Meshfree particle methods:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [453] - 478 |
| Beschreibung: | III, 502 S. Ill., graph. Darst. |
| ISBN: | 3540222561 |
Internformat
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| 100 | 1 | |a Li, Shaofan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Meshfree particle methods |c Shaofan Li ; Wing Kam Liu |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a III, 502 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. [453] - 478 | ||
| 650 | 4 | |a Méthodes particulaires (Analyse numérique) | |
| 650 | 4 | |a Méthodes sans maillage (Analyse numérique) | |
| 650 | 7 | |a Método dos elementos finitos |2 larpcal | |
| 650 | 4 | |a Meshfree methods (Numerical analysis) | |
| 650 | 4 | |a Particle methods (Numerical analysis) | |
| 650 | 0 | 7 | |a Gitterfreie Methode |0 (DE-588)4796173-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Theoretische Mechanik |0 (DE-588)4185100-6 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Liu, Wing Kam |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch Darmstadt |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015194527&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804135952483876864 |
|---|---|
| adam_text | SHAOFAN LI * WING KAM LIU MESHFREE PARTICLE METHODS WITH 189 FIGURES, 74
IN COLOUR 4Y SPRINGER CONTENTS 1. INTRODUCTION 7 1.1 WHY DO WE NEED
MESHFREE PARTICLE METHODS ? 7 1.2 PRELIMINARY 12 1.2.1 NOTATION 12 1.2.2
PARTITION OF UNITY 14 1.2.3 WINDOW FUNCTION AND MOLLIFIER 15 1.2.4
HILBERT SPACE 16 1.2.5 VARIATIONAL WEAK FORMULATION 18 1.2.6 GALERKIN
METHODS 19 1.2.7 TIME-STEPPING ALGORITHMS 20 1.2.8 VORONOI DIAGRAM AND
DELAUNAY TESSELLATION 22 2. SMOOTHED PARTICLE HYDRODYNAMICS (SPH) 25 2.1
SPH INTERPOLATION 26 2.1.1 DELTA FUNCTION 26 2.1.2 SPH AVERAGING
OPERATOR 26 2.1.3 KERNEL FUNCTIONS 28 2.1.4 CHOICE OF SMOOTHING LENGTH H
30 2.2 APPROXIMATION THEORY OF SPH 31 2.2.1 SPH APPROXIMATION RULES 31
2.2.2 SPH APPROXIMATIONS OF DERIVATIVES (GRADIENTS) 33 2.3 DISCRETE
SMOOTH PARTICLE HYDRODYNAMICS 36 2.3.1 CONSERVATION LAWS IN CONTINUUM
MECHANICS 36 2.3.2 SPH CONTINUITY EQUATION 37 2.3.3 SPH MOMENTUM
EQUATION 38 2.3.4 SPH ENERGY EQUATION 39 2.3.5 SPH ARTIFICIAL VISCOSITY
39 2.3.6 TIME INTEGRATION OF SPH CONSERVATION LAWS 42 2.3.7 SPH
CONSTITUTIVE UPDATE 43 2.4 INVARIANT PROPERTIES OF SPH EQUATIONS 44
2.4.1 GALILEAN INVARIANCE 44 2.4.2 CONSERVATION OF MASS 45 2.4.3
CONSERVATION OF LINEAR MOMENTUM 45 2.4.4 CONSERVATION OF ANGULAR
MOMENTUM 46 CONTENTS 2.4.5 CONSERVATION OF MECHANICAL ENERGY 47 2.4.6
VARIATIONAL SPH FORMULATION 47 2.5 CORRECTIVE SPH AND OTHER IMPROVEMENTS
ON SPH 50 2.5.1 ENFORCING THE ESSENTIAL BOUNDARY CONDITION 50 2.5.2
TENSILE INSTABILITY 52 2.5.3 SPH INTERPOLATION ERROR 55 2.5.4 CORRECTION
FUNCTION (RKPM) 56 2.5.5 MOVING LEAST SQUARE HYDRODYNAMICS (MLSPH) 61
