Handbook of numerical analysis: 6 Numerical methods for solids (part 3), Numerical methods for fluids (part 1)
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| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
North-Holland
1998
|
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 681 - 688 |
| Physical Description: | X, 689 S. graph. Darst. |
| ISBN: | 044482569X |
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MARC
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| 245 | 1 | 0 | |a Handbook of numerical analysis |n 6 |p Numerical methods for solids (part 3), Numerical methods for fluids (part 1) |c general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| 264 | 1 | |a Amsterdam |b North-Holland |c 1998 | |
| 300 | |a X, 689 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. 681 - 688 | ||
| 700 | 1 | |a Ciarlet, Philippe G. |d 1938- |e Sonstige |0 (DE-588)143368362 |4 oth | |
| 700 | 1 | |a Lions, Jacques-Louis |d 1928-2001 |e Sonstige |0 (DE-588)124055397 |4 oth | |
| 700 | 1 | |a Du, Qiang |d 1964- |0 (DE-588)1188249320 |4 edt | |
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Record in the Search Index
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| adam_text | Contents
Chapter I. Introduction 7
1. Forward 7
2. The initial boundary value problem of nonlinear solid mechanics 10
3. Finite element solution of the initial boundary value problem 14
4. Linear equation solving 17
Chapter II. Iterative Linear Equation Solving 23
5. The conjugate gradient method 23
6. The preconditioned conjugate gradient method 27
7. Element by element preconditioning 32
Chapter III. Implementation of Element Operations 39
8. An operational view of element by element preconditioning 39
9. General concepts of vectorization 43
10. Vectorized element by element preconditioning 48
Chapter IV. Applications to Large Scale Continuum Problems 53
11. Fractal dimension of a finite element mesh 53
12. The computational environment 58
13. Example linear analyses 60
14. Example nonlinear analyses 77
Chapter V. Extensions to Contact/Impact Problems 85
15. Penalized symmetry planes 85
16. Penalized slidesurfaces 92
Chapter VI. Shell Analysis with Element by Element Methods 105
17. NIKE3D s shell element 105
18. Linear analysis of a plate 108
19. Analysis of a stiffened cylindrical shell 115
20. Example nonlinear analyses 122
Chapter VII. Experience with a Lanczos Based Iterative Solution Algorithm 129
21. Derivation of the method 129
22. The Lanczos algorithm in finite precision arithmetic 141
23. Numerical examples 146
Chapter VIII. Conclusions 167
6 R.M. Ferencz and T.J.R. Hughes
References 171
Subject Index 177
Contents
Preface 187
Chapter I. The Classical Models 191
1. Notation and brief summary of some standard results 191
2. Classical rate independent plasticity: Local evolution equations 196
3. The rate form of classical plasticity: Elastoplastic tangent moduli 200
4. Some specific models of classical plasticity 204
5. General rate independent multisurface plasticity 211
6. Dissipation: Interpretation of the model of associative plasticity 213
7. Rate dependent plasticity: The viscoplastic regularization 216
8. Example: Viscoplastic regularization of J2 flow theory 218
9. The weak formulation of dynamic plasticity 221
10. Contractivity, uniqueness, and dissipativity of the elastoplastic flow 224
CHAPTER II. Integration Algorithms 229
11. Local integration of rate independent plasticity: An overview 230
12. Motivation: The perfectly plastic model of J2 flow theory 234
13. Backward difference and implicit Runge Kutta methods: Basic results 240
14. Generalized backward difference return mapping algorithms 244
15. Generalized implicit Runge—Kutta return mapping algorithms 247
16. Algorithms for the computation of the closest point projection 249
17. The consistent algorithmic elastoplastic moduli 253
18. Examples: Closed form return mapping algorithms 254
19. Practical accuracy assessment: Iso error maps 261
20. Accuracy analysis of return mapping algorithms 264
21. Extension of return mapping algorithms to viscoplasticity 269
22. Return mapping algorithms for general models of viscoplasticity 271
23. The algorithmic initial boundary value problem 273
24. Nonlinear stability analysis: Uniqueness and dissipativity 277
25. Spatial finite element discretization: An illustration 283
26. Application: A class of mixed methods for incompressibility 291
27. Illustrative numerical simulations 296
Chapter III. Nonlinear Continuum Mechanics 303
28. Basic kinematic results in nonlinear continuum mechanics 304
29. Stress tensors and alternative forms of the equations of motion 311
30. Objective transformations and frame invariance 313
31. Elastic constitutive equations and isotropy group 317
32. Volumetric/deviatoric uncoupled finite elasticity 322
33. Isotropic elasticity formulated in principal stretches 327
186 J C. Simo
34. Multiplicative plasticity at finite strains: Basic concepts 330
35. Elastic response and free energy for multiplicative plasticity 335
36. Plastic flow evolution equations for multiplicative plasticity 336
37. Volumetric/deviatoric uncoupled finite plasticity: J2 flow theory 341
38. Rate form and variational inequality for multiplicative plasticity 346
