Microstructures in elastic media: principles and computional methods
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Oxford Univ. Press
1994
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 246 S. graph. Darst. |
| ISBN: | 0195090861 |
Staff View
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Record in the Search Index
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| adam_text | MICROSTRUCTURES IN ELASTIC MEDIA PRINCIPLES AND COMPUTATIONAL METHODS
NHAN PHAN-THIEN DEPARTMENT OF MECHANICAL ENGINEERING THE UNIVERSITY OF
SYDNEY AUSTRALIA SANGTAE KIM DEPARTMENT OF CHEMICAL ENGINEERING
UNIVERSITY OF WISCONSIN-MADISON MADISON, WISCONSIN NEW YORK OXFORD
OXFORD UNIVERSITY PRESS 1994 CONTENTS 1 FUNDAMENTAL EQUATIONS 3 1.1
INTRODUCTION AND MOTIVATION 3 1.2 STRESS AND STRAIN 4 1.3 EQUATIONS OF
EQUILIBRIUM 6 1.4 STRAIN ENERGY 8 1.4.1 UNIQUENESS 9 1.4.2 EXTREMUM
PRINCIPLES 10 1.5 BETTI S RECIPROCAL THEOREM 12 1.6 INTEGRAL
REPRESENTATION 13 1.6.1 CLASSIFICATION OF INTEGRAL EQUATIONS 13 1.6.2
KELVIN STATE 15 1.6.3 INTEGRAL REPRESENTATION 17 1.6.4 RIGID INCLUSION
19 1.6.5 ELIMINATING SINGLE OR DOUBLE LAYER 21 1.7 SINGLE AND DOUBLE
LAYER POTENTIALS 22 1.7.1 SINGLE LAYER 22 1.7.2 DOUBLE LAYER 25 1.7.3
LIAPUNOV-TAUBER THEOREM 29 1.8 BOUNDARY INTEGRAL EQUATIONS 29 1.8.1
DIRECT BEM 30 1.8.2 INDIRECT BEM 32 1.9 SPECTRAL PROPERTIES 35 1.9.1
BANACH S THEOREM 37 1.9.2 A = -L 37 1.9.3 A = +L 38 1.9.4 TYPE II
PROBLEMS 39 1.9.5 SPECTRAL RADIUS OF * 40 1.10 EXERCISES 41 1.10.1
RIGID-BODY DISPLACEMENT 41 1.10.2 STRETCHING 42 1.10.3 SIMPLE SHEARING
42 1.10.4 MODULI OF ELASTICITY 42 1.10.5 INTEGRAL REPRESENTATION 42
1.10.6 TRANSMISSION OF FORCE AND TORQUE 43 1.10.7 RECIPROCAL RELATION 43
1.10.8 TRANSLATING RIGID SPHERE 1 43 1.10.9 TRANSLATING RIGID SPHERE 2
44 VIII CONTENTS 1.10.10 KELVIN S SOLUTION 44 1.10.11 ON GREEN S
EQUATIONS 45 1.10.12 PAPKOVICH-NEUBER REPRESENTATION 45 1.10.13 GALERKIN
VECTOR 46 1.10.14 SELF-ADJOINT PROPERTY OF Q 46 1.10.15 ELASTIC
INCLUSION 47 1.10.16 CONSTANT CIJ 47 1.10.17 THIN, RIGID INCLUSION 47
1.10.18 LIAPUNOV-TAUBER THEOREM 47 2 MULTIPOLE EXPANSION AND RIGID
INCLUSIONS 49 2.1 SINGULARITY SOLUTIONS 49 2.1.1 PAPKOVICH-NEUBER
REPRESENTATION 49 2.1.2 POTENTIAL DEFORMATION 51 2.1.3 ROTLET
DEFORMATION 52 2.1.4 KELVINLET DEFORMATION 53 2.1.5 HALF-SPACE SOLUTIONS
55 2.1.6 INTERIOR DEFORMATION 58 2.2 MULTIPOLE EXPANSION 59 2.2.1
STRESSLET 62 2.3 SPHERICAL RIGID INCLUSION 63 2.3.1 TRANSLATING A RIGID
SPHERE 63 2.3.2 ROTATING A RIGID SPHERE 65 2.3.3 RIGID SPHERE IN A
LINEAR DEFORMATION 66 2.3.4 RIGID SPHERE IN A QUADRATIC AMBIENT FIELD 70
2.3.5 TRANSLATING AN ELASTIC SPHERICAL INCLUSION 71 2.4 EXERCISES . . 73
2.4.1 NAVIER SOLUTIONS 73 2.4.2 NAVIER SOLUTIONS 73 2.4.3 NAVIER
SOLUTIONS 73 2.4.4 GALERKIN VECTOR 74 2.4.5 FORCE AND TORQUE ON A RIGID