2.5.6 JOHNSON-BEISSEL CORRECTION 62 2.5.7 RANDLES-LIBERSKY CORRECTION 63
2.5.8 KRONGAUZ-BELYTSCHKO CORRECTION 63 2.5.9 CHEN-BERAUN CORRECTION 64
2.6 REMARKS 65 EXERCISES 66 3. MESHFREE GALERKIN METHODS 68 3.1 MOVING
LEAST SQUARE REPRODUCING KERNEL INTERPOLANT 68 3.1.1 POLYNOMIAL
REPRODUCING PROPERTY 72 3.1.2 THE SHEPARD INTERPOLANT 74 3.1.3
INTERPOLATING MOVING LEAST SQUARE INTERPOLANT 75 3.1.4 ORTHOGONAL BASIS
FOR THE LOCAL APPROXIMATION 79 3.1.5 EXAMPLES OF RKPM KERNEL FUNCTION 80
3.1.6 CONSERVATION PROPERTIES OF RKPM INTERPOLANT 88 3.1.7
ONE-DIMENSIONAL MODEL PROBLEM 91 3.1.8 PROGRAM DESCRIPTION 94 3.2
MESHFREE WAVELET INTERPOLANT 96 3.2.1 VARIATION IN A THEME: GENERALIZED
MOVING LEAST SQUARE REPRODUCING KERNEL 96 3.2.2 INTERPOLATION FORMULAS
101 3.2.3 HIERARCHICAL PARTITION OF UNITY AND HIERARCHICAL BASIS . 103
3.3 MLS INTERPOLANT AND DIFFUSE ELEMENT METHOD 109 3.3.1 DIFFUSE ELEMENT
METHOD 109 3.3.2 EVALUATE THE DERIVATIVE OF MLS INTERPOLANT 109 3.4
ELEMENT-FREE GALERKIN METHOD (EFGM) ILL 3.4.1 LAGRANGIAN MULTIPLIER
METHOD ILL 3.4.2 PENALTY METHOD 113 3.4.3 NITSCHE S METHOD 114 3.4.4
TRANSFORM METHOD 116 3.4.5 BOUNDARY SINGULAR KERNEL METHOD 120 3.4.6
COUPLED FINITE ELEMENT AND PARTICLE APPROACH 121 3.5 H-P CLOUDS METHOD
123 3.6 THE PARTITION OF UNITY METHOD (PUM) 125 3.6.1 EXAMPLES OF
PARTITION OF UNITY 126 3.6.2 EXAMPLES OF PUM INTERPOLANTS 127 3.7
MESHFREE QUADRATURE AND FINITE SPHERE METHOD 128 CONTENTS 3 3.7.1
CUBATURE ON ANNULAR SECTORS IN IR 2 132 3.8 MESHFREE LOCAL
PETROV-GALERKIN (MLPG) METHOD 133 3.9 FINITE POINT METHOD 135 3.10
MESHFREE LOCAL BOUNDARY INTEGRAL EQUATION 137 3.11 MESHFREE QUADRATURE
AND NODAL INTEGRATION 138 4. APPROXIMATION THEORY OF MESHFREE
INTERPOLANTS 142 4.1 REQUIREMENTS AND PROPERTIES OF MESHFREE
DISCRETIZATION 142 4.1.1 REGULARITY OF PARTICLE DISTRIBUTIONS 143 4.1.2
BOUNDS ON SHAPE FUNCTIONS AND THEIR DERIVATIVES .... 152 4.2
COMPLETENESS AND CONSISTENCY OF MESHFREE INTERPOLANTS 154 4.2.1 P-TH
ORDER CONSISTENCY CONDITION 155 4.2.2 DIFFERENTIAL CONSISTENCY
CONDITIONS 157 4.3 MESHFREE INTERPOLATION ERROR ESTIMATE 160 4.3.1 LOCAL
INTERPOLATION ESTIMATE 160 4.4 CONVERGENCE OF MESHFREE GALERKIN
PROCEDURES 165 4.4.1 THE NEUMANN BOUNDARY VALUE PROBLEM (BVP) 165 4.4.2
THE DIRICHLET BOUNDARY VALUE PROBLEM 169 4.4.3 NUMERICAL EXAMPLES 172
4.5 APPROXIMATION THEORY OF MESHFREE WAVELET FUNCTIONS 177 4.5.1 THE
GENERALIZED CONSISTENCY CONDITIONS 177 4.5.2 INTERPOLATION ESTIMATE 181
5. APPLICATIONS 187 5.1 EXPLICIT MESHFREE COMPUTATIONS IN LARGE
DEFORMATION 187 5.2 MESHFREE SIMULATION OF LARGE DEFORMATION 192 5.2.1
SIMULATIONS OF LARGE DEFORMATION OF THIN SHELL STRUC- TURES 192 5.2.2 J2
HYPOELASTIC-PLASTIC MATERIAL AT FINITE STRAIN 194 5.2.3 HEMISPHERIC
SHELL UNDER CONCENTRATED LOADS 196 5.2.4 CRASH TEST OF A BOXBEAM 198 5.3
