Willam, K.J., Warnke, E.P.: Constitutive Model for the Triaxial Behaviour of Concrete.. In: IABSE International Association of Bridge and Structural Engineers, Seminar on: Conccrete Stru
Trang 1References 709
849 Willam, K.J., Warnke, E.P.: Constitutive Model for the Triaxial Behaviour
of Concrete In: IABSE International Association of Bridge and Structural Engineers, Seminar on: Conccrete Structures Subjected to Triaxial Stresses, Ismes – Bergamo, Italy (May 1974)
850 Wilson, E.L., Taylor, R.L., Doherty, W.P., Ghaboussi, J.: Incompatible dis-placement models In: Fenves, S.J., Perrone, N., Robinson, A.R., Sehnobrich, W.C (eds.) Numerical and Computer Methods in Structural Mechanics, New York, pp 43–57 Academic Press, London (1973)
851 Wilson, E.L., Yuan, M., Dickens, J.M.: Dynamic analysis by direct superpo-sition of Ritz vectors Earthquake Engineering and Structural Dynamics 10, 813–821 (1982)
852 Woehler, A.: Versuche zur Ermittlung der auf die Eisenbahnwagenachsen einwirkenden Kr¨afte und der Widerstandsf¨ahigkeit der Achsen Zeitschrift f Bauwesen 10, 601–616 (1860)
853 Wood, W.L.: Practical Time-Stepping Schemes Clarendon Press, Oxford (1990)
854 Wood, W.L., Bossak, M., Zienkiewicz, O.C.: An alpha modification of New-mark’s method International Journal for Numerical Methods in Engineer-ing 15, 1562–1566 (1981)
855 Wriggers, P.: Nichtlineare Finite-Element-Methoden Springer, Berlin (2001)
856 Wriggers, P.: Computational Contact Mechanics Wiley-Verlag, Chichester (2002)
857 Wright, G.: Subjective probability Wiley, Chichester (1994)
858 Xia, Y., Hao, H., Brownjohn, J.N.M., Xia, P.-Q.: Damage identification of structures with uncertain frequency and mode shape data Earthquake Engi-neering and Structural Dynamics 31, 1053–1066 (2002)
859 Xie, M., Gerstle, W.H., Rahulkumar, P.: Energy-based automatic mixed-mode crack-propagation modeling J Eng Mech 121, 914–923 (1995)
860 Xiqiao, F., Shouwen, Y.: A new damage model for microcrack-weakened brittle solids Acta Mechanica Sinica 9(3), 251–260 (1993)
861 Xu, X., Setzer, M.J.: Life-time prediction of concrete under special environ-mental influences such as frost and frost de-icing salt attack in laboratory and field conditions In: Stangenberg, F., Bruhns, O.T., Hartmann, D., Meschke,
G (eds.) Lifetime-oriented Design Concepts, pp 179–185 Ruhr-Universit¨at Bochum (2004)
862 Yamamoto, M., Nakamura, S.: The study on Shear Connectors The Public Works Research Institute, Construction Ministry Japan, Research Paper 9, 5 (March 1962)
863 Yamazaki, F., Shinozuka, M., Dasgupta, S.P.: Neumann expansion for stochas-tic finite element analysis Journal of Engineering Mechanics 114(8), 1335–1354 (1988)
864 Yang, H.T.Y., Saigal, S., Masud, A., Kapania, R.K.: A survey of recent shell finite elements International Journal for Numerical Methods in Engineering 47, 101–127 (2000)
865 Zhang, B., Phillips, D.V., Wu, K.: Effects of loading frequency and stress rever-sal on fatigue lief of plain concrete Mag Conc Res 48(117), 361–375 (1996)
866 Zhang, B., Wu, K.: Residual fatigue strength and stiffness of ordinary concrete under bending Cem Conc Res 27(1), 115–126 (1997)
Trang 2867 Ziegeldorf, S.: Phenomenological aspects of the fracture of concrete In: Wittmann, F.H (ed.) Fracture Mechnics of Concrete, pp 31–41 Elsevier Pub-lishers, Amsterdam (1983)
868 Zienkiewicz, O.C., Xie, Y.M.: A simple error and adaptive time stepping pro-cedure for dynamic analysis Earthquake Engineering and Structural Dynam-ics 20, 871–887 (1991)
869 Zienkiewicz, O.C., Zhu, J.C.: The superconvergent patch recovery (spr) and adaptive finite element refinement Computer Methods in Applied Mechanics and Engineering 101, 207–224 (1992)
870 Zienkiewicz, O.J., Taylor, R.L.: The Finite Element Method The Basis, vol 1 Butterworth-Heinemann, Oxford (2000)
