Augmented Lagrangian and operator-splitting methods in nonlinear mechanics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
SIAM
1989
|
| Series: | Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 295 S. graph. Darst. |
| ISBN: | 0898712300 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface jx
Chapter 1. Some Continuous Media and Their Mathematical Modeling 1
1. The physical problems 1
2. Kinematics 1
3. Kinetics and thermodynamics of deformation 5
4. Standard materials in small strains 7
5. Incompressible viscous fluids 13
6. Finite elasticity 15
Chapter 2. Variational Formulations of the Mechanical Problems . . 19
1. Preliminaries 19
2. Quasi static viscoplasticity 24
3. Time dependent flows of viscoplastic fluids 32
4. Elastoviscoplasticity in small strains 34
5. Static finite elasticity 37
Chapter 3. Augmented Lagrangian Methods for the Solution of Vari¬
ational Problems 45
1. Introduction and synopsis 45
2. Augmented Lagrangian methods in quadratic programming . . 46
3. Application to the Stokes problem 66
4. Decomposition of variational problems by augmented Lagrangian
techniques 79
5. Relations between augmented Lagrangian methods and alternating
direction methods 89
6. Application to the solution of linear and nonlinear eigenvalue
problems 105
7. Liquid crystals theory and further comments Ill
V
Vi CONTENTS
Chapter 4. Viscoplasticity and Elastoviscoplasticity in Small Strains 123
1. Introduction 123
2. Mixed variational formulations of elastoviscoplasticity 124
3. Finite element formulations of elastoviscoplasticity 128
4. Quasi static viscoplasticity 137
5. Numerical algorithms 141
6. The problem in plastic strain rates 150
7. Numerical results 158
Chapter 5. Limit Load Analysis 169
1. Limit loads in plasticity 169
2. Limit load analysis 177
3. Viscoplastic regularization and numerical algorithm 180
4. Computation of Gs(f,g) and convergence results 183
5. Examples of computations of limit loads 187
Chapter 6. Two Dimensional Flow of Incompressible Viscoplastic
Fluids 197
1. Classical formulation of the flow problem 197
2. Stream function formulation 198
3. Approximation of the steady state problem 200
4. Approximation of the time dependent problem (2.8) 204
5. Solution of Problems (3.1) and (4.2) by augmented Lagrangian
methods 205
6. Numerical experiments 211
7. Further comments 213
Chapter 7. Finite Elasticity 217
1. Classical formulations 217
2. Augmented Lagrangian formulation 219
3. Finite element discretization 224
4. Iterative numerical solution of the augmented Lagrangian formula¬
tions 233
5. Solution of local problems formulated in deformation gradients 235
6. Numerical results 240
7. Equilibrium problems with contact 248
Chapter 8. Large Displacement Calculations of Flexible Rods . . . 259
1. Introduction and description of the physical problem 259
2. Mathematical modeling of the torsion free static problem . . . 260
CONTENTS Vii
3. Finite element approximation of the static problem 262
4. Augmented Lagrangian solution of the static problem 266
5. Applications and extensions 270
6. Solution of the dynamical problem 280
References 287
Index 293
|
| any_adam_object | 1 |
| author | Glowinski, Roland 1937-2022 Le Tallec, Patrick 1954- |
| author_GND | (DE-588)120514737 (DE-588)124325653 |
| author_facet | Glowinski, Roland 1937-2022 Le Tallec, Patrick 1954- |
| author_role | aut aut |
| author_sort | Glowinski, Roland 1937-2022 |
| author_variant | r g rg t p l tp tpl |
| building | Verbundindex |
| bvnumber | BV003568364 |
| classification_rvk | SK 950 |
| classification_tum | PHY 200f |
| ctrlnum | (OCoLC)468146762 (DE-599)BVBBV003568364 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV003568364 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:02:02Z |
| institution | BVB |
| isbn | 0898712300 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002271154 |
| oclc_num | 468146762 |
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| owner_facet | DE-384 DE-739 DE-703 DE-20 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-706 DE-188 |
| physical | X, 295 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | SIAM |
| record_format | marc |
| series | Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics |
| series2 | Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics |
| spelling | Glowinski, Roland 1937-2022 Verfasser (DE-588)120514737 aut Augmented Lagrangian and operator-splitting methods in nonlinear mechanics Roland Glowinski and Patrick Le Tallec Philadelphia SIAM 1989 X, 295 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics 9 Calcul des variations ram Milieux continus, Mécanique des ram Mécanique non linéaire ram Opérateurs, Théorie des ram Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Lagrange-Funktion (DE-588)4166459-0 gnd rswk-swf Zerlegung Mathematik (DE-588)4190746-2 gnd rswk-swf Zerlegung Mathematik (DE-588)4190746-2 s Operator (DE-588)4130529-2 s Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Lagrange-Funktion (DE-588)4166459-0 s Nichtlineare Mechanik (DE-588)4042095-4 s Operatortheorie (DE-588)4075665-8 s Le Tallec, Patrick 1954- Verfasser (DE-588)124325653 aut Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics 9 (DE-604)BV001889480 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002271154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Glowinski, Roland 1937-2022 Le Tallec, Patrick 1954- Augmented Lagrangian and operator-splitting methods in nonlinear mechanics Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics Calcul des variations ram Milieux continus, Mécanique des ram Mécanique non linéaire ram Opérateurs, Théorie des ram Nichtlineare Mechanik (DE-588)4042095-4 gnd Operatortheorie (DE-588)4075665-8 gnd Operator (DE-588)4130529-2 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Lagrange-Funktion (DE-588)4166459-0 gnd Zerlegung Mathematik (DE-588)4190746-2 gnd |
| subject_GND | (DE-588)4042095-4 (DE-588)4075665-8 (DE-588)4130529-2 (DE-588)4032296-8 (DE-588)4166459-0 (DE-588)4190746-2 |
| title | Augmented Lagrangian and operator-splitting methods in nonlinear mechanics |
| title_auth | Augmented Lagrangian and operator-splitting methods in nonlinear mechanics |
| title_exact_search | Augmented Lagrangian and operator-splitting methods in nonlinear mechanics |
| title_full | Augmented Lagrangian and operator-splitting methods in nonlinear mechanics Roland Glowinski and Patrick Le Tallec |
| title_fullStr | Augmented Lagrangian and operator-splitting methods in nonlinear mechanics Roland Glowinski and Patrick Le Tallec |
| title_full_unstemmed | Augmented Lagrangian and operator-splitting methods in nonlinear mechanics Roland Glowinski and Patrick Le Tallec |
| title_short | Augmented Lagrangian and operator-splitting methods in nonlinear mechanics |
| title_sort | augmented lagrangian and operator splitting methods in nonlinear mechanics |
| topic | Calcul des variations ram Milieux continus, Mécanique des ram Mécanique non linéaire ram Opérateurs, Théorie des ram Nichtlineare Mechanik (DE-588)4042095-4 gnd Operatortheorie (DE-588)4075665-8 gnd Operator (DE-588)4130529-2 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Lagrange-Funktion (DE-588)4166459-0 gnd Zerlegung Mathematik (DE-588)4190746-2 gnd |
| topic_facet | Calcul des variations Milieux continus, Mécanique des Mécanique non linéaire Opérateurs, Théorie des Nichtlineare Mechanik Operatortheorie Operator Kontinuumsmechanik Lagrange-Funktion Zerlegung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002271154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001889480 |
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