SIMULATIONS OF STRAIN LOCALIZATION 201 5.3.1 MODEL PROBLEMS 201 5.3.2
MESH-ALIGNMENT SENSITIVITY 201 5.3.3 MESHFREE TECHNIQUES FOR SIMULATIONS
OF STRAIN LOCAL- IZATION 205 5.3.4 ADAPTIVE PROCEDURES 210 5.4
SIMULATIONS OF DYNAMICS SHEARBAND PROPAGATION 215 5.4.1
THERMAL-VISCOPLASTIC MODEL 217 5.4.2 CONSTITUTIVE MODELING IN
POST-BIFURCATION PHASE 221 5.4.3 NUMERICAL EXAMPLES 223 5.4.4 CASE I:
INTERMEDIATE SPEED IMPACT (V = 30 M/S) 224 5.4.5 CASE II: HIGH SPEED
IMPACT (V = 33 M/S) 228 5.5 SIMULATIONS OF CRACK GROWTH 228 5.5.1
VISIBILITY CONDITION 228 CONTENTS 5.5.2 CRACK SURFACE REPRESENTATION AND
PARTICLE SPLITTING ALGORITHM 231 5.5.3 PARAMETRIC VISIBILITY CONDITION
233 5.5.4 REPRODUCING ENRICHMENT TECHNIQUE 238 5.6 MESHFREE CONTACT
ALGORITHM 241 5.6.1 CONTACT DETECTION ALGORITHM 241 5.6.2 EXAMPLES OF
CONTACT SIMULATIONS 247 5.7 MESHFREE SIMULATIONS OF FLUID DYNAMICS 249
5.7.1 MESHFREE STABILIZATION METHOD 249 5.7.2 MULTISCALE SIMULATION OF
FLUID FLOWS 255 5.8 IMPLICIT RKPM FORMULATION 258 5.8.1 THE GOVERNING
EQUATIONS 258 5.8.2 ESSENTIAL BOUNDARY CONDITIONS 260 5.8.3
DISCRETIZATION OF THE WEAK FORM 263 5.8.4 TIME INTEGRATION SCHEME 264
5.8.5 COMMUNICATION STRUCTURE 266 5.8.6 PARTITIONING SCHEMES 268 5.8.7
OUTLINE OF PROCEDURES 268 5.9 NUMERICAL EXAMPLES OF MESHFREE SIMULATIONS
269 5.9.1 SIMPLE 3-D FLOW PAST A CIRCULAR CYLINDER 269 5.9.2 3-D FLOW
PAST A BUILDING 270 6. REPRODUCING KERNEL ELEMENT METHOD (RKEM) 276 6.1
INTRODUCTION 276 6.2 REPRODUCING KERNEL ELEMENT INTERPOLANT 278 6.2.1
GLOBAL PARTITION POLYNOMIALS 278 6.2.2 SOME PROPERTIES 283 6.2.3 ERROR
ANALYSIS OF THE METHOD WITH LINEAR REPRODUC- ING PROPERTY 288 6.2.4
NUMERICAL EXAMPLES 291 6.3 GLOBALLY CONFORMING I M /C N HIERARCHIES 299
6.4 GLOBALLY CONFORMING I M /C N HIERARCHY I 300 6.4.1 ID I 2 /C N
INTERPOLATION 304 6.4.2 2D I/C N QUADRILATERAL ELEMENT 305 6.4.3
GLOBALLY COMPATIBLE Q12P1I1 QUADRILATERAL ELEMENT . 308 6.4.4 GLOBALLY
COMPATIBLE Q16P2I2 QUADRILATERAL ELEMENT . 310 6.4.5 SMOOTH I/C N
TRIANGLE ELEMENT 311 6.4.6 GLOBALLY COMPATIBLE T9P1I1 TRIANGLE ELEMENT
313 6.4.7 GLOBALLY COMPATIBLE T18P2I2 TRIANGLE ELEMENT 315 6.5 GLOBALLY
CONFORMING I M /C N HIERARCHY II 317 6.5.1 CONSTRUCTION 317 6.5.2 ID
EXAMPLE: AN I L /C A /P 3 INTERPOLANT 320 6.5.3 2D EXAMPLE I: COMPATIBLE
GALLAGHER ELEMENT 322 6.5.4 2D EXAMPLE II: T12P3/(4/3) TRIANGLE ELEMENT
323 6.5.5 2D EXAMPLE III: Q12P3I1 QUADRILATERAL ELEMENT 326 CONTENTS 5
6.6 NUMERICAL EXAMPLES 328 6.6.1 EQUILATERAL TRIANGULAR PLATE 328 6.6.2
CLAMPED CIRCULAR PLATE 331 7. MOLECULAR DYNAMICS AND MULTI-SCALE METHODS
333 7.1 CLASSICAL MOLECULAR DYNAMICS 333 7.1.1 LAGRANGIAN EQUATIONS OF
MOTION 334 7.1.2 HAMILTONIAN EQUATIONS OF MOTION 336 7.1.3 INTERATOMIC
POTENTIALS 338 7.1.4 TWO-BODY (PAIR) POTENTIALS 339 7.1.5 ENERGETIC LINK
BETWEEN MD AND QUANTUM MECHANICS . 343 7.2 AB INITIO METHODS 346 7.2.1