SPHERICAL INCLUSION . . 74 2.4.6 RIGID SPHERICAL INCLUSION IN HIGH-ORDER
FIELD . . . . 74 3 FAXEN RELATIONS AND ELLIPSOIDAL INCLUSIONS 75 3.1
FAXEN RELATIONS 75 3.2 RIGID SPHERICAL INCLUSION 78 3.3 RIGID
ELLIPSOIDAL INCLUSION 79 3.3.1 SINGULARITY SOLUTION FOR TRANSLATION 81
3.3.2 SINGULARITY SOLUTION FOR LINEAR AMBIENT FIELD . . . . 83 3.3.3
DEGENERATE CASES 86 3.3.4 FAXEN RELATIONS FOR THE RIGID ELLIPSOID 88
3.3.5 INTERACTIONS BETWEEN TWO ELLIPSOIDS 88 3.4 EXERCISES 89 3.4.1
TRACTION FUNCTIONALS 89 3.4.2 FAXEN RELATIONS FOR TORQUE AND STRESSLET
89 CONTENTS IX 3.4.3 MULTIPOLE EXPANSION FOR ELLIPSOIDS 90 3.4.4
TRACTIONS FOR THE TRANSLATING ELLIPSOID 90 4 LOAD TRANSFER PROBLEM AND
BOUNDARY COLLOCATION 91 4.1 THE METHOD OF REFLECTION . 92 4.2 LOAD
TRANSFER BETWEEN TWO SPHERES 93 4.2.1 FAR FIELD BY REFLECTION 94 4.2.2
NEAR TOUCHING 99 4.3 KELVIN SOLUTIONS 102 4.3.1 SPHERICAL HARMONICS 102
4.3.2 KELVIN S GENERAL SOLUTIONS 104 4.4 BOUNDARY COLLOCATION 108 4.4.1
TWIN MULTIPOLE EXPANSIONS 109 4.4.2 COLLOCATION EQUATIONS FOR
TRANSLATION PROBLEMS . . . 110 4.5 COMPARISON 114 4.6 CONSTITUTIVE
RELATION 119 4.6.1 CONSTITUTIVE THEORY 120 4.6.2 CUBIC LATTICES 122 4.7
KELVINLET NEAR A RIGID SPHERE 124 4.7.1 THE AXISYMMETRIC KELVINLET 126
4.7.2 THE TRANSVERSE KELVINLET 132 4.8 EXERCISES 137 4.8.1 SOLID
SPHERICAL HARMONICS 137 4.8.2 LURIE SOLUTION 137 4.8.3 TYPE I PROBLEMS
138 5 COMPLETED DOUBLE LAYER BOUNDARY ELEMENT METHOD 139 5.1
INTRODUCTION 139 5.2 DIRECT FORMULATION 141 5.3 COMPLETED DOUBLE LAYER
BOUNDARY ELEMENT METHOD . . . . 144 5.3.1 RANGE COMPLETER 145 5.3.2 NULL
FUNCTIONS OF (1 + K) 146 5.3.3 COMPLETION PROCESS 147 5.3.4 CONTAINER
SURFACE 149 5.3.5 A SUMMARY 152 5.4 RIGID INCLUSION 153 5.4.1
TRANSLATIONAL DISPLACEMENT 153 5.4.2 ON PICARD ITERATION 155 5.4.3
ROTATIONAL DISPLACEMENT . . . 157 5.4.4 HOMOGENEOUS DEFORMATION 157 5.5
STRESSLET 160 5.6 SPECTRUM FOR A SPHERE 161 5.6.1 TYPE I PROBLEMS -
ILL-POSED 166 5.7 COMPLETED DOUBLE LAYER TRACTION PROBLEM 167 5.8
EXERCISES 169 5.8.1 SYMMETRY RELATIONS 169 X CONTENTS 5.8.2 ON
EIGENFUNCTIONS 169 5.8.3 INCOMPRESSIBLE CASE 169 5.8.4 GRAM-SCHMIDT
ORTHONORMALIZATION 169 5.8.5 HADAMARD ILL-POSED PROBLEM 170 6 NUMERICAL
IMPLEMENTATION 171 6.1 NUMERICAL QUADRATURE 172 6.2 BOUNDARY
DISCRETIZATION 176 6.2.1 CONSTANT ELEMENT 176 6.2.2 HIGHER ORDER ELEMENT
177 6.3 EVALUATION OF BOUNDARY INTEGRALS 182 6.3.1 MULTIVALUED TRACTION
182 6.3.2 REGULAR INTEGRALS 183 6.3.3 SINGULAR INTEGRALS 185 6.3.4
RIGID-BODY DISPLACEMENT 187 6.3.5 ADAPTIVE INTEGRATION SCHEMES 188 6.3.6
FAR-FIELD APPROXIMATION 191 6.4 SOLUTION METHODS 193 6.4.1 DIRECT SOLVER
193 6.4.2 ITERATIVE METHODS 193 6.4.3 DOMAIN DECOMPOSITION 194 6.5
DISTRIBUTED COMPUTING UNDER PVM 195 6.5.1 SOME CONCEPTS IN DISTRIBUTED
COMPUTING 196 6.5.2 MASTER/SLAVE IMPLEMENTATION 199 6.6 EXERCISES 201
