Green's functions and finite elements:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIII, 327 S. Ill., graph. Darst. |
| ISBN: | 9783642295225 |
Internformat
MARC
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| 100 | 1 | |a Hartmann, Friedel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Green's functions and finite elements |c Friedel Hartmann |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XIII, 327 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Green-Funktion |0 (DE-588)4158123-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 WHAT ARE GREEN'S FUNCTIONS? 2
1.2 THE IMPORTANCE OF GREEN'S FUNCTIONS FOR FE-ANALYSIS 3
1.3 A 1-D PROBLEM 4
1.3.1 THE ANALYTICAL SOLUTION 4
1.3.2 GREEN'S FUNCTION 4
1.3.3 FINITE ELEMENTS 6
1.3.4 FINITE ELEMENTS AND GREEN'S FUNCTION 7
1.4 ENTANGLEMENT 9
1.4.1 FUNCTIONALS 12
1.4.2 PROOF 16
1.5 GOAL ORIENTED REFINEMENT 18
1.6 MODEL ADAPTIVITY 19
1.6.1 LOCAL & GLOBAL 2 6
1.7 HOW TO CALCULATE INFLUENCE FUNCTIONS WITH FINITE ELEMENTS . . . 27
REFERENCES 34
2 BASIC CONCEPTS 35
2.1 ELEMENTS O F FUNCTIONAL ANALYSIS 36
2.1.1 NOTATION 37
2.1.2 VECTOR SPACES AND SCALAR PRODUCT 38
2.1.3 LINEAR FUNCTIONALS 39
2.1.4 PROJECTION 4 1
2.1.5 VARIATIONAL PROBLEMS 4 2
2.1.6 EQUIVALENT NORMS 4 3
2.1.7 GALERKIN METHOD 4 6
2.1.8 SOBOLEV SPACES 4 6
2.2 GREEN'S IDENTITIES 4 9
2.2.1 GAUSS' THEOREM 4 9
2.2.2 THE LAPLACE OPERATOR 4 9
IX
HTTP://D-NB.INFO/1020761407
IMAGE 2
X CONTENTS
2.2.3 LINEAR SELF-ADJOINT OPERATORS 53
2.3 DUALITY 5 4
2.3.1 LINEAR ALGEBRA 55
2.3.2 VECTORS AND LINEAR FUNCTIONALS 57
2.4 INFLUENCE FUNCTIONS 58
2.4.1 INFLUENCE FUNCTION FOR U(X) 59
2.4.2 INFLUENCE FUNCTION FOR U'(X) 61
2.4.3 WEAK INFLUENCE FUNCTION FOR U(X) 63
2.4.4 A SEQUENCE THAT CONVERGES TO G\ 67
2.4.5 ELEVATORS AND ESCALATORS 69
2.4.6 INFLUENCE FUNCTIONS IN HIGHER DIMENSIONS 71
2.4.7 WEAK INFLUENCE FUNCTIONS 73
2.4.8 NON-ZERO BOUNDARY VALUES 7 4
2.4.9 AVERAGE VALUES O F STRESSES 75
2.5 PROPERTIES O F GREEN'S FUNCTIONS 79
2.5.1 MODERN APPROACH 82
2.5.2 MAXWELL 82
2.5.3 MODES OF DECAY 83
2.5.4 DIPOLES AND MONOPOLES 85
2.5.5 MULTIPOLE EXPANSION 87
2.5.6 INFINITE ENERGY 9 1
2.5.7 GENEALOGY O F INFLUENCE FUNCTIONS 92
2.6 SOBOLEV'S EMBEDDING THEOREM 93
2.7 FUNDAMENTAL SOLUTIONS 95
2.7.1 INFLUENCE FUNCTION 96
2.8 ILL-POSED PROBLEMS 97
2.9 NONLINEAR PROBLEMS 98
2.9.1 LAGRANGE MULTIPLIER 99
2.9.2 LAGRANGE MULTIPLIER AND LINEAR ALGEBRA 100
2.9.3 NONLINEAR FUNCTIONALS 101
2.9.4 NONLINEAR PROBLEMS 103
2.10 MIXED PROBLEMS 106
REFERENCES 107
3 FINITE ELEMENTS AND GREEN'S FUNCTIONS 109
3.1 POISSON EQUATION 110
3.2 THE FE-LOAD CASE P/, 112
3.2.1 DISTRIBUTIONS 114
