Finite elements: 5 Special problems in solid mechanics
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Englewood Cliffs, N.J.
Prentice-Hall
1984
|
| Ausgabe: | 1. print |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 273 S. graph. Darst. |
| ISBN: | 013317073X |
Internformat
MARC
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| 245 | 1 | 0 | |a Finite elements |n 5 |p Special problems in solid mechanics |c J. Tinsley Oden ... |
| 250 | |a 1. print | ||
| 264 | 1 | |a Englewood Cliffs, N.J. |b Prentice-Hall |c 1984 | |
| 300 | |a XI, 273 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Becker, Eric B. |e Sonstige |4 oth | |
| 700 | 1 | |a Carey, Graham F. |e Sonstige |4 oth | |
| 700 | 1 | |a Oden, John Tinsley |e Sonstige |4 oth | |
| 773 | 0 | 8 | |w (DE-604)BV021866581 |g 5 |
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Datensatz im Suchindex
| _version_ | 1804136091724283904 |
|---|---|
| adam_text | CONTENTS
PREFACE ix
Chapter 1 NUMERICAL ANALYSIS OF THIN SHELL
PROBLEMS 1
1.1 Study of the Continuous Problem 1
1.1.1 Introduction 1
1.1.2 The Linear Continuous Problem 13
1.1.3 Class of Nonlinear Shallow Shell Problems 13
1.2 Conforming Finite Element Methods with Numerical
Integration 20
1.2.1 Introduction 20
1.2.2 Conforming Finite Element Methods 21
1.2.3 Effect of Numerical Integration: Abstract Error
Estimate 25
1.2.4 Local Error Estimates: Uniform Vft
Ellipticity 28
1.2.5 Asymptotic Error Estimates 41
1.2.6 Examples 48
1.3 Application to the Computation of an Arch Dam Problem
53
1.3.1 Introduction 53
1.3.2 Geometrical Definition of the Dam 54
1.3.3 Variational Formulation of the Problem 58
1.3.4 Approximations of the Solution uGVby Conform¬
ing Finite Element Methods 59
V
vi Contents
1.3.5 Implementation 59
1.3.6 Numerical Experiments 61
Chapter 2 FINITE ELEMENTS IN NONLINEAR INCOMPRESSIBLE
ELASTICITY 67
2.1 Introduction 67
2.2 Physical Problem 68
2.2.1 Mechanical Preliminaries 68
2.2.2 Equilibrium Equations 69
2.2.3 Minimization Formulation 70
2.3 Mathematical Formulation 71
2.3.1 Presentation and Notations 71
2.3.2 Minimization 71
2.3.3 Equilibrium Equations 72
2.4 The Approximate Problem 73
2.4.1 Discrete Spaces 73
2.4.2 Compatibility Conditions 74
2.4.3 Examples 75
2.4.4 Minimization and Penalty Formulation 76
2.4.5 Mixed Formulations 78
2.5 Newton s Method 79
2.5.1 Description of the Method 79
2.5.2 Improvements of the Method 81
2.5.3 Conclusions 82
2.6 Augmented Lagrangian Algorithm 83
2.6.1 New Formulations of the Problem 83
2.6.2 Approximate Augmented Lagrangian
Formulation 85
2.6.3 Description of the Basic Iterative Method 86
2.6.4 Solution of (2.6.17) (N = 2, F Piecewise
Constant) 88
2.6.5 Numerical Results 90
Chapter 3 FINITE ELEMENT ANALYSIS OF LOCALIZATION IN
PLASTICITY 94
3.1 Introduction 94
3.2 Some Examples of Localized Plastic Flow 97
3.3 Field Equations 104
Contents vii
3.4 Constitutive Relations 109
3.4.1 Classical Smooth Yield Surface Plasticity
Theory 109
3.4.2 Deformation Theory 111
3.4.3 J2 Corner Theory 113
3.4.4 Single Crystal Plasticity 115
3.4.5 Continuum Model of a Ductile Porous
Material 119
3.5 Bifurcation and Uniqueness 122
3.6 Computational Considerations 129
3.7 Numerical Results 133
3.7.1 Plane Strain Tension 133
3.7.2 Localization from Highly Nonhomogeneous Defor¬
mation States 145
3.7.3 Void Sheet Formation 152
3.8 Concluding Remarks 155
Chapter 4 CONTACT PROBLEMS IN ELASTOSTATICS 158
4.1 Introduction 158
4.2 Signorini s Problem with Friction 159
4.2.1 Equilibrium Equations 160
4.2.2 Boundary Conditions 161
