structural-analysis-with-finite-elements-by-friedel-hartmann-and-casimir-katz

594 Index

corner force 421 energy norm 151 378
coupling degrees of freedom 224 equilibrium 86, 184, 420 570
cracks in a beam 316 equilibrium of resultant forces
critical angles, plane problem 336 equilibrium point 20
critical load 302 error estimators 566
CST element 338 error in energy 151
cubic elements 338 error indicator 566
cycloid 175 essential boundary conditions
Euler equation 25, 40
d-adaptivity 154 Euler-beam I 193
deformation space 6 explicit error estimators 567
degenerate shell elements 490
dichotomy 149 finite element 197
dimension argument 45 first fundamental form 486
dipole 97 flat elements 493
Dirac delta 69 flexibility matrix 198
Dirac energy 110, 111 folded plates 463
direct design method 476 forces 40
direct product 504 foundation slabs 469
discontinuities 389 fundamental solution 241
displaced point supports 354
displacement methods 393 Galerkin method 193
displacement model of slabs 421 Galerkin orthogonality 11
displacements 40 Gateaux derivative 402
distance 37 Gaussian curvature 488
DKT element 440 Generalized Finite Element method
drilling degrees of freedom 344
drop panels and column capitals 451 213
DST element 441 geometric matrix 301
dual load 69 global equilibrium 185
dual quantities 70 goal-oriented recovery 160, 520
dual weighted residual error estimate goal-oriented refinement 412
Green’s first identity 508
525 Green’s function 51, 57, 516
duality 40 Green’s identities 508
duality techniques 156, 160, 520 Green-Lagrangian strain tensor 401

effective length factor 302 215 h-methods 154
effective width 467 half-space model 256, 470
efficiency of estimator 567 hard support 436
eigenvalue 230 hat functions 197
eigenvector 230 Heaviside function 218
eigenwork 17 Hellinger–Reissner principle 396
Element Free Galerkin method Hermite Polynomials 201
element stresses 357 hierarchical elements 309
elements 220 higher-order elements 344
elements, plane problems 338 homogeneous deflection curve 289
elements, slabs 422 hourglass modes 230
ellipticity 21 How to predict changes 113
energy method 4 hp-method 154

Index 595

HSM element 425 missing member 325
hybrid elements 425 mixed methods 393
hyperelastic material 402 Mohr’s integral 240, 535

implicit error estimators 567 natural boundary conditions 570
incompressible material 393 Nitsche trick 540
infinite energy 208 nodal influence functions 77
influence functions 42, 69 nodal stresses 357
influence functions for mixed formula- nonlinear problems 123, 161, 167, 401,

tions 399 526
influence of a single element 126 normal equations 34
integral operators 82
integration by parts 508 order of the singularity 46
interpolation 197 order of the strain energy 46
isotropy 221 output 181

kernel of a matrix 231 58 p-methods 154
kernel of an influence function particular deflection curve 289
kinematic constraints 347 partition of unity 211
Kirchhoff plates 416 Partition of Unity method 213
Kirchhoff shear 420 Pascal’s triangle 200
Kronecker delta 199 patch test 344
peaks 102
Lagrange element 200, 343 piecewise polynomials 197
Lagrange multipliers 226 piled raft foundations 258
Lagrange polynomials 200 plane elements 338
least action 20 plane strain 222, 334
least squares 33 plane stress 222, 334
linear elements 338 point supports 353, 477
linear strain triangle 341 Poisson’s ratio 416, 419
lintels 356 polynomials 199
load case δ 17 potential energy 6
load case p 17 primal problem 157
loads 255 primary load case 386
local equilibrium 185 principal stresses 336
local solution 136 principle of minimum potential energy
locking 437
loss of a frame member 320 7
loss of a support 317 principle of virtual displacements 25
LST element 341 principle of virtual forces 240
projection 515
m-adaptivity 154 projection method 2
mapped polynomials 203 pulley 111
master degree of freedom 226 Pythagorean theorem 573
Maxwell’s theorem 550
membrane locking 491, 492 Q4 340 338
membrane stresses 487 Q4 + 2 341
membranes 498 Q8 343
Mindlin shell elements 490 quadratic elements

596 Index Sobolev norms 12
Sobolev’s Embedding Theorem 46
r-adaptivity 154 soft support 436
Rayleigh quotient 195 spurious modes 211
recovery based error estimators 567 St. Venant’s principle 172
reduced global stiffness matrix 228 stability problems 193
reduced integration 228 stiffness matrices 221
reduced stiffness matrix 185, 224 stiffness matrices for 1-D elements 292
Reissner–Mindlin plates 431 stiffness matrices, slabs 424
remeshing 154 stiffness matrices, three properties 223
residual 236 stiffness matrix, 2-D 339
residual forces 15 strain energy product 31, 35, 221, 339,
restriction 1
retrofitting structures 130 395
Riesz’ representation theorem 521, stream model 330
substitute load case 2
559 superconvergence 206
rigid-body motions 221 support conditions 183
rope 6 support reactions 99, 353
rotational invariance 221, 338 supports 441
rounding errors 230 symmetries 354

safety of structures 326 T beams 226
scalar product 33, 40, 503 tangential supports 354
scalar product of matrices 504 Taylor series 199
second fundamental form 486 temperature 187
second Piola-Kirchhoff stress tensor tension 6
tension stiffening 288
401 test range 36
self-equilibrated stresses 386 test space 22
sensitivity analysis 313 three-moment equation 198
serendipity elements 200, 343 Timoshenko beam 296
set theory 16 Timoshenko beam element 301
settlement of supports 187 Tottenham’s equation 64
settlements 387 translations 212
shape functions 337 trial space 6, 22
shear forces 451 truss models 363
shear locking 437
shear modulus 336, 393 values at a point 62
shearing strain 432 variable thickness 452
shell equations 485 virtual displacements 24
shells 485 volume elements 490
shells of revolution 488
shift 82 weak convergence 40 535
Shifted Green’s Function Theorem weak equal sign 4
weak form of influence functions
547 weak solution 40
shifted Green’s functions 541 weighted least squares 35
singular matrices 227 weighted residual method 194
singularities 175 wheel loads 460
skew projection 13, 22
slabs, Reissner–Mindlin 431
slave degree of freedom 226
smoothing process 362

Index 597

Wilson’s Element 341 yielding of a rigid support 319
Winkler model 255, 469 zero-energy modes 230

X-FEM 215