3.2.2 NOTATION 114
3.3 EXTENSIONS 118
3.3.1 BETTI'S THEOREM: EXTENDED 118
3.3.2 TOTTENHAM'S EQUATION 119
3.3.3 MAXWELL'S THEOREM: EXTENDED 122
IMAGE 3
CONTENTS X I
3.4 PROXIES 124
3.4.1 G H = G O N V ; 125
3.4.2 S H = 6 ON V H 126
3.4.3 JH{U) = J(U) ON V/, 129
3.4.4 SUMMARY 133
3.5 DIRAC ENERGY 135
3.6 GENERALIZED GREEN'S FUNCTIONS 139
3.6.1 ARBITRARY DELTAS 140
3.7 INFLUENCE FUNCTIONS FOR INTEGRAL VALUES 144
3.7.1 NODAL FORCES 145
3.8 WEAK INFLUENCE FUNCTIONS 147
3.9 WEAK INFLUENCE FUNCTIONS HAVE MORE CHOICES 151
3.10 NODAL FORM O F INFLUENCE FUNCTIONS 153
3.10.1 NUMERICAL EFFORT 155
3.10.2 SENSITIVITY PLOTS 155
3.10.3 WHAT I S / M ? 158
3.11 NODAL VALUES O F GREEN'S FUNCTIONS 158
3.11.1 FINITE DIFFERENCES AND FINITE ELEMENTS 159
3.11.2 INFLUENCE FUNCTION FOR P{X) 159
3.11.3 THE FOOT PRINT OF PI, 162
3.12 THE INVERSE STIFFNESS MATRIX 163
3.12.1 EXAMPLES 165
3.13 CONDITION O F A STIFFNESS MATRIX 167
3.13.1 THE TRIPLE PRODUCT 170
3.14 INTERPOLATION 171
3.14.1 THE NODAL VECTOR / 173
3.15 INFINITE STRESSES 178
3.15.1 ARCHIMEDES' LEVER 179
3.15.2 CONTINUOUS BEAM 182
3.15.3 CANTILEVER PLATE 183
3.15.4 SUMMARY 185
3.16 WHY DO SINGULARITIES MATTER? 185
3.17 NATURE MAKES NO JUMPS: FINITE ELEMENTS DO 186
3.18 INFLUENCE FUNCTIONS FOR SUPPORT REACTIONS 188
3.18.1 GLOBAL EQUILIBRIUM 190
3.18.2 A PARADOX? 192
3.19 THE PATH THE LOAD TAKES 192
3.20 THE PATH THE INFLUENCE FUNCTION TAKES 195
3.21 MIXED PROBLEMS 197
3.21.1 TOTTENHAM'S EQUATION FOR MIXED PROBLEMS 202
3.22 CONDENSATION O F A STIFFNESS MATRIX 203
3.23 P-METHOD 205
REFERENCES 208
IMAGE 4
XIJ CONTENTS
4 THE DISCRETIZATION ERROR 209
4.1 ASYMPTOTIC ERROR ANALYSIS 210
4.2 GOAL-ORIENTED REFINEMENT 213
4.3 COMPARISON 214
4.4 PRIMAL AND DUAL ERROR 216
4.5 AN ANALYSIS O F THE GOAL-ORIENTED ERROR ESTIMATOR 217
4.6 THE ALGEBRA O F THE RESIDUALS 219
4.7 GOAL-ORIENTED REFINEMENT FOR NONLINEAR PROBLEMS 220
4.7.1 ESTIMATES 221
4.7.2 NONLINEAR FUNCTIONALS 224
4.7.3 IMPLEMENTATION 224
4.8 DRIFT 227
4.9 COMBINATION OF MODELING AND DISCRETIZATION ERROR 229
4.10 POLLUTION 230
4.11 GAUSS POINTS AND GREEN'S FUNCTIONS 237
REFERENCES 239
5 MODELING ERROR 241
5.1 LINEAR ALGEBRA 242
5.2 SUMMARY 244
5.2.1 DETERMINING U C 244
5.2.2 DETERMINING EFFECTS 245
5.3 WOODBURY-SHERMAN-MORRISON FORMULA 248
5.3.1 ONE ENTRY ON THE DIAGONAL CHANGES, KA + AK 248
5.3.2 THE INVERSE O F THE UPDATED STIFFNESS MATRIX K C 2 4 9
5.4 DIRECT FORMULATIONS 251
5.5 FORCE METHOD 251
5.5.1 NOTATION 253
5.5.2 CHANGES ON THE DIAGONAL 254
5.5.3 THE INVERSE 255
5.6 EXAMPLE 256
5.6.1 WHAT IT MEANS 257
5.6.2 THE INVERSE O F AK E 2 5 9
5.6.3 EXAMPLE 262
5.6.4 COLLAPSE 265