871 Zienkiewicz, O.J., Taylor, R.L.: The Finite Element Method Solid Mechanics, vol 2 Butterworth-Heinemann, Oxford (2000)
872 Zilch, K., Zehetmaier, G.: Bemessung im konstruktiven Betonbau nach DIN 1045-1 und DIN EN 1992-1-1 Springer, Heidelberg (2006)
873 Ziyaeifar, M., Noguchi, H.: A refined model for beam elements and beam-column joints Computers and Structures 76, 551–564 (2000)
874 Zoback, M.D., Byerlee, J.D.: The effect of microcrack dilatancy on the per-meability of westerly granite Journal of Geophysical Research 80, 752–755 (1975)
Trang 3Subject Index
3D-p-finite element method 392
abrasion 1, 162
abstract multi field problem 372
abutment of a bridge 649
accumulation 111, 160, 198, 313, 626
acid attack 152
acidic fluids 152
acoustic emissions 169, 204
across-wind force 26
dimensionless lift coefficient, 26
Strouhal-number, 26
across-wind vibrations 29
action 4
adaptive
method, 368, 372, 424, 425
time
step control, 594
stepping procedure, 446
stepping scheme, 369, 412, 443
adaptivity
error-controlled temporal, 443
in space and time, 425
advanced directional factors 23
aerodynamic admittance, 24
applicable characteristic suction
force, 25
directional wind effect, 24
iteration, 24
suction force on the fa¸cade element,
24
ageing 3
chemically caused, 367
aggregate 189, 302, 307
algebraic equation 369 algorithmic balance equation 415 alkali-aggregate reaction 158 alkali-carbonate reaction 160 alkali-silica reaction 158, 302, 305,
311, 359 amplitude counting 574 analytical counting method 578 anchor pull-out test 495 angular frequency 115 anisotropic
shape function, 380 softening law, 478 apodization 120 approximation of state variable 381, 414
approximativ solution 368 arbitrary order of accuracy 410 arbitrary polynomial degree 380 arc-length controlled iteration method 407
arched steel bridge 512, 607 assembling 384
assumed natural strain 362, 380 asymptotic displacement 469 asymptotic state 112 Babuˇska-Brezzi-condition 398, 585 back polarization 315
back stress tensor 246, 256 balance equation 373–375 balance of linear momentum 296,
426, 427 band-pass 120
Trang 4Bauschinger effect 255, 256
beam finite elements 369
beat 118
Bernoulli formulation 397
biaxial strength 126
Biot
coefficients, 286, 288
modulus, 286
Biot-Coussy theory 285
black-box modelling 635
blending function method 402
BMW 3-serie 572
Bossak-α method 411
boundary condition 373
brittle failure 307
Bubnov-Galerkin
discontinuous method, 412, 421
building class 4, 659
C0-continous 476
C0-discontinuous 476
calcium
diffusion, 296
dissolution, 295, 296, 300, 356
ion concentration, 297, 298, 300, 354
leaching, 107, 150, 152, 297, 591, 592
cantilever beam 563
capillary
pressure, 285, 289, 292, 307
tension, 143
carbonation 1
Cauchy-Green tensor 437
cementitious
beam, 601
material, 124, 236, 591
cement paste 124
centrifuge model test 646
change of position 367
chaos theory 370
chemical
dissolution, 354
equilibrium, 295
expansive process, 359
loading, 592
range, 600
porosity, 300
chemo-mechanical
damage model, 374
tangent coupling tensor, 386
chloride 1 CMDSS device 200 coalescence 256 coaxial states 116 complementary energy, 238 strain energy, 271 compliance tensor 238, 269, 278 composite structure 207 compressive strength 246, 262, 265,
270, 290, 622, 629 computational durability mechanics 285
computer-aided design 372 concrete 180, 237, 244, 265 corrosion, 95
cover, 625 high strength, 187 permeability, 590 properties, 618 shell structure, 583 strength, 628 conductivity tensor 297 connection plate 613 consistent linearization 367, 369, 377, 415
constitutive equation, 373, 427 law, 374
continuity 412 condition, 409, 418 continuum damage theory 307 continuum mechanics 294 control cycle 519
controllable numerical dissipation 409–411
convection 37 convergence 422 convex modelling 370 cooling 351
rate, 101 coordinate modal assurance criterion 569
corrector iteration 405, 408 correlation length 631 corrosion 1
