Holdings: Meshfree particle methods

Meshfree particle methods:

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Bibliographic Details
Main Authors:	Li, Shaofan (Author), Liu, Wing Kam (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2004
Subjects:	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
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. [453] - 478
Physical Description:	III, 502 S. Ill., graph. Darst.
ISBN:	3540222561

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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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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
work_keys_str_mv	AT lishaofan meshfreeparticlemethods AT liuwingkam meshfreeparticlemethods

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