DENSITY FUNCTIONAL THEORY 349 7.2.2 AB INITIO MOLECULAR DYNAMICS 350
7.2.3 TIGHT BINDING METHOD 351 7.2.4 NUMERICAL EXAMPLES 352 7.3 COUPLING
BETWEEN MD AND FEM 355 7.3.1 MAAD 355 7.3.2 MD/FE COUPLING - ID EXAMPLE
357 7.3.3 QUASICONTINUUM METHOD AND CAUCHY-BORN RULE 365 7.3.4
CAUCHY-BORN NUMERICAL EXAMPLES 370 7.3.5 MULTI-SCALE ALGORITHMS 373
7.3.6 GENERALIZED LANGEVIN EQUATION 376 7.3.7 MULTISCALE BOUNDARY
CONDITIONS 379 7.4 INTRODUCTION OF BRIDGING SCALE METHOD 385 7.4.1
MULTI-SCALE EQUATIONS OF MOTION 388 7.4.2 LANGEVIN EQUATION FOR BRIDGING
SCALE 390 7.4.3 STAGGERED TIME INTEGRATION ALGORITHM 395 7.4.4 BRIDGING
SCALE NUMERICAL EXAMPLES 396 7.5 APPLICATIONS 398 7.5.1 TWO-DIMENSIONAL
WAVE PROPAGATION 400 7.5.2 DYNAMIC CRACK PROPAGATION IN TWO DIMENSIONS
405 7.5.3 SIMULATIONS OF NANOCARBON TUBES 413 8. IMMERSED
MESHFREE/FINITE ELEMENT METHOD AND APPLICA- TIONS 422 8.1 INTRODUCTION
422 8.2 FORMULATIONS OF IMMERSED FINITE ELEMENT METHOD 423 8.3
COMPUTATIONAL ALGORITHM 426 8.4 APPLICATION TO BIOLOGICAL SYSTEMS 427
8.4.1 THREE RIGID SPHERES FALLING IN A TUBE 428 8.4.2 20 SOFT SPHERES
FALLING IN A CHANNEL 429 8.4.3 FLUID-FLEXIBLE STRUCTURE INTERACTION 429
8.4.4 IFEM COUPLED WITH PROTEIN MOLECULAR DYNAMICS 432 8.4.5 CELL-CELL
INTERACTION AND SHEAR RATE EFFECTS 434 6 CONTENTS 8.4.6 MICRO- AND
CAPILLARY VESSELS 435 8.4.7 ADHESION OF MONOCYTES TO ENDOTHELIAL CELLS
437 8.4.8 FLEXIBLE VALVE-VISCOUS FLUID INTERACTION 439 9. OTHER MESHFREE
METHODS 440 9.1 NATURAL ELEMENT METHOD 440 9.1.1 CONSTRUCTION OF NATURAL
NEIGHBOR 440 9.1.2 NATURAL NEIGHBOR INTERPOLATION 441 9.1.3 EXAMPLES OF
NATURAL NEIGHBOR INTERPOLANT 443 9.2 FREE MESH METHOD 443 9.3 MESHFREE
FINITE DIFFERENCE METHODS 443 9.4 VORTEX-IN-CELL METHODS 446 9.5
MATERIAL POINT METHOD (PARTICLE-IN-CELL METHOD) 448 9.6 LATTICE
BOLTZMANN METHOD 449 REFERENCES 453 10. PROGRAM LISTINGS 479
|
| adam_txt |
SHAOFAN LI * WING KAM LIU MESHFREE PARTICLE METHODS WITH 189 FIGURES, 74
IN COLOUR 4Y SPRINGER CONTENTS 1. INTRODUCTION 7 1.1 WHY DO WE NEED
MESHFREE PARTICLE METHODS ? 7 1.2 PRELIMINARY 12 1.2.1 NOTATION 12 1.2.2
PARTITION OF UNITY 14 1.2.3 WINDOW FUNCTION AND MOLLIFIER 15 1.2.4
HILBERT SPACE 16 1.2.5 VARIATIONAL WEAK FORMULATION 18 1.2.6 GALERKIN
METHODS 19 1.2.7 TIME-STEPPING ALGORITHMS 20 1.2.8 VORONOI DIAGRAM AND
DELAUNAY TESSELLATION 22 2. SMOOTHED PARTICLE HYDRODYNAMICS (SPH) 25 2.1
SPH INTERPOLATION 26 2.1.1 DELTA FUNCTION 26 2.1.2 SPH AVERAGING
OPERATOR 26 2.1.3 KERNEL FUNCTIONS 28 2.1.4 CHOICE OF SMOOTHING LENGTH H
30 2.2 APPROXIMATION THEORY OF SPH 31 2.2.1 SPH APPROXIMATION RULES 31
2.2.2 SPH APPROXIMATIONS OF DERIVATIVES (GRADIENTS) 33 2.3 DISCRETE
SMOOTH PARTICLE HYDRODYNAMICS 36 2.3.1 CONSERVATION LAWS IN CONTINUUM
MECHANICS 36 2.3.2 SPH CONTINUITY EQUATION 37 2.3.3 SPH MOMENTUM
EQUATION 38 2.3.4 SPH ENERGY EQUATION 39 2.3.5 SPH ARTIFICIAL VISCOSITY