attack, 625 rate, 625 reinforcement, 625
Trang 5Subject Index 713
COSSAN 538
coupled balance equation 377
coupled field problem 372, 376
covariance analysis 520
crack
band, 625
elliptical, 270, 272, 274, 278, 280
extension, 492
formation, 190
growth, 489
growth criteria, 488
initiation, 207
kinked, 274, 276
kinking, 453
microcrack, 190
elliptical, 284
mixed mode, 272, 274, 278
propagation, 174, 225, 369, 474
simulation, 493
surface, 476
tip, 454, 469
topology, 493
cracking strains 244
Craig-Bampton approach 499
creep 143, 285, 291
effects, 133
long-term, 286
strain, 265–267
critical degree of saturation 95
crown cracks 351
crushing energy 246
CSH 293, 300, 356
cumulative distribution function 531
cycle
amplitude
double amplitude, 120
scalar amplitude, 118
tensorial amplitude, 114, 316
average, 114
circulation, 117
counting, 575
in-phase (=IP) cycles, 114
irregular cycle, 116, 198, 518
multiaxial, 115
out-of-phase (=OOP) cycles, 115
ovality, 114
packages of cycles, 205
polarization, 114, 202, 315
polarization changes, 203
regular cycles, 198 shape, 203 span, 117 strain cycles, 114 uniaxial, 115 cyclic
flow rule, 161, 201 loading, 123, 129, 256, 519, 623, 647, 650
mobility, 113, 162, 206 multidimensional simple shear tests, 198
preloading, 112, 203, 315 tensile and flexural load, 136 test, 180, 621
triaxial tests, 198 Dahlquist theorem 411 Daltons law 307 damage 237, 366 accumulation, 7, 579, 581 chemical, 298
chemo-mechanical, 295, 367 creep, 367
criterion, 300, 478 detection, 634, 640 driving forces, 627 evolution, 167, 626 fatigue, 367 gradient enhanced, 307 hygro-mechanical, 367 isotropic, 238
mechanisms, 625 model
anisotropic, 244 anisotropic elastoplastic, 244 continuum, 270, 274, 284 micropore, 255, 259 parameter, 238, 295, 300, 307 thermo-mechanical, 367 damage equivalent factors 69 damaging process 139 Darcys law 307 data windowing 120 Debye-H¨uckel-Onsager theory 298 degeneration of a trajectory 118 degradation 3, 262, 411, 654 macroscopic, 367
process, 131, 182, 623
Trang 6stiffness, 134
structural, 180, 359
degraded road bridge 617
deionized water 356
derivative-based method 552
derivative-free strategy 555
design
concept, 93
process, 371
working life, 659
destructive test 619
deterioration 1, 307, 366
brittle, 367
ductile, 367
mechanic, 369
mechanism, 411
model, 372
deterministic subspace identification
527
detrended strain path 118
detrending 116
differential settlements 109
diffusion 292
direction of accumulation 161, 200,
201, 314
direct search algorithm 555
Dirichlet boundary condition 374,
411, 591, 598
Dirlik distribution function 579
discontinuous
displacement approximation, 369
finite elements, 448
discrete-time system matrix 526
discrete Fourier transform (DFT)
119
discrete inverse Fourier transform
(DIFT) 120
discretization 414
method, 294
disjoining pressure 143, 291, 293
dissipation potential 297
dissolution 152, 305
front, 356
process, 150, 152, 374
drilling core 618
driving force 373
Drucker-Prager
plasticity model, 290
potential, 246, 269
drying 351 creep, 291 process, 590 shrinkage, 285 ductile mode 129 durability 92, 150, 294, 411, 424, 574, 659
analysis, 354 mechanics model, 424 structural, 368 dynamic
influence coefficient, 634 load parameters, 82 distance between the pulse peaks, 84
pressure coefficients, 82 pulse amplitudes, 82 wall distance factor, 86 wall height factor, 86 response, 90
critical damping ratio, 91 modal decomposition, 91 resonant amplification factors, 91 stiffness requirement, 572
E-Modulus 134 earthquake 113, 162, 362, 649 edge modes 393
effective balance equation, 415 elastic properties, 271, 276 linearized system of equation, 421, 422
right hand side, 416 stress, 244, 285, 289, 307 elastic, 289
plastic, 289 tangent matrix, 416 eigenfrequency 634 elastoplastic models 244 electrical resistance method 163 electrophoretic effect 298 element 379
