Approximate solution of plastic flow theory problems:
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | Russian French German English |
| Veröffentlicht: |
Leipzig
Teubner
1984
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| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Teubner-Texte zur Mathematik
69 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | 252 S. |
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Datensatz im Suchindex
| _version_ | 1804114897575870464 |
|---|---|
| adam_text | CONTENTS
Introduction 8
Chapter 1. Linear Theory of Elasticity: Basic Relations
and Boundary Value Problems 14
1.1. The State of Stress 14
1.1.1. The State of Stress at a Point and the Stress Tensor 14
1.1.2. Differential Equations of Equilibrium, Symmetry of
the Stress Tensor 17
1.1.3. Stress Boundary Conditions 18
1.1.4. Principal Stresses and Invariants of the Stress
Tensor 18
1.1.5. Spherical and Deviatoric Stress Tensors,
Deviatoric Plane 20
1.1.6. Extreme Values of Shear Stresses 22
1.1.7. Octahedral Shear Stress 22
1.2. The State of Strain 23
1.2.1. Strain Displacement Relations 23
1.2.2. Tensor and Deviator of Strain and their Invariants 25
1.2.3. Compatibility Equations 27
1.3. Stress Strain Relations 27
1.3.1. Linear Stress Strain Relations and the Elastic
Potential 27
1.3.2. The Isotropic Body 29
1.3.3. Streas Strain Relations in Matrix Form 31
1.4. Some Particular Cases of Stress and Strain States 33
1.4.1. Tension and Compression of a Bar with a Constant
Cross Section 33
1.4.2. Torsion of a Bar with a Constant Cross Section 34
1.4.3. The State of Plane Strain 35
1.4.4. The State of Generalized Plane Stress 37
1.5. Basic Boundary Value Problems of the Linear Theory
of Elasticity and their Solvability in Sobolev s
Spaces 39
1.5.1. Lame s Equations and Boundary Conditions 39
1.5.2. Lagrange s Principle of Virtual Displacements and
the Generalized Formulations of the Basic Boundary
Value Problems in the Linear Theory of Elasticity 42
1.5.3. Some Function Spaces 44
1.5*4. On the Generalized Solutions of Boundary Value
Problems in the Theory of Elasticity 46
4
1.5.5. Boundary Value Problems in the Theory of Elasticity
and the Principle of Minimum Potential Energy 48
1.5.6. Korn s Inequality, Bxistence and Uniqueness of the
Generalized Solution 50
1.5.7. On the Regularity of the Generalized Solution 51
Chapter 2. Basic Relations of the Flow Theory of Plasticity
and Generalized Formulations of Boundary Value
Problems 55
2.1. On the Behaviour of Elastic Plastic Solid Bodies 55
2.1.1. Stress Strain Diagrams 55
2.1.2. Simple and Complex Loading 61
2.1.3. Some Notions of the Plastic Flow Theory 63
2.2. Yield Conditions 64
2.2.1. The Tresca Saint Venant Yield Condition of the
Constant Maximum Shear Stress 64
2.2.2. The von Mises Yield Condition 65
2.2.3. The Coulomb Yield Condition 67
2.2.4. The Modified Tresca and von Miaes Yield Conditions,
the Yield Condition of Drucker and Prager 71
2.3. Hardening Laws 73
2.3.1. Initial Yield Surfaces and Loading Yield Surfaces 73
2.3.2. Isotropic Hardening 76
2.3.3. Kinematic Hardening 78
2.3.4. Some other Hardening Laws 79
2.4. Flow Rules and Drucker s Postulate 80
2.4.1. The Plastic Potential, Associated and Nonassociated
Flow Rules 80
2.4.2. The Generalized Associated Flow Rule for an Irregular
Point of the Loading Surface 81
2.4.3. Drucker s Postulate and the Convexity of the Loading
Surface 82
2.4.4. On the Definition of the Hardening Parameters 84
2.5. The Relations between the Rates of Stresses and Strains 85
2.5.1. Loading and Unloading Criteria 85
2.5.2. The Stress Strain Relations for the Associated
Flow Rule 87
2.5.3. The Material Law at Irregular Points of the
Loading Surface 91
2.5.4. The Material Law for the Nonassociated Flow Rule 92
5
2.5.5. On some Properties of the Differential Stress Strain
Relations for Hardening Materials 93
2.6. Some Special Cases of the Differential Stress Strain
Relations 98
2.6.1. The von Mises Yield Condition in the Case of the Iflo
