Smooth particle applied mechanics : the state of the art

This book takes readers through all the steps necessary for solving hard problems in continuum mechanics with smooth particle methods. Pedagogical problems clarify the generation of initial conditions, the treatment of boundary conditions, the integration of the equations of motion, and the analysis of the results. Particular attention is paid to the parallel computing necessary for large problems and to the graphic displays, including debugging software, required for the efficient completion of computational projects.The book is self-contained, with summaries of classical particle mechanics and continuum mechanics for both fluids and solids, computer languages, the stability of numerical methods, Lyapunov spectra, and message-passing parallel computing. The main difficulties faced by meshless particle methods are discussed and the means of overcoming them are illustrated with worked examples.

Dedication and Motivation	p. v
Preface	p. vii
1 Physical Ideas Underlying SPAM	p. 1
1.1 Motivation and Summary	p. 1
1.2 Particles versus Continua	p. 3
1.3 Newton's Particle Mechanics	p. 4
1.4 Eulerian and Lagrangian Continuum Mechanics	p. 9
1.5 Computer Simulation of Microscopic Particle Motion	p. 14
1.6 Liouville's Theorem; Statistical Mechanics	p. 16
1.7 Simulating Continua with Particles	p. 20
1.8 SPAM [ Smooth Particle Applied Mechanics ]	p. 24
1.9 Example: A Molecular Dynamics Simulation	p. 26
1.10 References	p. 31
2 Continuum Mechanics	p. 33
2.1 Summary and Scope of Continuum Mechanics	p. 33
2.2 Evolution Equations for Fluids and Solids	p. 35
2.3 Initial and Boundary Conditions	p. 39
2.4 Constitutive Equations for Equilibrium Fluids	p. 42
2.5 Constitutive Relations for Nonequilibrium Fluids	p. 45
2.6 Artificial Viscosity and Conductivity	p. 46
2.7 Constitutive Relations for Elastic Solids	p. 48
2.8 Constitutive Relation for Nonequilibrium Plasticity	p. 52
2.9 Plasticity Algorithm	p. 55
2.10 Example: Heat Conduction in One Dimension	p. 58
2.11 Example: Sound Propagation in One Dimension	p. 59
2.12 Example: Rayleigh-Benard Flow in Two Dimensions	p. 60
2.13 References	p. 64
3 Smooth Particle Methods	p. 65
3.1 Summary	p. 65
3.2 Motivation	p. 66
3.3 Basic Equations	p. 67
3.4 Interpolation on an Irregular Grid	p. 68
3.5 Alternative Averages: [ f0, f1, f2,...]	p. 71
3.6 Weight Functions	p. 74
3.7 Continuity Equation from [nabla middot] v with SPAM	p. 80
3.8 Evaluating the Spatial Derivatives {{[nabla rho], [nabla middot] P, [nabla middot] Q}}	p. 82
3.9 SPAM Equation of Motion and Energy Equation	p. 83
3.10 Rezoning; Does Particle Size Matter?	p. 84
3.11 Ideal-Gas Isomorphism with SPAM	p. 85
3.12 Evaluating the Spatial Derivatives {{[nabla]v, [nabla]T}}	p. 87
3.13 von Neumann-Richtmyer Artificial SPAM Viscosity	p. 89
3.14 Example: Adiabatic Atmospheric Equilibrium	p. 91
3.15 Example: Isothermal Atmospheric Equilibrium	p. 94
3.16 References	p. 97
4 Computer Programming	p. 99
4.1 Summary	p. 99
4.2 FORmula TRANslation languages	p. 100
4.3 Designing a SPAM program	p. 105
4.4 Runge-Kutta Integration with Fortran and C	p. 112
4.5 A Useful Random Number Generator	p. 117
4.6 Graphic Displays and Analysis	p. 119
4.7 "Debugging" Tools-Finding Errors	p. 125
4.8 Parallel Computing	p. 128
4.9 Mesh Partitioning	p. 131
4.10 Message Passing Techniques	p. 133
4.11 Material Interfaces in Parallel Computing	p. 136
4.11.1 Concentric Annuli Undergoing Rotation	p. 137
4.11.2 Free Expansion Problem	p. 138