embedded crack models, 252 discontinuity approach, 369 endochronic models 518 energy
complementary, 272
Trang 7Subject Index 715
conserving, 369
decaying method, 369
enhanced assumed strain 252, 362,
380, 427, 448
enriched finite elements 372
entropy 286
enumeration strategy 555
environmental
attack, 583
humidity, 143
equivalent
elliptical crack, 278
elliptical microcrack, 276
strain, 238, 307
error
criterion, 431, 432
estimate, 412, 444, 594
h-method, 443
local, 443
p-method, 444
estimator, 391, 445
indicator, 391, 444
h-method, 444
local, 443
p-method, 444
measure, 372, 425
ettringite formation 157
Eurocode 659
evolution
algorithm, 555
long-term, 629
strategy, 556
excessive displacement 367
exchangeable salt 152
expansion 157, 307, 311
experimental results 40
macroscopic temperature behaviour,
42
explicit mode 518
exponential convergency 388
exposure classes 93
extended finite element method 369,
448
external damage 95
fabric 109, 162
face modes 394
failure
function, 238
probability, 529, 530, 534, 541, 612
Falancs 581 Faraday constant 298 fatigue 1, 163, 169, 180, 626, 653,
655, 659 analysis of bridge hangers, 29 crack, 272
damage, 267, 367 process, 612 failure, 262 high-cycle, 262, 270 high cycle, 129, 174, 207 life, 627
lifetime, 270 load, 270 low-cycle, 259, 262 low cycle, 129, 255 Newmark-Wilson time-step method, 31
strain, 185, 266 test, 259 ultra low cycle, 255 Ficks law 297 filtering 119 finite difference method 649 finite element method 367–369 first-order reliability method 531 first order kinetic law 305 first passage 540
probability, 541 flattened strain trajectory 117 foundations 109, 646
Fourier transform 119 fracture
energy, 187, 238, 252, 290, 478 approach, 625
mechanism, 124 process, 369 fragmentation 162 free energy 238, 286, 297 freeze thaw attack 148, 293 frost
attack, 194 damage, 293 deicing salt attack, 148 suction, 95
full scale experiments 32 Galerkin 377
continuous method, 369, 408, 412, 416
Trang 8discontinuous method, 369, 408, 412,
416
solution, 594
temporal approximation, 419
time integration scheme, 372, 411,
416, 594, 598, 600
type finite element method, 410
Gˆateaux derivative 385
Gauss-Legendre
integration, 421, 460
quadrature, 386, 458
generalized
external force vector, 413
internal force
tensor, 383
vector, 403, 413
mid-point approximations, 414, 415
tangent
damping matrix, 413
damping tensor, 385
mass matrix, 413
stiffness matrix, 403, 413
stiffness tensor, 385
genetic algorithm 556
geogrids 650
global balance equation 373
gradient-based algorithm 561
grading curve 189
grain size distribution curve 205
grey-box modelling 635
Griffith criterion 493
gust response factor 11
equivalent quasi-static load, 12
fatigue analysis of gust-induced
effects, 18
h-finite element method 379, 388
h-method 412
H¨unxer Br¨ucke 617, 648
hanging node concept 431
Hankel matrix 523, 638
hardening
isotropic, 256
kinematic, 256
modulus, 246
harmonic
excitation, 649
oscillation, 115
harmony with nature 6
Hasofer-Lind-algorithm 533 hazard 654
headed stud 207 heat
capacity, 286 conduction, 36, 292
of hydration, 142 transmission, 39 Helmholtz energy 246 Hessian matrix 568 hierarchical
concept, 388 polynomial interpolation, 426 high-cycle model for soils 517, 646 high-speed railway lines 79 aerodynamic loads, 79 critical train speed, 81 noise barrier, 80 prevailing frequencyf p, 81
wind shelter walls, 80 higher order finite elements 380 Hilber-α method 411
historiotropy 203, 315 history
integration, 583 variable, 434, 440, 478 hodograph 116 hoop stress 489 hourglass control 380 hydration products 302 hydraulic pressure 148 hygral
behaviour, 143 conditions, 359 hygro-mechanical analysis, 583, 590 damage, 367 identification 637 implicit
backward Euler scheme, 238 mode, 518
Importance Sampling 534 indicator function 533 inf-sub-condition 398 initial condition 412
in situ test stand 39 inspection 6 instability 367
