115
5.7. Other Field Equations 116
CONTENTS xiii
6 ELASTIC AND PLASTIC BEHAVIOR OF MATERIALS 118
6.1. Generalized Hooke s Law 118
6.2. Stress-Strain Relationship for Isotropic Elastic Materials 119
6.3. Ideal Plastic Solids 122
6.4. Some Experimental Information 128
6.5. A Basic Assumption of the Mathematical Theory of
Plasticity: Existence of Yield Function 132
6.6. Loading and Unloading Criteria 133
6.7. Isotropic Stress Theories of Yield Function 134
6.8. Further Examples of Yield Functions 136
6.9. Work Hardening - Drucker s Hypothesis and Definition 141
6.10. Ideal Plasticity 142
6.11. Flow Rule for Work Hardening Materials 145
6.12. Subsequent Loading Surfaces - Isotropic and Kinematic
Hardening Rules 150
6.13. Mroz s, Dafalias and Popov s, and Valanis Plasticity
Theories 160
6.14. Strain Space Formulations 165
6.15. Deformation Theory of Plasticity 169
6.16. Finite Deformation 170
6.17. Plastic Deformation of Crystals 170
7 LINEARIZED THEORY OF ELASTICITY 173
7.1. Basic Equations of Elasticity 173
7.2. Equilibrium Under Zero Body Force 175
7.3. Boundary Value Problems 176
7.4. Equilibrium and Uniqueness of Solutions 179
7.5. Saint-Venant s Theory of Torsion 182
7.6. Soap Film Analogy 190
7.7. Bending of Beams 191
7.8. Plane Elastic Waves 196
7.9. Rayleigh Surface Waves 197
7.10. Love Waves 201
8 SOLUTION OF PROBLEMS IN LINEARIZED
THEORY OF ELASTICITY BY POTENTIALS 204
8.1. Scalar and Vector Potentials for Displacement Vector Fields 204
8.2. Equations of Motion in Terms of Displacement Potentials 206
xiv CONTENTS
8.3. Strain Potential 208
8.4. Galerkin Vector 210
8.5. Equivalent Galerkin Vectors 212
8.6. Example - Vertical Load on the Horizontal Surface of a
Semi-Infinite Solid 213
8.7. Love s Strain Function 215
8.8. Kelvin s Problem - A Single Force Acting in the
Interior of an Infinite Solid 216
8.9. Perturbation of Elasticity Solutions by a Change of
Poisson s Ratio 219
8.10. Boussinesq s Problem 222
8.11. On Biharmonic Functions 223
8.12. Neuber-Papkovich Representation 226
8.13. Reflection and Refraction of Plane P and S Waves 228
8.14. Lamb s Problem - Line Load Suddenly Applied on
Elastic Half-Space 230
9 TWO-DIMENSIONAL PROBLEMS IN LINEARIZED
THEORY OF ELASTICITY 236
9.1. Plane State of Stress or Strain 236
9.2. Airy Stress Functions for 2-D Problems 238
9.3. Airy Stress Function in Polar Coordinates 243
9.4. General Case 248
9.5. Representation of Two-Dimensional Biharmonic Functions
by Analytic Functions of a Complex Variable 252
9.6. Kolosoff-Muskhelishvili Method 253
10 VARIATIONAL CALCULUS, ENERGY THEOREMS,
SAINT-VENANT S PRINCIPLE 264
10.1. Minimization of Functionals 264
10.2. Functional Involving Higher Derivatives of the Dependent
Variable 269
10.3. Several Unknown Functions 270
10.4. Several Independent Variables 272
10.5. Subsidiary Conditions - Lagrange multipliers 274
10.6. Natural Boundary Conditions 277
10.7. Theorem of Minimum Potential Energy Under Small
Variations of Displacements 278
CONTENTS xv
10.8. Example of Application: Static Loading on a Beam -
Natural and Rigid End Conditions 282
10.9. The Complementary Energy Theorem Under Small
Variations of Stresses 286
10.10. Variational Functionals Frequently Used in Computational
Mechanics 292
10.11. Saint-Venant s Principle 298
10.12. Saint-Venant s Principle -
Boussinesq-Von Mises-Sternberg Formulation 301
10.13. Practical Applications of Saint-Venant s Principle 304
10.14. Extremum Principles for Plasticity 307
10.15. Limit Analysis 310
11 HAMILTON S PRINCIPLE, WAVE PROPAGATION,
APPLICATIONS OF GENERALIZED COORDINATES 319
11.1. Hamilton s Principle 319
11.2. Example of Application - Equation of Vibration of a
Beam 322
11.3. Group Velocity 331
11.4. Hopkinson s Experiment 334
11.5. Generalized Coordinates 336
11.6. Approximate Representation of Functions 337
11.7. Approximate Solution of Differential Equations 339
11.8. Direct Methods of Variational Calculus 339
12 THERMODYNAMICS AND THERMOELASTICITY 344
12.1. Laws of Thermodynamics 344
12.2. Energy Equation 348
12.3. Stability Conditions of Thermodynamic Systems 350