6.6.1 NEWTON-COTES RULES 201 6.6.2 QUADRATURE 201 6.6.3 GALERKIN
EXPANSION 201 6.6.4 JACOBIAN 203 6.6.5 EVALUATION OF F^GIJDS AND J^KIJDS
203 7 SOME APPLICATIONS OF CDL-BIEM 205 7.1 TRANSLATING SPHERE 205 7.1.1
DIRECT FORMULATION 205 7.1.2 CDL-BIEM 209 7.2 SPHERE IN HOMOGENEOUS
DEFORMATION 212 7.3 TWO SPHEROIDS 215 7.4 CDL IN HALF-SPACE 218 7.5
CONTAINER SURFACE 220 7.6 DEFORMATION OF A CLUSTER 222 7.7 DISTRIBUTED
COMPUTING UNDER PVM 225 7.7.1 ARRAYS OF SPHERES 225 7.7.2 EPILOGUE:
SEDIMENTATION THROUGH AN ARRAY OF SPHERES 226 REFERENCES 231 INDEX 240
|
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| author | Phan-Thien, Nhan 1952- Kim, Sangtae |
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| institution | BVB |
| isbn | 0195090861 |
| language | English |
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| physical | 246 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Oxford Univ. Press |
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| spelling | Phan-Thien, Nhan 1952- Verfasser (DE-588)123614457 aut Microstructures in elastic media principles and computional methods Nhan Phan-Thien ; Sangtae Kim New York [u.a.] Oxford Univ. Press 1994 246 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Elastischer Werkstoff (DE-588)4151686-2 gnd rswk-swf Mikrostruktur (DE-588)4131028-7 gnd rswk-swf Elastischer Werkstoff (DE-588)4151686-2 s Mikrostruktur (DE-588)4131028-7 s DE-604 Kim, Sangtae Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006741922&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Phan-Thien, Nhan 1952- Kim, Sangtae Microstructures in elastic media principles and computional methods Elastischer Werkstoff (DE-588)4151686-2 gnd Mikrostruktur (DE-588)4131028-7 gnd |
| subject_GND | (DE-588)4151686-2 (DE-588)4131028-7 |
| title | Microstructures in elastic media principles and computional methods |
| title_auth | Microstructures in elastic media principles and computional methods |
| title_exact_search | Microstructures in elastic media principles and computional methods |
| title_full | Microstructures in elastic media principles and computional methods Nhan Phan-Thien ; Sangtae Kim |
| title_fullStr | Microstructures in elastic media principles and computional methods Nhan Phan-Thien ; Sangtae Kim |
| title_full_unstemmed | Microstructures in elastic media principles and computional methods Nhan Phan-Thien ; Sangtae Kim |
| title_short | Microstructures in elastic media |
| title_sort | microstructures in elastic media principles and computional methods |
| title_sub | principles and computional methods |
| topic | Elastischer Werkstoff (DE-588)4151686-2 gnd Mikrostruktur (DE-588)4131028-7 gnd |
| topic_facet | Elastischer Werkstoff Mikrostruktur |
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