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| Stein E. (ed.), Ramm E. — Error-controlled adaptive finite elements in solid mechanics |
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| Предметный указатель |
 -norms 214
-seminorms 10 214 217
 flow theory 290 291
 -error 222 323
-error estimates 7 11
-norms 13 25 36 126 139 214 216 228 230
-norms, displacement error 221 222
-norms, errors 247
-norms, global 168
-norms, material-dependent 23
 -elements 26 377
 -elements 26
 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, -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, -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 -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  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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