12.4. Irreversible Thermodynamics 351
12.5. Phenomenological Relations - Onsager Principle 354
12.6. Basic Equations of Thermomechanics 357
12.7. Energy Density Function and Dissipation Potential for
Hyper-Thermoelasticity 358
12.8. Coupled Thermoelastic Constitutive Relations 360
12.9. Strain and Complementary Energy Functions 362
12.10. Thermal Effects: Kelvin s Formula 364
12.11. Uncoupled, Quasi-Static Thermoelastic Theory 365
xvi CONTENTS
12.12. Plane Strain (Plane Stress) 369
12.13. Variational Principle for Uncoupled Thermoelasticity 372
12.14. Variational Principle for Coupled Thermoelasticity 376
12.15. Lagrangian Equations for Heat Conduction and
Thermoelasticity 378
13 LARGE DEFORMATION 383
13.1. Coordinate Systems and Tensor Notation 383
13.2. Deformation Gradient 388
13.3. Strains 390
13.4. Right and Left Stretch and Rotation Tensors 392
13.5. Strain Rates 393
13.6. Material Derivatives of Line, Area and Volume Elements 394
13.7. Stresses 396
13.8. Example: Combined Tension and Torsion Loads 402
13.9. Objectivity 406
13.10. Equation of Motion 410
13.11. Constitutive Equations of Thermoelastic Bodies 412
13.12. Variational Principles for Nonlinear Elasticity:
Compressible Materials 424
13.13. Variational Principles for Nonlinear Elasticity:
Nearly Incompressible or Incompressible Materials 428
13.14. Small Deflection of Thin Plates 432
13.15. Large Deflections of Plates 438
14 VISCOELASTICITY AND
THERMOVISCOELASTICITY 444
14.1. Linear Solids with Memory 444
14.2. Anisotropic Linear Viscoelastic Materials 446
14.3. Stress-Strain Relations in Differential Equation Form 450
14.4. Steady State Harmonic Oscillation 454
14.5. Boundary-Value Problems and Integral Transforms 456
14.6. Waves in an Infinite Medium 458
14.7. Quasi-Static Problems 460
14.8. Problems of Constant Poisson s Ratio 462
14.9. Reciprocity Relations 464
14.10. Functional Thermodynamics and Coupled Constitutive
Relations 468
CONTENTS xvii
14.10.1. Fundamental principles 469
14.10.2. Coupled constitutive relations based on Helmholtz
free energy functional 469
14.10.3. Coupled constitutive relations based on Gibbs free
energy functional 472
14.11. Coupled Thermoviscoelastic Boundary-Initial Value
Problems 475
14.12. Linearized Theory and Integral Transforms 476
14.13. Representation of Thermodynamic Property Functions for
Materials with Memory on Intrinsic Time Scale 478
14.13.1. Thermo-rheological and piezo-rheological simple
materials 478
14.13.2. Effective time theory for aging materials 480
14.13.3. Time-aging-temperature-strain superposition 481
14.13.4. Time-aging-temperature-stress superposition 481
15 THERMODYNAMICS WITH INTERNAL STATE
VARIABLES AND THERMO-ELASTO-
VISCOPLASTICITY 483
15.1. Thermodynamics with Internal State Variables 483
15.2. Energy-Momentum Tensor and Invariant Integral 486
15.3. Potentials or Pseudo-Potentials of Dissipation 488
15.4. Alternative Formulation of Theories of Plasticity 489
15.4.1. Thermo-elasto-plasticity 489
15.4.2. Thermo-elasto-viscoplasticity 491
15.5. Connecting Viscoplasticity to Viscoelasticity with
Intrinsic Time Scale 492
16 ELECTRO-THERMO-
VISCOELASTICITY/VISCOPLASTICITY 497
16.1. Introduction 497
16.2. Physical Notations 497
16.2.1. Electromagnetic field quantities 497
16.2.2. Electromagnetic body force and couple 498
16.2.3. Electromagnetic stress tensor and momentum
vector 500
16.2.4. Electromagnetic power 501
16.3. Basic Field Equations for Electrosensitive Materials 502
xviii CONTENTS
16.4. Augmented Helmholtz and Gibbs Free Energy Functionals 503
16.4.1. Expansion of augmented Helmholtz free energy
functional 503
16.4.2. Expansion of augmented Gibbs free energy
functional 504
16.5. Finite Electro-Thermo-Viscoelasticity 505
16.5.1. Finite electro-thermo-viscoelasticity based on
augmented Helmholtz free energy functional 505
16.5.2. Finite electro-thermo-viscoelasticity based on
augmented Gibbs free energy functional 508
16.6. Boundary-Initial Value Problems for Electrosensitive
Materials 509
16.7. Linearized Theory and Integral Transforms 510
16.8. Representation of Thermodynamic Property Functions for
