Computer simulation of dynamic phenomena:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1999
|
| Schriftenreihe: | Scientific computation
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 246 S. Ill., graph. Darst. |
| ISBN: | 3540630708 |
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| 100 | 1 | |a Wilkins, Mark L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Computer simulation of dynamic phenomena |c Mark L. Wilkins |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1999 | |
| 300 | |a XVI, 246 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Scientific computation | |
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Datensatz im Suchindex
| _version_ | 1804126829290717184 |
|---|---|
| adam_text | Table of Contents
1. Elements of Fluid Mechanics 1
1.1 Fundamental Equations 2
1.1.1 Equation of Motion 2
1.1.2 Continuity Equation 2
1.1.3 Energy Equation 2
1.1.4 Equation of State 2
1.2 Solutions to the Fundamental Equations 3
1.3 Propagation of Discontinuities 4
1.3.1 Sound Speed 4
1.3.2 Speed of Discontinuity Propagation 5
1.3.3 Characteristics 6
1.3.4 Shock Waves 8
1.4 Derivation of the Hugoniot Relations 9
1.4.1 Conservation of Mass 9
1.4.2 Conservation of Momentum 10
1.4.3 Conservation of Energy 10
1.5 Rayleigh Line 11
1.6 Applications of Hugoniot Equations to a Perfect Gas 13
1.6.1 Calculation of Shock Speed 13
1.6.2 Calculation of Shock Pressure 14
1.6.3 Calculation of Volume Behind the Shock 14
1.6.4 Graphical Representation 15
1.6.5 Reflection of a Uniform Shock 15
1.6.6 Conditions Behind the First Reflected Shock
from a Fixed Boundary 16
1.7 Detonation Waves 17
1.8 Elastic Plastic Waves 17
1.9 Units and Orders of Magnitude 20
1.10 Measurements to Obtain Equation of State Data 20
1.10.1 Experimental Methods 20
1.10.2 Relation of the Free Surface Velocity
to the Shock Particle Velocity in a Solid 22
1.10.3 Form of the Equation of State for Solids 23
1.10.4 Detonation Pressure Measurement 25
VIII Table of Contents
2. Numerical Techniques 27
2.1 Von Neumann Finite Difference Scheme 27
2.1.1 Time Centering 28
2.1.2 Space Centering 28
2.2 Artificial Viscosity 28
2.2.1 Generalized Artificial Viscosity 28
2.2.2 Applications of the Generalized Artificial Viscosity
in One Space Dimension 29
2.3 Stability Conditions 32
2.3.1 Courant Condition 32
2.3.2 Von Neumann Stability Analysis 32
2.4 Finite Difference Scheme in Two Dimensions 33
2.4.1 Integral Definition of a Derivative 33
2.4.2 Integration Paths 34
2.4.3 Properties of the Integration Scheme 34
2.4.4 Continuity Equation 34
2.5 Finite Difference Scheme in Three Dimensions 35
2.6 Finite Difference Scheme for Double Operators
in Two Dimensions 35
2.7 Grid Stabilization 36
3. Modeling the Behavior of Materials 37
3.1 Introduction 37
3.1.1 Hooke s Law 37
3.1.2 Rigid Body Rotation 39
3.2 Plastic Flow Region 39
3.2.1 Yield Strength 41
3.2.2 Von Mises Yield Condition 43
3.2.3 Plastic Strain 45
3.2.4 Tresca Yield Condition 46
3.3 Flow Stress 48
3.3.1 Strain Hardening 50
3.3.2 A General Form of Strain Hardening 50
3.4 Rate Dependent Yield Models 52
3.4.1 Maxwell Solid 52
3.4.2 Dislocation Theory 53
3.4.3 Flow Stress Measurements 57
3.5 Upper Yield Point 59
3.6 Nonhomogeneous Properties 60
3.7 Hydrostatic Pressure Equation of State 60
3.8 Modeling Fracture 62
3.8.1 Fracture Toughness Testing 65
3.8.2 Spallation 67
3.8.3 Ductile Fracture 68
3.8.4 Strain Damage 68
Table of Contents IX
3.8.5 Damage in Elastic Regime 69
3.8.6 Computer Simulation of Fracture 70
3.8.7 Damage in Plastic Regime 71
3.9 Equation of State of Explosive Detonation Products 75
3.9.1 Numerical Calculation of a Detonation 79
4. Two Dimensional Elastic—Plastic Flow 83
4.1 Fundamental Equations 83
4.1.1 Equation of Motion in x, y Coordinates with Cylindri¬
cal Symmetry and Rotation About the x Axis 83
4.1.2 Conservation of Mass 84