4.2.3 Boundary Value Problems 167
4.3 Variational Formulations of Signorini s Problem 168
4.3.1 Abstract Signorini s Problem with
Friction 168
4.3.2 Special Case I: Prescribed Tangential Stress 171
4.3.3 Special Case II: Prescribed Normal Stress 172
4.4 Special Case I: Prescribed Tangential Stress 173
4.4.1 Existence of a Unique Solution: Resolution of the
Contact Condition 174
4.4.2 Penalty Resolution of the Contact
Condition 175
4.4.3 Finite Element Approximations 180
4.4.4 Convergence of the Finite Element
Approximation 183
4.4.5 Numerical Examples 193
viii Contents
4.5 Special Case II: Prescribed Normal Stress 197
4.5.1 Existence of a Unique Solution 197
4.5.2 Regularization of the Functional j (•) 198
4.5.3 Finite Element Approximations 203
4.5.4 Convergence of the Finite Element
Method 204
4.5.5 Numerical Examples 207
Chapter 5 NONLOCAL FRICTION IN CONTACT PROBLEMS IN
PLANE ELASTICITY 213
5.1 Introduction 213
5.2 Nature of Friction and Basis for Nonlocal Law 215
5.2.1 Micromechanics of Friction 215
5.2.2 Nonlocal Friction Model 216
5.3 Variational Principle for Signorini s Problem with Nonlocal
Friction 220
5.3.1 Notations and Preliminaries 220
5.3.2 Variational Principle 224
5.3.3 Existence and Uniqueness of Solutions to the Non¬
local Friction Problem 229
5.4 Finite Element Approximations 239
5.4.1 The Approximate Problem 239
5.4.2 Error Estimate 241
5.4.3 Algorithms for Nonlocal Friction
Problems 248
5.5 Numerical Example 250
REFERENCES 253
INDEX 268
|
| adam_txt |
CONTENTS
PREFACE ix
Chapter 1 NUMERICAL ANALYSIS OF THIN SHELL
PROBLEMS 1
1.1 Study of the Continuous Problem 1
1.1.1 Introduction 1
1.1.2 The Linear Continuous Problem 13
1.1.3 Class of Nonlinear Shallow Shell Problems 13
1.2 Conforming Finite Element Methods with Numerical
Integration 20
1.2.1 Introduction 20
1.2.2 Conforming Finite Element Methods 21
1.2.3 Effect of Numerical Integration: Abstract Error
Estimate 25
1.2.4 Local Error Estimates: Uniform Vft
Ellipticity 28
1.2.5 Asymptotic Error Estimates 41
1.2.6 Examples 48
1.3 Application to the Computation of an Arch Dam Problem
53
1.3.1 Introduction 53
1.3.2 Geometrical Definition of the Dam 54
1.3.3 Variational Formulation of the Problem 58
1.3.4 Approximations of the Solution uGVby Conform¬
ing Finite Element Methods 59
V
vi Contents
1.3.5 Implementation 59
1.3.6 Numerical Experiments 61
Chapter 2 FINITE ELEMENTS IN NONLINEAR INCOMPRESSIBLE
ELASTICITY 67
2.1 Introduction 67
2.2 Physical Problem 68
2.2.1 Mechanical Preliminaries 68
2.2.2 Equilibrium Equations 69
2.2.3 Minimization Formulation 70
2.3 Mathematical Formulation 71
2.3.1 Presentation and Notations 71
2.3.2 Minimization 71
2.3.3 Equilibrium Equations 72
2.4 The Approximate Problem 73
2.4.1 Discrete Spaces 73
2.4.2 Compatibility Conditions 74
2.4.3 Examples 75
2.4.4 Minimization and Penalty Formulation 76
2.4.5 Mixed Formulations 78
2.5 Newton's Method 79
2.5.1 Description of the Method 79
2.5.2 Improvements of the Method 81
2.5.3 Conclusions 82
2.6 Augmented Lagrangian Algorithm 83
2.6.1 New Formulations of the Problem 83
2.6.2 Approximate Augmented Lagrangian
Formulation 85
2.6.3 Description of the Basic Iterative Method 86
2.6.4 Solution of (2.6.17) (N = 2, F Piecewise
Constant) 88
2.6.5 Numerical Results 90
Chapter 3 FINITE ELEMENT ANALYSIS OF LOCALIZATION IN
PLASTICITY 94
3.1 Introduction 94
3.2 Some Examples of Localized Plastic Flow 97
3.3 Field Equations 104
Contents vii
3.4 Constitutive Relations 109
3.4.1 Classical Smooth Yield Surface Plasticity
Theory 109