Electrosensitive Materials with Memory on Intrinsic Time
Scale 512
16.8.1. Time-aging-temperature-strain-electric
displacement superposition 513
16.8.2. Time-aging-temperature-stress-electric field
superposition 513
16.9. Reduction to Electro-Thermo-Elasticity 514
17 INCREMENTAL APPROACH TO SOLVING SOME
NONLINEAR PROBLEMS 517
17.1. Updated Lagrangian Description 517
17.2. Linearized Rate of Deformation 519
17.3. Linearized Rates of Stress Measures 521
17.4. Incremental Equations of Motion 524
17.5. Constitutive Laws 526
o
17.6. Incremental Variational Principles in Terms of T 530
17.7. Incremental Variational Principles in Terms of r* 535
17.8. Incompressible and Nearly Incompressible Materials 536
17.9. Updated Solution 540
17.10. Incremental Loads 543
17.11. Infinitesimal Strain Theory 545
18 FINITE ELEMENT METHODS 547
18.1. Basic Approach 54g
CONTENTS xix
18.2. One-Dimensional Problems Governed by Second Order
Differential Equations 550
18.3. Shape Functions and Element Matrices for Higher Order
Ordinary Differential Equations 557
18.4. Assembling and Constraining Global Matrices 561
18.5. Equation Solving 564
18.6. Two-Dimensional Problems by One-Dimensional Elements 568
18.7. General Finite Element Formulation 569
18.8. Convergence 574
18.9. Two-Dimensional Shape Functions 575
18.10. Element Matrices for Second-Order Elliptical Equations 581
18.11. Coordinate Transformation 584
18.12. Triangular Elements with Curved Sides 585
18.13. Quadrilateral Elements 587
18.14. Plane Elasticity 593
18.15. Three-Dimensional Shape Functions 601
18.16. Three-Dimensional Elasticity 605
18.17. Dynamic Problems of Elastic Solids 609
18.18. Numerical Integration 617
18.19. Patch Test 621
18.20. Locking-Free Elements 624
18.21. Spurious Modes in Reduced Integration 635
18.22. Perspective 639
19 MIXED AND HYBRID FORMULATIONS 641
19.1. Mixed Formulations 641
19.2. Hybrid Formulations 644
19.3. Hybrid Singular Elements (Super-Elements) 649
19.4. Elements for Heterogeneous Materials 656
19.5. Elements for Infinite Domain 656
19.6. Incompressible or Nearly Incompressible Elasticity 662
20 FINITE ELEMENT METHODS FOR PLATES AND
SHELLS 666
20.1. Linearized Bending Theory of Thin Plates 666
20.2. Reissner-Mindlin Plates 672
20.3. Mixed Functional of Reissner Plate Theory 678
20.4. Hybrid Formulation for Plates 682
XX CONTENTS
20.5. General Shell Elements 684
20.6. Locking and Stabilization in Shell Applications 694
20.7. Elements for Heterogeneous Materials 697
21 FINITE ELEMENT MODELING OP NONLINEAR
ELASTICITY, VISCOELASTICITY, PLASTICITY,
VISCOPLASTICITY, AND CREEP 702
21.1. Updated Lagrangian Solution for Large Deformation 703
21.2. Incremental Solution 705
21.3. Dynamic Solution 706
21.4. Newton-Raphson Iteration Method 707
21.5. Viscoelasticity 709
21.6. Plasticity 711
21.7. Viscoplasticity 720
21.8. Creep 721
21.9. Return Mapping Formulation with Von Mises Yield Surface 723
21.10. Implicit Scheme For General Yield Surfaces 730
22 MESHLESS LOCAL PETROV-GALERKIN AND
ESHELBY-ATLURI METHODS 734
22.1. Weak Forms 734
22.2. Interpolation with a Local Support 736
22.2.1. Moving least-square interpolation 736
22.2.2. Shepard functions 743
22.2.3. Interpolation errors 744
22.2.4. Summary 746
22.3. Domain Discretization 746
22.3.1. Weight functions as test functions 747
22.3.2. Dirac delta function as test function 751
22.3.3. Heaviside step function as test function in Qje 752
22.3.4. Shape function as test function 753
22.3.5. Summary 754
22.4. Approximation in Rigid Boundary Condition 754
22.5. Numerical Integration of the Weak Forms 757
22.6. Eshelby-Atluri Methods (EAMs) 760
22.6.1. Balance laws of Eshelby stress tensor T 760
22.6.2. Stress tensors f, P, S, T 763
CONTENTS xxi
22.6.3. Noether/Eshelby energy-momentum conservation
laws in terms of f, P, S, T 765
22.6.4. Tangential material stiffness coefficients of
Noether/Eshelby energy-momentum conservation
laws 765
22.6.5. MLP G weak-forms of energy-momentum
conservation laws 766
22.7. Summary 773
BIBLIOGRAPHY 774
AUTHOR INDEX 809
SUBJECT INDEX 819
|