5.7 FUNCTIONALS 266
5.7.1 THE GRADIENT O F A FUNCTIONAL 267
5.8 WEAK FORMULATIONS AND THE D-TERM 268
5.8.1 LINEAR PROBLEMS 269
5.8.2 THE ERROR IN FUNCTIONALS 271
5.9 THE BASIC IDEA 278
5.9.1 CONTINUOUS AND DISCRETE CASE 278
5.9.2 LONG & STRONG AND SHORT & WEAK 280
5.9.3 ESTIMATES 281
IMAGE 5
CONTENTS X I I I
5.10 THE APPROXIMATION U C U 281
5.11 LINEARIZATION 283
5.12 ENGINEERING SENSITIVITY ANALYSIS 286
5.12.1 FOCUS ON A POINT 286
5.12.2 FOCUS ON AN ELEMENT 295
5.12.3 BEAMS 301
5.12.4 POISSON PROBLEM 303
5.12.5 KIRCHHOFF PLATES 305
5.12.6 ANALYSIS 306
5.13 EQUATIONS FOR THE UNKNOWN STRESSES ON Q F 307
5.13.1 COMPUTATIONAL ASPECTS 309
5.14 ADJOINT METHOD O F SENSITIVITY ANALYSIS 313
5.15 LINEAR VERSUS NONLINEAR 315
REFERENCES 317
6 APPENDIX 319
6.1 NONLINEAR ELASTICITY 319
6.1.1 LINEARIZATION 321
6.2 SOFTWARE 322
REFERENCE 323
INDEX 325 |
| any_adam_object | 1 |
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| discipline | Maschinenbau / Maschinenwesen Mathematik |
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| indexdate | 2024-08-21T00:09:19Z |
| institution | BVB |
| isbn | 9783642295225 |
| language | English |
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| spelling | Hartmann, Friedel Verfasser aut Green's functions and finite elements Friedel Hartmann Berlin [u.a.] Springer 2013 XIII, 327 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Green-Funktion (DE-588)4158123-4 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Green-Funktion (DE-588)4158123-4 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-29523-2 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3994283&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025263303&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hartmann, Friedel Green's functions and finite elements Green-Funktion (DE-588)4158123-4 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4158123-4 (DE-588)4017233-8 |
| title | Green's functions and finite elements |
| title_auth | Green's functions and finite elements |
| title_exact_search | Green's functions and finite elements |
| title_full | Green's functions and finite elements Friedel Hartmann |
| title_fullStr | Green's functions and finite elements Friedel Hartmann |
| title_full_unstemmed | Green's functions and finite elements Friedel Hartmann |
| title_short | Green's functions and finite elements |
| title_sort | green s functions and finite elements |
| topic | Green-Funktion (DE-588)4158123-4 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Green-Funktion Finite-Elemente-Methode |
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