tropic Hardening and the Associated Flow Rule 98
2.6.2. The A Properties of the Differential Stress Strain
Relations under the von Mises Yield Condition 101
2.6.3. Coulomb s Yield Condition for Plane Problems 105
2.6.4. On the Regularization of the Stress Strain Relations
at the Irregular Points of Coulomb s Yield Surfaces 109
2.6.5. The Simple Loading and the Deformation Theory of
Plasticity 116
2.7. Generalized Boundary Value Problems of Plastic
Plow Theory 117
2.7.1. Basic Boundary Value Problems 117
2.7.2. Regularized Boundary Value Problems 119
Chapter 3. Existence, Uniqueness and Regularity Results for
Boundary Value Problems of the Plastic Plow Theory 123
3.1. Auxiliary Results 123
3.1.1. Some Inequalities 123
3.1.2. Gronwall s Lemma 127
3.2. Some Properties of the Differential Operators of
Boundary Value Problems in the Plastic Plow Theory 130
3.2.1. The Partial Differential Operator with Fixed Stresses
and Hardening Parameters 130
3.2.2. The Solvability in the Space if 136
3.3. The Solvability of Boundary Value Problems of the
Plastic Plow Theory in Sobolev s Spaces 144
3.3.1. Uniqueness of the Solution 144
3.3.2. Dependence of the Solution on the Quasitime Variable 148
3.3.3. The Variable Stiffness Parameter Method and the
Existence of the Solution 150
3.3.4. Solvability in the Space w| 153
Chapter 4. Numerical Analysis of Plastic Plow Theory Problems 160
4.1. On the Convergence of the Incremental Loading Method 160
4.1.1. The Incremental Loading Method 160
4.1.2. Convergence Estimates 163
6
4.1.3. On the Convergence of an Implicit Scheme of the
Incremental Loading Method 168
4.2. The Combination of the Finite Element Method and
the Incremental Loading Method 179
4.2.1. On the Use of the Finite Element Method for Plastic
Flow Theory Problems 179
4.2.2. Linear Tetrahedral Finite Elements 182
4.2.3. Finite Element Complices, Triangulations and Finite
Element Spaces 184
4.2.4. The Numerical Scheme Composed of the Incremental
Loading Method and the Finite Element Method 190
4.2.5. On the Convergence of the Incremental Finite
Element Method 194
4.2.6. The Incremental Finite Element Method of the Second
Order of Accuracy with respect to the Time Variable 201
4.2.7. Systems of Nonlinear Algebraic Equations Arising in
the Incremental Finite Element Method 209
Chapter 5. On the Solution of Systems of Linear and Nonlinear
Finite Element Algebraic Equations 213
5.1. Two level Iteration Methods and Direct Methods 214
5.1.1. Two level Iteration Mexhods for Systems Arising in
the Incremental Finite Element Method 214
5.1.2. The Condition Number of the Stiffness Matrix and the
Explicit Iteration Method 220
5.1.3. On some Direct Methods for Solving Systems of Finite
Element Algebraic Equations for Linear Elasticity
Problems 222
5.2. Some Further Iterative Schemes 225
5.2.1. Two stage Iterative Schemes 225
5.2.2. Multigrid Methods 233
References 243
7
|
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| author | Korneev, Vadim G. Langer, Ulrich |
| author_facet | Korneev, Vadim G. Langer, Ulrich |
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| discipline | Physik Mathematik |
| edition | 1. Aufl. |
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| id | DE-604.BV000437246 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:14:01Z |
| institution | BVB |
| language | Russian French German English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000270831 |
| oclc_num | 12143381 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-83 DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-83 DE-188 |
| physical | 252 S. |