39 2.3.6 TIME INTEGRATION OF SPH CONSERVATION LAWS 42 2.3.7 SPH
CONSTITUTIVE UPDATE 43 2.4 INVARIANT PROPERTIES OF SPH EQUATIONS 44
2.4.1 GALILEAN INVARIANCE 44 2.4.2 CONSERVATION OF MASS 45 2.4.3
CONSERVATION OF LINEAR MOMENTUM 45 2.4.4 CONSERVATION OF ANGULAR
MOMENTUM 46 CONTENTS 2.4.5 CONSERVATION OF MECHANICAL ENERGY 47 2.4.6
VARIATIONAL SPH FORMULATION 47 2.5 CORRECTIVE SPH AND OTHER IMPROVEMENTS
ON SPH 50 2.5.1 ENFORCING THE ESSENTIAL BOUNDARY CONDITION 50 2.5.2
TENSILE INSTABILITY 52 2.5.3 SPH INTERPOLATION ERROR 55 2.5.4 CORRECTION
FUNCTION (RKPM) 56 2.5.5 MOVING LEAST SQUARE HYDRODYNAMICS (MLSPH) 61
2.5.6 JOHNSON-BEISSEL CORRECTION 62 2.5.7 RANDLES-LIBERSKY CORRECTION 63
2.5.8 KRONGAUZ-BELYTSCHKO CORRECTION 63 2.5.9 CHEN-BERAUN CORRECTION 64
2.6 REMARKS 65 EXERCISES 66 3. MESHFREE GALERKIN METHODS 68 3.1 MOVING
LEAST SQUARE REPRODUCING KERNEL INTERPOLANT 68 3.1.1 POLYNOMIAL
REPRODUCING PROPERTY 72 3.1.2 THE SHEPARD INTERPOLANT 74 3.1.3
INTERPOLATING MOVING LEAST SQUARE INTERPOLANT 75 3.1.4 ORTHOGONAL BASIS
FOR THE LOCAL APPROXIMATION 79 3.1.5 EXAMPLES OF RKPM KERNEL FUNCTION 80
3.1.6 CONSERVATION PROPERTIES OF RKPM INTERPOLANT 88 3.1.7
ONE-DIMENSIONAL MODEL PROBLEM 91 3.1.8 PROGRAM DESCRIPTION 94 3.2
MESHFREE WAVELET INTERPOLANT 96 3.2.1 VARIATION IN A THEME: GENERALIZED
MOVING LEAST SQUARE REPRODUCING KERNEL 96 3.2.2 INTERPOLATION FORMULAS
101 3.2.3 HIERARCHICAL PARTITION OF UNITY AND HIERARCHICAL BASIS . 103
3.3 MLS INTERPOLANT AND DIFFUSE ELEMENT METHOD 109 3.3.1 DIFFUSE ELEMENT
METHOD 109 3.3.2 EVALUATE THE DERIVATIVE OF MLS INTERPOLANT 109 3.4
ELEMENT-FREE GALERKIN METHOD (EFGM) ILL 3.4.1 LAGRANGIAN MULTIPLIER
METHOD ILL 3.4.2 PENALTY METHOD 113 3.4.3 NITSCHE'S METHOD 114 3.4.4
TRANSFORM METHOD 116 3.4.5 BOUNDARY SINGULAR KERNEL METHOD 120 3.4.6
COUPLED FINITE ELEMENT AND PARTICLE APPROACH 121 3.5 H-P CLOUDS METHOD
123 3.6 THE PARTITION OF UNITY METHOD (PUM) 125 3.6.1 EXAMPLES OF
PARTITION OF UNITY 126 3.6.2 EXAMPLES OF PUM INTERPOLANTS 127 3.7
MESHFREE QUADRATURE AND FINITE SPHERE METHOD 128 CONTENTS 3 3.7.1
CUBATURE ON ANNULAR SECTORS IN IR 2 132 3.8 MESHFREE LOCAL
PETROV-GALERKIN (MLPG) METHOD 133 3.9 FINITE POINT METHOD 135 3.10
MESHFREE LOCAL BOUNDARY INTEGRAL EQUATION 137 3.11 MESHFREE QUADRATURE
AND NODAL INTEGRATION 138 4. APPROXIMATION THEORY OF MESHFREE
INTERPOLANTS 142 4.1 REQUIREMENTS AND PROPERTIES OF MESHFREE
DISCRETIZATION 142 4.1.1 REGULARITY OF PARTICLE DISTRIBUTIONS 143 4.1.2
BOUNDS ON SHAPE FUNCTIONS AND THEIR DERIVATIVES . 152 4.2
COMPLETENESS AND CONSISTENCY OF MESHFREE INTERPOLANTS 154 4.2.1 P-TH
ORDER CONSISTENCY CONDITION 155 4.2.2 DIFFERENTIAL CONSISTENCY
CONDITIONS 157 4.3 MESHFREE INTERPOLATION ERROR ESTIMATE 160 4.3.1 LOCAL
INTERPOLATION ESTIMATE 160 4.4 CONVERGENCE OF MESHFREE GALERKIN
PROCEDURES 165 4.4.1 THE NEUMANN BOUNDARY VALUE PROBLEM (BVP) 165 4.4.2