39. Variational formulation: Weak form of the momentum equations 351
40. The total and incremental weak forms of momentum balance 355
41. Initial boundary value problem: Dissipativity and a priori estimate 357
Chapter IV. The Discrete Initial Boundary Value Problem 361
42. The Galerkin projection: The spatially discrete problem 363
43. The linearized (semidiscrete) initial value problem 365
44. Matrix form of the semidiscrete initial value problem 369
45. Mixed finite element discretization: An illustration 373
46. Exponential return mapping algorithms for multiplicative plasticity 383
47. Exponential return mappings for isotropic elastic response 387
48. Implementation of exponential return mapping algorithms 390
49. Linearization: The exact algorithmic tangent moduli 394
50. A generalization of Jo flow theory to finite strains 398
51. Two stage projected exponential return mapping algorithms 402
52. Closed form of the two stage projected IRK for elastic isotropy 408
53. Global time stepping algorithms for dynamic plasticity 411
54. Remarks on the implementation of return mapping algorithms 414
55. Representative numerical simulations 416
Chatter V. The Coupled Thermomechanical Problem 433
56. Integral, local and weak forms of the general conservation laws 435
57. Constitutive equations for multiplicative thermoplasticiry 439
58. Formal a priori stability estimate and conservation laws 447
59. Time integration of the coupled problem: General considerations 451
60. Monolithic and staggered schemes: Product formula algorithms 456
61. Model problem: The coupled system of linearized thermoelasticity 460
62. Generalization: A staggered scheme for nonlinear thermoplasticity 469
63. Representative numerical simulations 475
References 489
Contents
Preface 507
Chapter I. Elements of the Mathematical Theory 509
Introduction 509
1. The Navier Stokes equations 511
2. Energy and enstrophy 515
3. Boundary value problems: First examples 517
4. Helmholtz decomposition of a vector field and applications 521
5. Weak formulation 524
6. Other equations. Other boundary value problems 527
7. Other boundary conditions 531
8. The space periodic case 535
9. The main existence and uniqueness theorems in space dimension two 538
10. The main existence and uniqueness theorems in space dimension three 545
11. About the initial condition 549
12. The exponential decay of the Fourier coefficients 551
13. Long time behaviour. Attractors and their approximation 553
14. Remarks on the Euler equations 558
Chapter II. Discretization of the Navier Stokes Equations 565
Introduction 565
15. Time discretization: Stability 566
15.1. Appendix A: Properties of b 573
15.2. Appendix B: Existence of u 574
16. Time discretization: Convergence 575
17. Error analysis and estimates on the enstrophy 586
18. Space and time discretizations: A first order scheme 592
19. A second order scheme 598
Chapter III. The Incompressibility Condition and the Computation of Laminar Flows 605
Introduction 605
20. The projection method (I) 606
21. The projection method (II) 6!6
22. Uzawa algorithm °
Chapter IV. Multi Level Methods and the Simulation of Turbulent Flows 637
Introduction 637
23. Multi level spatial discretization: The spectral Fourier case 638
24. Multi level spatial discretization: The finite elements case 642
506 M. Marion and R. Temam
25. Multi level spatial and temporal discretization 653
26. Computational results 665
References 681
Subject Index 689
|
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| indexdate | 2024-07-09T18:24:58Z |
| institution | BVB |
| isbn | 044482569X |
| language | English |
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| physical | X, 689 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| spelling | Handbook of numerical analysis 6 Numerical methods for solids (part 3), Numerical methods for fluids (part 1) general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions Amsterdam North-Holland 1998 X, 689 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 681 - 688 Ciarlet, Philippe G. 1938- Sonstige (DE-588)143368362 oth Lions, Jacques-Louis 1928-2001 Sonstige (DE-588)124055397 oth Du, Qiang 1964- (DE-588)1188249320 edt (DE-604)BV002745459 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008330347&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Handbook of numerical analysis |
| title | Handbook of numerical analysis |
| title_auth | Handbook of numerical analysis |
| title_exact_search | Handbook of numerical analysis |
| title_full | Handbook of numerical analysis 6 Numerical methods for solids (part 3), Numerical methods for fluids (part 1) general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_fullStr | Handbook of numerical analysis 6 Numerical methods for solids (part 3), Numerical methods for fluids (part 1) general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_full_unstemmed | Handbook of numerical analysis 6 Numerical methods for solids (part 3), Numerical methods for fluids (part 1) general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_short | Handbook of numerical analysis |
| title_sort | handbook of numerical analysis numerical methods for solids part 3 numerical methods for fluids part 1 |
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