| psigel | TUB-nveb |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Korneev, Vadim G. Verfasser aut Approximate solution of plastic flow theory problems Vadim G. Korneev ; Ulrich Langer 1. Aufl. Leipzig Teubner 1984 252 S. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 69 Aus d. Russ. übers. Boundary value problems Numerical solutions Finite element method Plasticity Strömung (DE-588)4058076-3 gnd rswk-swf Plastizität (DE-588)4046283-3 gnd rswk-swf Rheologie (DE-588)4049828-1 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Näherungsverfahren (DE-588)4206467-3 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Elastizität (DE-588)4014159-7 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Fließen (DE-588)4017547-9 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Lösung Mathematik (DE-588)4120678-2 gnd rswk-swf Rheologie (DE-588)4049828-1 s Randwertproblem (DE-588)4048395-2 s Näherungsverfahren (DE-588)4206467-3 s DE-604 Fließen (DE-588)4017547-9 s Approximation (DE-588)4002498-2 s Plastizität (DE-588)4046283-3 s 1\p DE-604 Sobolev-Raum (DE-588)4055345-0 s 2\p DE-604 Mechanik (DE-588)4038168-7 s 3\p DE-604 Elastizität (DE-588)4014159-7 s 4\p DE-604 Lösung Mathematik (DE-588)4120678-2 s 5\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 6\p DE-604 Numerisches Verfahren (DE-588)4128130-5 s 7\p DE-604 Strömung (DE-588)4058076-3 s 8\p DE-604 Langer, Ulrich Verfasser aut Teubner-Texte zur Mathematik 69 (DE-604)BV000012607 69 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000270831&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 8\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Korneev, Vadim G. Langer, Ulrich Approximate solution of plastic flow theory problems Teubner-Texte zur Mathematik Boundary value problems Numerical solutions Finite element method Plasticity Strömung (DE-588)4058076-3 gnd Plastizität (DE-588)4046283-3 gnd Rheologie (DE-588)4049828-1 gnd Randwertproblem (DE-588)4048395-2 gnd Mechanik (DE-588)4038168-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd Näherungsverfahren (DE-588)4206467-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Elastizität (DE-588)4014159-7 gnd Sobolev-Raum (DE-588)4055345-0 gnd Fließen (DE-588)4017547-9 gnd Approximation (DE-588)4002498-2 gnd Lösung Mathematik (DE-588)4120678-2 gnd |
| subject_GND | (DE-588)4058076-3 (DE-588)4046283-3 (DE-588)4049828-1 (DE-588)4048395-2 (DE-588)4038168-7 (DE-588)4042805-9 (DE-588)4206467-3 (DE-588)4128130-5 (DE-588)4014159-7 (DE-588)4055345-0 (DE-588)4017547-9 (DE-588)4002498-2 (DE-588)4120678-2 |
| title | Approximate solution of plastic flow theory problems |
| title_auth | Approximate solution of plastic flow theory problems |
| title_exact_search | Approximate solution of plastic flow theory problems |
| title_full | Approximate solution of plastic flow theory problems Vadim G. Korneev ; Ulrich Langer |
| title_fullStr | Approximate solution of plastic flow theory problems Vadim G. Korneev ; Ulrich Langer |
| title_full_unstemmed | Approximate solution of plastic flow theory problems Vadim G. Korneev ; Ulrich Langer |
| title_short | Approximate solution of plastic flow theory problems |
| title_sort | approximate solution of plastic flow theory problems |
| topic | Boundary value problems Numerical solutions Finite element method Plasticity Strömung (DE-588)4058076-3 gnd Plastizität (DE-588)4046283-3 gnd Rheologie (DE-588)4049828-1 gnd Randwertproblem (DE-588)4048395-2 gnd Mechanik (DE-588)4038168-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd Näherungsverfahren (DE-588)4206467-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Elastizität (DE-588)4014159-7 gnd Sobolev-Raum (DE-588)4055345-0 gnd Fließen (DE-588)4017547-9 gnd Approximation (DE-588)4002498-2 gnd Lösung Mathematik (DE-588)4120678-2 gnd |
| topic_facet | Boundary value problems Numerical solutions Finite element method Plasticity Strömung Plastizität Rheologie Randwertproblem Mechanik Numerische Mathematik Näherungsverfahren Numerisches Verfahren Elastizität Sobolev-Raum Fließen Approximation Lösung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000270831&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
| work_keys_str_mv | AT korneevvadimg approximatesolutionofplasticflowtheoryproblems AT langerulrich approximatesolutionofplasticflowtheoryproblems |