Trang 9Subject Index 717
integration 377
scheme energy conserving, 411
scheme energy decaying, 411
integrity 289, 290
intensity of accumulation 161, 314
interaction 3
interactive effect 3
intermediate configuration 256
internal
damage, 96
modes, 394
interpolation property 390
interval algebra 370
intrinsic permeability 307
inverse Fourier transform 120
investment cost 5
ion transport 295, 374
isomorphic variables 198
isoparametric approximation 390
isotropic damage parameter 286
iteration methods 403
Jacobi
temporal transformer, 420
tensor, 383
transformation, 383
jump condition 418
kinematical relation 427
kinematic hardening law 255
kinking angle 272
Kirchhoff-Love formulation 397
Kohlrauschs law 297, 298
Krylov-based model reduction methods
500, 504
Kuhn-Tucker conditions 238, 300,
478
Lagrange 390
multipliers, 507, 511
non-hierarchical concept, 388
polynomials, 369, 380
shape function, 380, 381, 412
latent heat 286
Latin hypercube sampling 535, 536,
617, 627, 631
leaching 354
leakage 356
least squares problem 567 Legendre 380, 389, 390 modified polynomials, 389 polynomials, 369, 389 shape function, 389 type, 392
Leon model 244 life-cycle
design, 7 investigation, 499 lifetime 207 analysis of bridge hangers, 34 lock-in effect, 34
stochastic excitation force, 34 assessment, 610
control, 659 lifetime-oriented analysis, 562, 583 design, 1, 371, 548, 562 concept, 365, 607 model, 365 limit state 367 serviceability, 367 ultimate, 367 linear convergence rate 388 linearized
discrete balance equation, 385 weak form, 419
liquefaction 113, 162, 206 liquid saturation 289 load
-deflection curve, 493 -independent influences, 92 cycles, 266, 269
pattern, 87 static and dynamic design calculations, 87
symmetric load pattern, 90 scenario, 7
loading biaxial, 256 cycles, 280 cyclic, 278 local balance equation 373 localization 634
lock-in 25 effect, 26 aerodynamic damping, 26 large oscillation amplitudes, 26
Trang 10Scruton number, 26
range, 28
lift force, 28
locking-free element formulation 430
locking phenomena 379
Lode angle 314
long-term
calculation, 499
creep, 285
degradation mechanisms, 632
experiments, 39
loss of equilibrium 367
low-frequency vibration comfort 573
low order
approximation, 379
finite elements, 379
macro time 657
maintenance 6
Markov parameters 638, 640
material
degradation, 124
failure, 374
model, 625
matrix dissolution 295
Matsuoka and Nakai condition 313
Maxwell symmetry 288
mean wind speeds 15
Gumbel-distribution, 16
logistic distribution, 16
occurrence probability of an extreme
value, 20
rosettes of 10-minutes means of wind
velocities, 18
terrain factor, 21
Weibull-distribution, 16
wind direction, 18
wind effect admittance, 22
wind rosette, 18
mesh
dependency, 246
locking, 519
metallic materials 137
micro-ice-lens model 95, 148, 194
micro and macro time domain 33
microcrack 124, 133
formation, 194
micromechanical model 293
micromechanics 271 microplasticity 137 microprestress 291 microscopic
alteration, 367 analysis, 621 microstructure 133, 150 micro time 657
Mindlin-Reissner formulation, 397 kinematics, 362 Miner’s rule 205 minimum energy 492 modal
analysis, 527, 634
of wind-induced oscillations, 13 assurance criterion, 569
damping, 634 reduction, 503 mode-I-crack extension 490 model
adaptivity, 426 reduction, 498, 499, 503 mode shapes 634 moisture
permeability, 147 transport, 147, 285, 359, 586 uptake, 194
molar conductivity 298 monopile foundation 650 Monte Carlo
method, 627 Simulation, 533, 534, 617, 654 distance-controlled, 542 strategy, 555
multi-axial stress state 269 multi-dimensional multi-field element 377
multi-field numerical method, 365 problem, 367, 369, 380 multi-level solution philosophy 367 multi-scale 658
modeling, 616, 657 multi-stage cyclic loading 136 multi-surface models 518 multiaxial loading 126 multiphysics problems 373, 379, 380 multisurface