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Stein E. (ed.), Ramm E. — Error-controlled adaptive finite elements in solid mechanics
Stein E. (ed.), Ramm E. — Error-controlled adaptive finite elements in solid mechanics



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Название: Error-controlled adaptive finite elements in solid mechanics

Авторы: Stein E. (ed.), Ramm E.

Аннотация:

Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic.
This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications.
* First book to go beyond the Finite Element Method in itself
* Covers material from a new research area
* Presents benchmarks of 2D- and 3D- applications
* Fits with the new trend for genetic strategies in engineering


Язык: en

Рубрика: Математика/Численные методы/Конечные элементы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 410

Добавлена в каталог: 20.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H_1$-norms      214
$H_1$-seminorms      10 214 217
$J_2$ flow theory      290 291
$L_2$-error      222 323
$L_2$-error estimates      7 11
$L_2$-norms      13 25 36 126 139 214 216 228 230
$L_2$-norms, displacement error      221 222
$L_2$-norms, errors      247
$L_2$-norms, global      168
$L_2$-norms, material-dependent      23
$P_0$-elements      26 377
$P_1$-elements      26
$Z^2$ gradient-type error indicator      229—230
a posteriori, error estimates      1 9 12 17 27 38 43 45 168 196—201
a posteriori, error estimates, $L_2$-norm      14
a posteriori, error estimates, dual problems      49
a posteriori, error estimates, energy norm      13
a posteriori, error estimates, Hencky model      31
a posteriori, error estimates, mesh adaptation      16 34
a posteriori, error estimates, static      41 42
a posteriori, error estimates, weighted      5 8
a priori, error estimates      1 23 24 42 43 45 198
Absolute errors      331 332
ACIS-kernel      276
Active contact zone      181 184 185 192 193
Active set      152
Adaptive algorithms      84—90 205 242
Adaptive discretization      339—340
Adaptive FE analysis      309
Adaptive strategy      123 144 171
Adaptivity      1 91 181—209 236 358 381
Additional regularity      184
Adjoint operator      254
Alexander scheme      371 372 373t
Anisotropic Ansatz spaces      270 271
Anisotropic tensor product space      269
ANS (assumed natural strain element)      329
Ansatz spaces      264—272 287 289 303
Approximation property      195
Aspect ratio      132 217
Associated plasticity      349
Asymptotics      188 189 191 194 195 373 376—379
Aubin — Nitsche trick      6 11 221 222
Averaging error estimators      1 72
Averaging techniques      223 227 228
Babuska — Brezzi condition      119
Backward Euler      7 24 41 42 156 158
Backward Euler scheme      23 115 127 238 293
Backwards-in-time problems      240 249 252
Benchmarks      385—404
Benchmarks, 2D      385
Benchmarks, 3D      92
Benchmarks, asymptotic results      373
Benchmarks, example      240—242
Beta-regular      198
Betti — Maxwell      169 218 320
Biaxial test      134—137 144
Bifurcation      2 110 160 236 314
Bilinear form      214 327
Blending function method      272 273 276 293
Block Gauss — Seidel      317 381
Block Gauss — Seidel iteration      302 304 315
Block skew-symmetric linear system      196
boundary conditions      113 114 137 183 184 185 301 310 337
Boundary elements      193—196
Boundary integral equations      194
Boundary representation model      275
Boundary tractions      28 182 203f 204f
Boundary value problems      187 190 215 217 218 226 243 248
Boundary value problems, adjoint      221
Boundary value problems, finite deformations      152—153
Boundary value problems, linearized      155—156
Boundary value problems, mixed      187 190 193—196
Boundary value problems, stress singularities      186
Bubble modes      265
Buckner’s function      187
CAD      276 277
Cauchy Green tensor      154
Cauchy stress tensor      161 213
Cauchy — Schwartz inequality      164 170 216 222 225 227 250
Cell-residuals      12 27 42
Clausius Duhem inequality      58 255
Client — Server structure      276
Closest point return      116 117 120 127 133
Coarsening      86 87 325 342 365
Coleman’s exploitation method      255
Commutators      197 198
Conjugate gradient method      196