THE DIRICHLET BOUNDARY VALUE PROBLEM 169 4.4.3 NUMERICAL EXAMPLES 172
4.5 APPROXIMATION THEORY OF MESHFREE WAVELET FUNCTIONS 177 4.5.1 THE
GENERALIZED CONSISTENCY CONDITIONS 177 4.5.2 INTERPOLATION ESTIMATE 181
5. APPLICATIONS 187 5.1 EXPLICIT MESHFREE COMPUTATIONS IN LARGE
DEFORMATION 187 5.2 MESHFREE SIMULATION OF LARGE DEFORMATION 192 5.2.1
SIMULATIONS OF LARGE DEFORMATION OF THIN SHELL STRUC- TURES 192 5.2.2 J2
HYPOELASTIC-PLASTIC MATERIAL AT FINITE STRAIN 194 5.2.3 HEMISPHERIC
SHELL UNDER CONCENTRATED LOADS 196 5.2.4 CRASH TEST OF A BOXBEAM 198 5.3
SIMULATIONS OF STRAIN LOCALIZATION 201 5.3.1 MODEL PROBLEMS 201 5.3.2
MESH-ALIGNMENT SENSITIVITY 201 5.3.3 MESHFREE TECHNIQUES FOR SIMULATIONS
OF STRAIN LOCAL- IZATION 205 5.3.4 ADAPTIVE PROCEDURES 210 5.4
SIMULATIONS OF DYNAMICS SHEARBAND PROPAGATION 215 5.4.1
THERMAL-VISCOPLASTIC MODEL 217 5.4.2 CONSTITUTIVE MODELING IN
POST-BIFURCATION PHASE 221 5.4.3 NUMERICAL EXAMPLES 223 5.4.4 CASE I:
INTERMEDIATE SPEED IMPACT (V = 30 M/S) 224 5.4.5 CASE II: HIGH SPEED
IMPACT (V = 33 M/S) 228 5.5 SIMULATIONS OF CRACK GROWTH 228 5.5.1
VISIBILITY CONDITION 228 CONTENTS 5.5.2 CRACK SURFACE REPRESENTATION AND
PARTICLE SPLITTING ALGORITHM 231 5.5.3 PARAMETRIC VISIBILITY CONDITION
233 5.5.4 REPRODUCING ENRICHMENT TECHNIQUE 238 5.6 MESHFREE CONTACT
ALGORITHM 241 5.6.1 CONTACT DETECTION ALGORITHM 241 5.6.2 EXAMPLES OF
CONTACT SIMULATIONS 247 5.7 MESHFREE SIMULATIONS OF FLUID DYNAMICS 249
5.7.1 MESHFREE STABILIZATION METHOD 249 5.7.2 MULTISCALE SIMULATION OF
FLUID FLOWS 255 5.8 IMPLICIT RKPM FORMULATION 258 5.8.1 THE GOVERNING
EQUATIONS 258 5.8.2 ESSENTIAL BOUNDARY CONDITIONS 260 5.8.3
DISCRETIZATION OF THE WEAK FORM 263 5.8.4 TIME INTEGRATION SCHEME 264
5.8.5 COMMUNICATION STRUCTURE 266 5.8.6 PARTITIONING SCHEMES 268 5.8.7
OUTLINE OF PROCEDURES 268 5.9 NUMERICAL EXAMPLES OF MESHFREE SIMULATIONS
269 5.9.1 SIMPLE 3-D FLOW PAST A CIRCULAR CYLINDER 269 5.9.2 3-D FLOW
PAST A BUILDING 270 6. REPRODUCING KERNEL ELEMENT METHOD (RKEM) 276 6.1
INTRODUCTION 276 6.2 REPRODUCING KERNEL ELEMENT INTERPOLANT 278 6.2.1
GLOBAL PARTITION POLYNOMIALS 278 6.2.2 SOME PROPERTIES 283 6.2.3 ERROR
ANALYSIS OF THE METHOD WITH LINEAR REPRODUC- ING PROPERTY 288 6.2.4
NUMERICAL EXAMPLES 291 6.3 GLOBALLY CONFORMING I M /C N HIERARCHIES 299
6.4 GLOBALLY CONFORMING I M /C N HIERARCHY I 300 6.4.1 ID I 2 /C N
INTERPOLATION 304 6.4.2 2D I/C N QUADRILATERAL ELEMENT 305 6.4.3
GLOBALLY COMPATIBLE Q12P1I1 QUADRILATERAL ELEMENT . 308 6.4.4 GLOBALLY
COMPATIBLE Q16P2I2 QUADRILATERAL ELEMENT . 310 6.4.5 SMOOTH I/C N
TRIANGLE ELEMENT 311 6.4.6 GLOBALLY COMPATIBLE T9P1I1 TRIANGLE ELEMENT
313 6.4.7 GLOBALLY COMPATIBLE T18P2I2 TRIANGLE ELEMENT 315 6.5 GLOBALLY
CONFORMING I M /C N HIERARCHY II 317 6.5.1 CONSTRUCTION 317 6.5.2 ID
EXAMPLE: AN I L /C A /P 3 INTERPOLANT 320 6.5.3 2D EXAMPLE I: COMPATIBLE