| any_adam_object | 1 |
| author | Fung, Yuan-cheng 1919-2019 Tong, Pin Chen, Xiaohong |
| author_GND | (DE-588)124296920 |
| author_facet | Fung, Yuan-cheng 1919-2019 Tong, Pin Chen, Xiaohong |
| author_role | aut aut aut |
| author_sort | Fung, Yuan-cheng 1919-2019 |
| author_variant | y c f ycf p t pt x c xc |
| building | Verbundindex |
| bvnumber | BV044467849 |
| callnumber-first | Q - Science |
| callnumber-label | QA807 |
| callnumber-raw | QA807 |
| callnumber-search | QA807 |
| callnumber-sort | QA 3807 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 1000 UF 1100 |
| classification_tum | PHY 201f |
| ctrlnum | (OCoLC)1004333938 (DE-599)BVBBV044467849 |
| dewey-full | 620.1 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.1 |
| dewey-search | 620.1 |
| dewey-sort | 3620.1 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV044467849 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:53:46Z |
| institution | BVB |
| isbn | 9789814713658 9789814713641 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029868343 |
| oclc_num | 1004333938 |
| open_access_boolean | |
| owner | DE-29T DE-11 |
| owner_facet | DE-29T DE-11 |
| physical | xxi, 838 Seiten Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series in engineering science |
| series2 | Advanced series in engineering science |
| spelling | Fung, Yuan-cheng 1919-2019 Verfasser (DE-588)124296920 aut Classical and computational solid mechanics Y.C. Fung, University of California, San Diego, USA; Pin Tong, University of California, San Diego, USA & Hong Kong University of Science and Technology, Hong Kong, China; Xiaohong Chen, UTC Aerospace Systems, USA Second edition New Jersey World Scientific [2017] © 2017 xxi, 838 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Advanced series in engineering science Volume 2 Technische Mechanik (DE-588)4059231-5 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s Technische Mechanik (DE-588)4059231-5 s DE-604 Tong, Pin Verfasser aut Chen, Xiaohong Verfasser aut Advanced series in engineering science Volume 2 (DE-604)BV016824222 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029868343&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fung, Yuan-cheng 1919-2019 Tong, Pin Chen, Xiaohong Classical and computational solid mechanics Advanced series in engineering science Technische Mechanik (DE-588)4059231-5 gnd Festkörpermechanik (DE-588)4129367-8 gnd |
| subject_GND | (DE-588)4059231-5 (DE-588)4129367-8 |
| title | Classical and computational solid mechanics |
| title_auth | Classical and computational solid mechanics |
| title_exact_search | Classical and computational solid mechanics |
| title_full | Classical and computational solid mechanics Y.C. Fung, University of California, San Diego, USA; Pin Tong, University of California, San Diego, USA & Hong Kong University of Science and Technology, Hong Kong, China; Xiaohong Chen, UTC Aerospace Systems, USA |
| title_fullStr | Classical and computational solid mechanics Y.C. Fung, University of California, San Diego, USA; Pin Tong, University of California, San Diego, USA & Hong Kong University of Science and Technology, Hong Kong, China; Xiaohong Chen, UTC Aerospace Systems, USA |
| title_full_unstemmed | Classical and computational solid mechanics Y.C. Fung, University of California, San Diego, USA; Pin Tong, University of California, San Diego, USA & Hong Kong University of Science and Technology, Hong Kong, China; Xiaohong Chen, UTC Aerospace Systems, USA |
| title_short | Classical and computational solid mechanics |
| title_sort | classical and computational solid mechanics |
| topic | Technische Mechanik (DE-588)4059231-5 gnd Festkörpermechanik (DE-588)4129367-8 gnd |
| topic_facet | Technische Mechanik Festkörpermechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029868343&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV016824222 |
| work_keys_str_mv | AT fungyuancheng classicalandcomputationalsolidmechanics AT tongpin classicalandcomputationalsolidmechanics AT chenxiaohong classicalandcomputationalsolidmechanics |