4.1.3 First Law of Thermodynamics 84
4.1.4 Velocity Strains 84
4.1.5 Stress Deviator Tensor 85
4.1.6 Pressure Equation of State 85
4.1.7 Total Stresses 85
4.1.8 Artificial Viscosity 85
4.1.9 Von Mises Yield Condition 86
4.2 Finite Difference Equations 86
4.2.1 Mass Zoning 80
4.2.2 Equations of Motion 87
4.2.3 Conservation of Mass 88
4.2.4 Calculation of Incremental Strain 89
4.2.5 Calculation of Stresses 90
4.2.6 Von Mises Yield Condition 92
4.2.7 Equivalent Plastic Strain, £p 92
4.2.8 Artificial Viscosity for Calculating Shocks 93
4.2.9 Navier Stokes Artificial Viscosity
for Stabilizing the Grid 94
4.2.10 Material Internal Energy 96
4.2.11 Calculation of Time Steps. Atn+3/2 and Atn+1 97
4.2.12 Energy Summations (Edit Routine) 97
4.2.13 Principal Stresses (Edit Routine) 98
4.2.14 Calculation of Load, L. on a Given k Line
(Edit Routine) 98
4.3 Boundary Conditions 99
4.3.1 Fixed Boundary on the x Axis 99
4.3.2 Fixed Boundary on the y Axis 100
4.3.3 Corner Zone on the x Axis 100
4.3.4 Corner Zone on the y Axis 101
4.3.5 Free Surfaces 102
4.3.6 Discussion 102
4.4 Applications 103
X Table of Contents
5. Sliding Interfaces in Two Dimensions 113
5.1 Sliding Interfaces Between Quadrilateral Lagrange Zones .... 114
5.1.1 Location of Master Points Associated
with a Given Slave Point 115
5.1.2 Calculation of the Volume of Sliding Zones
Associated with the Slave Grid 115
5.1.3 Advancing a Slave Point / in Time 116
5.1.4 Location of Slave Points
Associated with a Given Master Point 120
5.1.5 Advancement in Time of Point j, k
on the Master Grid 121
5.1.6 Testing for Penetration of Grids 123
5.1.7 Adjusting the Velocities of All Void Closed Points
Where d 0 and Where in the Previous Cycle
the Point Was Void Open 124
5.1.8 Relocating Slave Points onto the Master Surface
when d 0 126
5.2 Intersecting Slide Lines 126
5.2.1 Acceleration of Points on the Intersection
of Two Slide Lines 126
5.2.2 Adjustment for Grid Penetration 127
5.2.3 Relocation of Points when a Void Has Opened 127
6. Elastic—Plastic Flow in Three Space Dimensions 129
6.1 Fundamental Equations 129
6.1.1 Equations of Motion 129
6.1.2 Conservation of Mass 129
6.1.3 First Law of Thermodynamics 129
6.1.4 Velocity Strains 130
6.1.5 Stress Deviator Tensor 130
6.1.6 Pressure Equation of State 130
6.1.7 Total Stresses 131
6.1.8 Artificial Viscosity for Calculating Shocks 131
6.1.9 Von Mises Yield Condition 131
6.2 Finite Difference Equations for HEMP 3D 131
6.2.1 Mass Zoning 131
6.2.2 Equations of Motion 133
6.2.3 Conservation of Mass 136
6.2.4 Calculation of Incremental Strains 136
6.2.5 Calculation of Stresses 139
6.2.6 Von Mises Yield Condition 140
6.2.7 Plastic Strain 140
6.2.8 Artificial Viscosity for Calculating Shocks 141
6.2.9 Tensor Artificial Viscosity for Stabilizing the Grid 142
6.2.10 Material Internal Energy 145
Table of Contents XI
6.2.11 Time Step Calculations 146
6.3 Boundary Conditions 146
6.4 Check Problems 146
6.4.1 Simple Harmonic Motion 146
6.4.2 Plasticity 149
7. Sliding Surfaces in Three Dimensions 151
7.1 Calculational Steps to Advance in Time Grid Points
on a Sliding Surface 153
7.2 Applications of Sliding Surface Routine 163
7.3 Zone Dimension Change and Subcycling 163
7.3.1 Zone Dimension Change at an Interface
in Two Dimensions 163
7.3.2 Zone Dimension Change of an Interface
in Three Dimensions 167
7.3.3 Subcycling with Zone Dimension Change
in Two Dimensions 169
7.3.4 Example for a Zone Size Change of Two to One 169
8. Magnetohydrodynamics of HEMP 171
8.1 Finite Difference Scheme for Double Operators 172
8.2 Fundamental Equations of Magnetohydrodynamics 174
8.2.1 Equation of Motion 174
8.2.2 Electromagnetic Field Equations 174
8.2.3 Energy Equation 175
8.2.4 Continuity Equation 176
8.2.5 Constitutive Relations 176
8.3 Difference Equations for Magnetohydrodynamics 176
8.3.1 Equations of Motion 176
8.3.2 Magnetic Diffusion 177