GALLAGHER ELEMENT 322 6.5.4 2D EXAMPLE II: T12P3/(4/3) TRIANGLE ELEMENT
323 6.5.5 2D EXAMPLE III: Q12P3I1 QUADRILATERAL ELEMENT 326 CONTENTS 5
6.6 NUMERICAL EXAMPLES 328 6.6.1 EQUILATERAL TRIANGULAR PLATE 328 6.6.2
CLAMPED CIRCULAR PLATE 331 7. MOLECULAR DYNAMICS AND MULTI-SCALE METHODS
333 7.1 CLASSICAL MOLECULAR DYNAMICS 333 7.1.1 LAGRANGIAN EQUATIONS OF
MOTION 334 7.1.2 HAMILTONIAN EQUATIONS OF MOTION 336 7.1.3 INTERATOMIC
POTENTIALS 338 7.1.4 TWO-BODY (PAIR) POTENTIALS 339 7.1.5 ENERGETIC LINK
BETWEEN MD AND QUANTUM MECHANICS . 343 7.2 AB INITIO METHODS 346 7.2.1
DENSITY FUNCTIONAL THEORY 349 7.2.2 AB INITIO MOLECULAR DYNAMICS 350
7.2.3 TIGHT BINDING METHOD 351 7.2.4 NUMERICAL EXAMPLES 352 7.3 COUPLING
BETWEEN MD AND FEM 355 7.3.1 MAAD 355 7.3.2 MD/FE COUPLING - ID EXAMPLE
357 7.3.3 QUASICONTINUUM METHOD AND CAUCHY-BORN RULE 365 7.3.4
CAUCHY-BORN NUMERICAL EXAMPLES 370 7.3.5 MULTI-SCALE ALGORITHMS 373
7.3.6 GENERALIZED LANGEVIN EQUATION 376 7.3.7 MULTISCALE BOUNDARY
CONDITIONS 379 7.4 INTRODUCTION OF BRIDGING SCALE METHOD 385 7.4.1
MULTI-SCALE EQUATIONS OF MOTION 388 7.4.2 LANGEVIN EQUATION FOR BRIDGING
SCALE 390 7.4.3 STAGGERED TIME INTEGRATION ALGORITHM 395 7.4.4 BRIDGING
SCALE NUMERICAL EXAMPLES 396 7.5 APPLICATIONS 398 7.5.1 TWO-DIMENSIONAL
WAVE PROPAGATION 400 7.5.2 DYNAMIC CRACK PROPAGATION IN TWO DIMENSIONS
405 7.5.3 SIMULATIONS OF NANOCARBON TUBES 413 8. IMMERSED
MESHFREE/FINITE ELEMENT METHOD AND APPLICA- TIONS 422 8.1 INTRODUCTION
422 8.2 FORMULATIONS OF IMMERSED FINITE ELEMENT METHOD 423 8.3
COMPUTATIONAL ALGORITHM 426 8.4 APPLICATION TO BIOLOGICAL SYSTEMS 427
8.4.1 THREE RIGID SPHERES FALLING IN A TUBE 428 8.4.2 20 SOFT SPHERES
FALLING IN A CHANNEL 429 8.4.3 FLUID-FLEXIBLE STRUCTURE INTERACTION 429
8.4.4 IFEM COUPLED WITH PROTEIN MOLECULAR DYNAMICS 432 8.4.5 CELL-CELL
INTERACTION AND SHEAR RATE EFFECTS 434 6 CONTENTS 8.4.6 MICRO- AND
CAPILLARY VESSELS 435 8.4.7 ADHESION OF MONOCYTES TO ENDOTHELIAL CELLS
437 8.4.8 FLEXIBLE VALVE-VISCOUS FLUID INTERACTION 439 9. OTHER MESHFREE
METHODS 440 9.1 NATURAL ELEMENT METHOD 440 9.1.1 CONSTRUCTION OF NATURAL
NEIGHBOR 440 9.1.2 NATURAL NEIGHBOR INTERPOLATION 441 9.1.3 EXAMPLES OF
NATURAL NEIGHBOR INTERPOLANT 443 9.2 FREE MESH METHOD 443 9.3 MESHFREE
FINITE DIFFERENCE METHODS 443 9.4 VORTEX-IN-CELL METHODS 446 9.5
MATERIAL POINT METHOD (PARTICLE-IN-CELL METHOD) 448 9.6 LATTICE
BOLTZMANN METHOD 449 REFERENCES 453 10. PROGRAM LISTINGS 479 |
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| author | Li, Shaofan Liu, Wing Kam |
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| bvnumber | BV021979418 |
| callnumber-first | Q - Science |
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| classification_rvk | SK 910 |
| ctrlnum | (OCoLC)56492274 (DE-599)BVBBV021979418 |
| dewey-full | 518/.2 |