3.4.2 Deformation Theory 111
3.4.3 J2 Corner Theory 113
3.4.4 Single Crystal Plasticity 115
3.4.5 Continuum Model of a Ductile Porous
Material 119
3.5 Bifurcation and Uniqueness 122
3.6 Computational Considerations 129
3.7 Numerical Results 133
3.7.1 Plane Strain Tension 133
3.7.2 Localization from Highly Nonhomogeneous Defor¬
mation States 145
3.7.3 Void Sheet Formation 152
3.8 Concluding Remarks 155
Chapter 4 CONTACT PROBLEMS IN ELASTOSTATICS 158
4.1 Introduction 158
4.2 Signorini's Problem with Friction 159
4.2.1 Equilibrium Equations 160
4.2.2 Boundary Conditions 161
4.2.3 Boundary Value Problems 167
4.3 Variational Formulations of Signorini's Problem 168
4.3.1 Abstract Signorini's Problem with
Friction 168
4.3.2 Special Case I: Prescribed Tangential Stress 171
4.3.3 Special Case II: Prescribed Normal Stress 172
4.4 Special Case I: Prescribed Tangential Stress 173
4.4.1 Existence of a Unique Solution: Resolution of the
Contact Condition 174
4.4.2 Penalty Resolution of the Contact
Condition 175
4.4.3 Finite Element Approximations 180
4.4.4 Convergence of the Finite Element
Approximation 183
4.4.5 Numerical Examples 193
viii Contents
4.5 Special Case II: Prescribed Normal Stress 197
4.5.1 Existence of a Unique Solution 197
4.5.2 Regularization of the Functional j (•) 198
4.5.3 Finite Element Approximations 203
4.5.4 Convergence of the Finite Element
Method 204
4.5.5 Numerical Examples 207
Chapter 5 NONLOCAL FRICTION IN CONTACT PROBLEMS IN
PLANE ELASTICITY 213
5.1 Introduction 213
5.2 Nature of Friction and Basis for Nonlocal Law 215
5.2.1 Micromechanics of Friction 215
5.2.2 Nonlocal Friction Model 216
5.3 Variational Principle for Signorini's Problem with Nonlocal
Friction 220
5.3.1 Notations and Preliminaries 220
5.3.2 Variational Principle 224
5.3.3 Existence and Uniqueness of Solutions to the Non¬
local Friction Problem 229
5.4 Finite Element Approximations 239
5.4.1 The Approximate Problem 239
5.4.2 Error Estimate 241
5.4.3 Algorithms for Nonlocal Friction
Problems 248
5.5 Numerical Example 250
REFERENCES 253
INDEX 268 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:16:05Z |
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| isbn | 013317073X |
| language | English |
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| physical | XI, 273 S. graph. Darst. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
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| publisher | Prentice-Hall |
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| spelling | Finite elements 5 Special problems in solid mechanics J. Tinsley Oden ... 1. print Englewood Cliffs, N.J. Prentice-Hall 1984 XI, 273 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Becker, Eric B. Sonstige oth Carey, Graham F. Sonstige oth Oden, John Tinsley Sonstige oth (DE-604)BV021866581 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332958&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Finite elements |
| title | Finite elements |
| title_auth | Finite elements |
| title_exact_search | Finite elements |
| title_exact_search_txtP | Finite elements |
| title_full | Finite elements 5 Special problems in solid mechanics J. Tinsley Oden ... |
| title_fullStr | Finite elements 5 Special problems in solid mechanics J. Tinsley Oden ... |
| title_full_unstemmed | Finite elements 5 Special problems in solid mechanics J. Tinsley Oden ... |
| title_short | Finite elements |
| title_sort | finite elements special problems in solid mechanics |
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