8.3.3 Energy Equations 179
8.3.4 Continuity Equation 182
8.3.5 Time Step Control 182
8.3.6 Boundary Conditions 183
8.3.7 Sliding Interfaces 183
8.3.8 Check Problems 185
Appendices 189
A. Effect of a Second Shock on the Principal Hugoniot 189
B. Finite Difference Program for One Space Dimension
and Time I91
B.I Fundamental Equations 191
B.2 Finite Difference Equations 192
B.3 Boundary Conditions 194
B.4 Opening and Closing Voids 195
XII Table of Contents
C. A Method for Determining
the Plastic Work Hardening Function 197
C.I Application to 6061 T6 Aluminum 199
D. Detonation of a High Explosive for a 7 Law Equation
of State 202
E. Magnetic Flux Calculation 211
F. Thermal Diffusion Calculation 224
G. Backward Substitution Method for Solving a System
of Linear Equations of the Form
AHi+i + BiHi + CtHi i =Di 238
References 241
Subject Index 245
|
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| discipline | Physik Informatik Mathematik |
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| id | DE-604.BV012211016 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:23:40Z |
| institution | BVB |
| isbn | 3540630708 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008275492 |
| oclc_num | 39890438 |
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| physical | XVI, 246 S. Ill., graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Scientific computation |
| spelling | Wilkins, Mark L. Verfasser aut Computer simulation of dynamic phenomena Mark L. Wilkins Berlin u.a. Springer 1999 XVI, 246 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Scientific computation Elastoplasticity Computer simulation Gas dynamics Computer simulation Hydrodynamics Computer simulation Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Fließen (DE-588)4017547-9 gnd rswk-swf Elastoplastizität (DE-588)4204381-5 gnd rswk-swf Gasdynamik (DE-588)4019339-1 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Computersimulation (DE-588)4148259-1 s Fließen (DE-588)4017547-9 s DE-604 Hydrodynamik (DE-588)4026302-2 s Gasdynamik (DE-588)4019339-1 s Elastoplastizität (DE-588)4204381-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008275492&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wilkins, Mark L. Computer simulation of dynamic phenomena Elastoplasticity Computer simulation Gas dynamics Computer simulation Hydrodynamics Computer simulation Hydrodynamik (DE-588)4026302-2 gnd Fließen (DE-588)4017547-9 gnd Elastoplastizität (DE-588)4204381-5 gnd Gasdynamik (DE-588)4019339-1 gnd Computersimulation (DE-588)4148259-1 gnd |
| subject_GND | (DE-588)4026302-2 (DE-588)4017547-9 (DE-588)4204381-5 (DE-588)4019339-1 (DE-588)4148259-1 |
| title | Computer simulation of dynamic phenomena |
| title_auth | Computer simulation of dynamic phenomena |
| title_exact_search | Computer simulation of dynamic phenomena |
| title_full | Computer simulation of dynamic phenomena Mark L. Wilkins |
| title_fullStr | Computer simulation of dynamic phenomena Mark L. Wilkins |
| title_full_unstemmed | Computer simulation of dynamic phenomena Mark L. Wilkins |
| title_short | Computer simulation of dynamic phenomena |
| title_sort | computer simulation of dynamic phenomena |
| topic | Elastoplasticity Computer simulation Gas dynamics Computer simulation Hydrodynamics Computer simulation Hydrodynamik (DE-588)4026302-2 gnd Fließen (DE-588)4017547-9 gnd Elastoplastizität (DE-588)4204381-5 gnd Gasdynamik (DE-588)4019339-1 gnd Computersimulation (DE-588)4148259-1 gnd |
| topic_facet | Elastoplasticity Computer simulation Gas dynamics Computer simulation Hydrodynamics Computer simulation Hydrodynamik Fließen Elastoplastizität Gasdynamik Computersimulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008275492&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wilkinsmarkl computersimulationofdynamicphenomena |