Conservation of mass      114
Consistency conditions      155 256 291 292
Consistent tangent operators      123
Consolidation      110 113 129—131 141
Constitutive relations      112 153—155
Contact kinematics      148 149—151
Contact problems      147—179
Contact with friction      165—166 183 184
Contact without friction      161—165 183 184—185
Convergence properties      199
Correction of the contact zone      192
Cosserat theory      111 112—113 114 124 136 144
Coulomb’s law      155 183 200
Couple stress tensor      111 115 116
Coupling 2D and 3D problems      302—305
Crank — Nicolson scheme      22 65 126
Curvature tensor      111 112 115 150
Curve fittings      118
Curved edges and faces      272
Cut-off frequency      338
Cyclic loading      293—296 390—393
Data transfer      132—133
Deformation gradients      154
Derivative of the stress intensity factor      191
Deteriorated velocities      323
Difference quotients      362
Dilatancy      141
Dimensionally reduced models      277 300 302—303
Dirichlet — Neumann map      194
Discontinuous Galerkin scheme      120 245—247 315—318 318 320 333 334 335 339 342
Discontinuous Galerkin scheme, Newmark type algorithm comparison      313—315
Discretization      156—159 199 236 271 286 288 356—358 374
Discretization errors      2 71 110 125 169 214 227 247
Discretization errors, temporal      126 128 129 130
dispersion      336—341
Displacement velocities      183
Displacement-pressure formulation      24 34 35
Dissipation inequality      255
Double layer potential      193
Dual principles      168—171
Dual problems      6 13 18 170 220 221 222 239 241 253
Dual problems, analysis      26
Dual problems, backward-in-time      44 252
Dual problems, characteristics      249 250
Dual problems, continuous      223
Dual problems, discretization errors      169
Dual problems, energetic constraints      248
Dual problems, global      49
Dual problems, goal-oriented error estimators      225
Dual problems, initial conditions      249
Dual problems, linearization      31 43 45
Dual problems, load cases      231
Dual problems, regularized      232
Dual problems, residuals and error      242
Dual problems, solution      15 230 235
Dual problems, static      41 250
Duality argument      11 30 159
DWR (dual-weighted-residual) method      5 7 8—18 25 26 37 49 50
Edge modes      266 269
Edge-residuals      12 27 30 42 45 215f 226
Effectivity index      16 28 37 74 77 78f 212 230 231 232 240
Elastic foundation      281 285
Elasticity problems      212
Elasticity problems, strong form of the BVP      213
Elasticity problems, weak form of the BVP      213 214
Elasto-plastic deformations      53—107
Elastodynamics      245 310 330
Elastoplasticity      2 290
Elastoplasticity flow theory      290
Element-wise transfer      94—97 103
Elliptic boundary value problem      1
Ellipticity      110 114 134 136 162 194 195
Energetic constraints      221 248
Energetic functions      187
Energy norm errors      166 218 225 288 289
Energy norms      1 27 37 41 50 211 212 214 217 231 321
Energy norms, a posteriori error estimate      13
Energy norms, average      326
Energy norms, error estimator      72
Energy norms, finite element error      228
Energy norms, natural      6 199
Energy norms, relative error      286 287f
Energy norms, strain      329 330
Energy norms, total      311
Energy-error estimates      11 14 27
Energy-norm of errors      322—324 325 326 327 331
Equilibrated local Neumann estimator      77—81
Error equations, strong form      215
Error equations, weak form      214 215 220 225 226 248
Error estimation      211 —261 330
Error estimation, elasto-plasticity      5—52 70—84
Error estimation, p-version FEM      282—285
Error estimation, space and time      247—250
Error estimators      78 82 211 225 226 230 335 359 365 369
Error estimators and indicators      71 159—171
Error estimators, contact problems      199—201
Error estimators, global      212
Error estimators, hanging nodes      88
Error estimators, quality      323
Error estimators, spatial distribution      72
Error indicators      33 92 124 127 128 134 226 286 336 369
Error indicators for elasto-plastic material      73
Error indicators for the flow rule      75—76
Error indicators for time discretization      83—84