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| dewey-raw | 518/.2 |
| dewey-search | 518/.2 |
| dewey-sort | 3518 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV021979418 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:09:52Z |
| indexdate | 2024-07-09T20:48:41Z |
| institution | BVB |
| isbn | 3540222561 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015194527 |
| oclc_num | 56492274 |
| open_access_boolean | |
| owner | DE-706 DE-634 |
| owner_facet | DE-706 DE-634 |
| physical | III, 502 S. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| spelling | Li, Shaofan Verfasser aut Meshfree particle methods Shaofan Li ; Wing Kam Liu Berlin [u.a.] Springer 2004 III, 502 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [453] - 478 Méthodes particulaires (Analyse numérique) Méthodes sans maillage (Analyse numérique) Método dos elementos finitos larpcal Meshfree methods (Numerical analysis) Particle methods (Numerical analysis) Gitterfreie Methode (DE-588)4796173-9 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 s Gitterfreie Methode (DE-588)4796173-9 s 1\p DE-604 Liu, Wing Kam Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015194527&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Li, Shaofan Liu, Wing Kam Meshfree particle methods Méthodes particulaires (Analyse numérique) Méthodes sans maillage (Analyse numérique) Método dos elementos finitos larpcal Meshfree methods (Numerical analysis) Particle methods (Numerical analysis) Gitterfreie Methode (DE-588)4796173-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd |
| subject_GND | (DE-588)4796173-9 (DE-588)4185100-6 |
| title | Meshfree particle methods |
| title_auth | Meshfree particle methods |
| title_exact_search | Meshfree particle methods |
| title_exact_search_txtP | Meshfree particle methods |
| title_full | Meshfree particle methods Shaofan Li ; Wing Kam Liu |
| title_fullStr | Meshfree particle methods Shaofan Li ; Wing Kam Liu |
| title_full_unstemmed | Meshfree particle methods Shaofan Li ; Wing Kam Liu |
| title_short | Meshfree particle methods |
| title_sort | meshfree particle methods |
| topic | Méthodes particulaires (Analyse numérique) Méthodes sans maillage (Analyse numérique) Método dos elementos finitos larpcal Meshfree methods (Numerical analysis) Particle methods (Numerical analysis) Gitterfreie Methode (DE-588)4796173-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd |
| topic_facet | Méthodes particulaires (Analyse numérique) Méthodes sans maillage (Analyse numérique) Método dos elementos finitos Meshfree methods (Numerical analysis) Particle methods (Numerical analysis) Gitterfreie Methode Theoretische Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015194527&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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