4.11.3 Crushing of an Elastic-Plastic Sheet	p. 139
4.11.4 Caricature of a Billiard Table	p. 140
4.12 References	p. 142
5 Initial and Boundary Conditions, Interpolation	p. 143
5.1 Summary	p. 143
5.2 Initial Coordinates	p. 144
5.3 Mesh Generation for SPAM with Free Boundaries	p. 147
5.4 Implementing Periodic and Mirror Boundaries	p. 150
5.5 Alternative Meshes-Regular Lattices	p. 156
5.6 Elastic Stability of Embedded-Atom Lattices	p. 157
5.7 Invariant Curvature Crystal Stabilization	p. 162
5.8 Example: Heat Transfer in One Dimension with SPAM	p. 164
5.9 Example: Periodic Shear Flow with SPAM	p. 167
5.10 Example: Rayleigh-Benard Flow with SPAM	p. 171
5.11 References	p. 175
6 Convergence and Stability	p. 177
6.1 Summary	p. 177
6.2 Existence and Uniqueness in Continuum Mechanics	p. 178
6.3 Accuracy and Precision in Numerical Solutions	p. 180
6.4 Convergence of Numerical Methods	p. 180
6.5 Runge-Kutta Integration of Linear Problems	p. 181
6.6 Stability	p. 184
6.7 Lyapunov Instability	p. 186
6.8 Stability Analysis for a Chaotic Problem	p. 188
6.9 Size Dependence: Lessons from Molecular Dynamics	p. 190
6.10 Smooth-Particle Spatial Integration Errors	p. 191
6.11 Lattice Instability	p. 192
6.12 Even-Odd Instability	p. 195
6.13 Example: Shear-Flow Convergence	p. 196
6.14 References	p. 199
7 Lucy and Embedded-Atom Fluids	p. 201
7.1 Summary	p. 201
7.2 Trajectory Isomorphism for the Lucy Fluid	p. 202
7.3 Statistical Thermodynamics for the Lucy Potential	p. 203
7.4 Trajectory Isomorphism for the Embedded-Atom Fluid	p. 205
7.5 Embedded-Atom Approach to Structural Relaxation	p. 207
7.6 Example: Embedded-Atom Gravitational Relaxation	p. 208
7.7 Example: Embedded-Atom Model of Falling Water	p. 211
7.8 Example: Free Expansion of a [gamma]-law Gas	p. 213
7.9 Example: Lucy-Fluid Shockwave Structure	p. 217
7.10 References	p. 225
8 SPAM: Limitations and Difficulties	p. 227
8.1 Summary	p. 227
8.2 Surface Tension	p. 227
8.3 Tensile Instability	p. 231
8.4 Monaghan's Motion Equations	p. 233
8.5 Continuum Mechanics: Stress; Rigid-Body Rotation	p. 236
8.6 Dynamic and Static Constitutive Relations	p. 237
8.7 Example Deformations with Stress and Strain Rates	p. 241
8.8 Dynamics with Jaumann's Stress Rotation Rate	p. 244
8.9 Conservation of Angular Momentum	p. 246
8.10 Artificial Transport Coefficients	p. 248
8.11 Residual Stress-Artificial Plasticity in SPAM	p. 249
8.12 References	p. 251
9 SPAM: Sample Applications to Solids	p. 253
9.1 Summary	p. 253
9.2 The Tension Test	p. 254
9.3 Tension Test via Standard Molecular Dynamics	p. 256
9.4 Boundary Conditions for Tension	p. 257
9.5 Initial Conditions for Tension Using SPAM	p. 260
9.6 Tension Test via SPAM-like Molecular Dynamics	p. 261
9.7 Tension Test via SPAM	p. 263
9.8 Failure Algorithms	p. 266
9.9 Penetration Mechanics	p. 266
9.10 Penetration via Continuum Mechanics	p. 267
9.11 Penetration via Standard Molecular Dynamics	p. 270
9.12 Penetration via SPAM-like Molecular Dynamics	p. 271
9.13 Penetration via SPAM	p. 272
9.14 A Research Suggestion	p. 275
9.15 References	p. 276
10 Summary, Literature, and Outlook	p. 277
10.1 Introduction	p. 277
10.2 Current State of the Art	p. 278
10.3 Cutting and Machining	p. 279
10.4 Structural Response to Waves	p. 280
10.5 Dynamics of Sea Ice	p. 281
10.6 Astrophysics	p. 283
10.7 The Near Future of Parallel Computing	p. 285
10.8 An Afterword	p. 286
10.9 References	p. 287
Alphabetical Bibliography	p. 289
Index	p. 295
Example Problem List	p. 299

Mevcut:*

Bound With These Titles

On Order

Özet

Özet

Table of Contents