Error indicators, $L_2$-norms      230
Error indicators, a posteriori      31
Error indicators, applicability      137
Error indicators, effectivity index      77
Error indicators, error bound      229
Error indicators, error estimators and      71 159—171 323
Error indicators, local      218 224 240
Error indicators, mesh adaption      359
Error indicators, mesh refinement      220
Error indicators, modified      147
Error indicators, relative error      39f
Error indicators, spatial discretization error      102
Error representation      9 12 15 30
Euler scheme      22 353 355 372 381
Euler’s methods of time interpretation      64
Expansion of operators      186
Exponential rate of convergence      263
Extended continuum formulations      109—146
Face modes      269 270
Finite deformations      152—153
Fission/fusion strategy      325
Flow theory      290 291
Fluid flow      110 111 114 120 124 125 134 136
Free Helmholtz energy      255
Galerkin method      6 69 205 245 311 342
Galerkin orthogonality      10 12 26 27 170 214 220 225 229 249
Galerkin orthogonality, discretization error      2
Galerkin orthogonality, nonlinear      30 44 239
Galerkin orthogonality, space-time finite element      248
Galerkin orthogonality, weak form of error equation      215
Gaussian quadrature      223 268 273 294
Geomaterials      109 113 115 118 131 136
Geometric model      272—277
Given friction      200
Global $L_2$-projection      228 229
Global residual based error estimator      218 226—227 234
Goal-oriented error estimators      225 231
Graded meshes      389f
Green’s function      6 7 169 220
h-adaptivity      86 87f 401
h-version      109 131 272 282 285 286 287
h-version, combination of p-version and      263 299—305
Hadamard’s curved coordinates      185
Hamilton’s principle      316
Hanging node      10 15 26 32 33 87 88 103 131
Hardening      350 352 353 354 359 360 375 382 isotropic
Hardening rule      62 291
Hardening, laws      61
Hardening, linear      21 45 347
Hencky model      5 7 19 22 31 32 35 38 41
Hencky model, static      36 49
Hencky model, stationary      25
Hertz contact      206
Hertzian problem      175—177 202
Hexahedral elements      268—272
Hierarchic shape functions      264 265—267
Hierarchical mesh refinement      131
High order basis      264
Hooke’s law      66 161 182 244
hp-d method      302
hp-version      263 290
Hydrogeology      110
Hyperbolic problem      249 330
Hyperelasticity      153
Hypersingular integral operator      193
iImodes      265 267 269 270
Incompressibility      113 115
Incompressible material      24
Incremental constitutive tensor      159
Incremental step      183
Influence function      219
Initial boundary value problem      62 110 114 212 239 245 247 250 252
Inner expansion      191
Internal length scale      111 113 136
Internal variables      256 347 353 358 359
Interpolation      342 357 359 361 370
Interpolation constant $C_i$      11 27 32 216 217 218 223
Interpolation operator      249
Interpolation operator of Clement      216 222
Isotropic hardening      61 118 254 255 292 296 348 350 371
Isotropic hardening, exponential      61
Isotropic hardening, linear      61 (see also “Hardening hardening hardening
Isotropic work hardening      116
Iteration matrix      317
Jacobian matrix      273 275
Jump residuals      15 224
Kelvin’s fundamental solution      193
Kinetic energy of error      322 342
Kirchhoff stress      153 154 156
Kirchhoff stress tensor      152 161
Korn’s inequality      20
Krylov method      361 381
Kuhn — Tucker conditions      59 62 66 75 77 118 127 152 292
Kuhn — Tucker conditions, discrete      65
Kuhn — Tucker conditions, loading/unloading      291
Lagrange multiplier      116 256
lame      55 154 182 185 213 217 218 255 267 271
Leading singularity      186
Least square approximation      99
Least-square fit      328
Legendre polynomials      264 265
Lie derivative      150
Limit loads      110 111 113 116 123 139 140 141 142f 143 144
Limit-load state      109
Linear elasticity      162 212—235 248 277
Linear elastodynamic problem      244—253
Linear elastodynamic problem, strong form of the IBVP      245
Linear elastodynamic problem, weak form of the IBVP      246
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