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| Bathe K.-J. — Finite element procedures |
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| Предметный указатель |
 problem 235
 space 236
Accuracy of calculations 227 (see also “Errors in solution”)
Acoustic fluid 666
Almansi strain tensor 585
Alpha  integration method in heat transfer analysis 830
Alpha integration method in inelastic analysis 606
Amplitude decay 811
Analogies 82 662
Angular distortion 381
Approximation of geometry 208 342
Approximation operator 803
Arbitrary Lagrangian — Eulerian formulation 672
Aspect-ratio distortion 381
Assemblage of element matrices 78 149 165 185 983
Associated constraint problems 728 846
Augmented Lagrangian method 146 147
Axial stress member see “Bar”; “Truss element”
Axisymmetric element 199 202 209 356 552
Axisymmetric shell element 419 568 574
Bandwith of matrix 20 714 985
bar 108 120 124 126
Base vectors, contravariant 46
Base vectors, covariant 46
Basis 36 46
Beam element 150 199 200 397 568
BFGS method 759
Bilinear form 228
Bisection method 943
Body force loading 155 164 165 204 213
Boundary conditions in analysis acoustic 667
Boundary conditions in analysis displacement and stress 154
Boundary conditions in analysis heat transfer 643 676
Boundary conditions in analysis incompressible inviscid flow 663
Boundary conditions in analysis seepage 662
Boundary conditions in analysis viscous fluid flow 675
Boundary conditions, convection 644
Boundary conditions, cyclic 192
Boundary conditions, displacement 154 187
Boundary conditions, essential 110
Boundary conditions, force 111
Boundary conditions, geometric 110
Boundary conditions, natural 110
Boundary conditions, phase change 656
Boundary conditions, radiation 644 658
Boundary conditions, skew 189
Boundary layer in fluid mechanics 684
Boundary layer in Reissner/Mindlin plates 434 449
Boundary value problems 110
Bubble function 373 432 690
Buckling analysis 90 114 630
bulk modulus 277 297
Cable element 543
Cauchy stress tensor 499
Cauchy-Green deformation tensor (left and right tensors) 506
Cauchy’s formula 516
Caughey series 799
Cea’s lemma 242
Central difference method 770 815 824
CFL number 816
Change of basis 43 49 60 189 786
Characteristic polynomial 52 888 938
Characteristic roots see “Eigenvalues”
Cholesky factorization 717
Collapse analysis 630
Column heights 708 986
Column space of a matrix 37
Compacted column storage 21 708 985
Compatibility of elements/meshes 161 229 377
Compatibility of norms 70
Compatible norm 70
Complete polynomial 244
Completeness condition of element 229
Completeness condition of element assemblage 263
Component mode synthesis 875
Computer programs for finite element analysis 988
Computer programs for Gauss elimination equation solution 708
Computer programs for isoparametric element 480
Computer programs for Jacobi generalized eigensolution 924
Computer programs for subspace iteration eigensolution 964
Computer-aided design (CAD) 7 11
Concentrated loads, modeling of 10 228 239
Condensation see “Static condensation”
Condition number 738
Conditional stability 773
Conductivity matrix 651
Conforming see “Compatibility”
Conjugate gradient method 749
Connectivity array 185 984
Consistent load vector 164 213 814
Consistent mass matrix 165 213
Consistent tangent stiffness matrix 758
Consistent tangent stress-strain matrix 583 602 758
Constant increment of external work criterion 763
Constant strain one-dimensional (truss) element 150 166 339
Constant strain three-dimensional 4-node element 366 373
Constant strain two-dimensional 3-node element 205 364 373
Constant-average-acceleration method 780
Constitutive equations see “Stress-strain relations”
Constraint equations 190
Constraint function method 626
Contact analysis 622
Contactor 623
Continuity of a bilinear form 237
Contravariant, base vectors 46
Contravariant, basis 46
Convection boundary conditions 644
Convergence criteria in conjugate gradient method 750
Convergence criteria in eigensolutions 892 914 920 949 963
Convergence criteria in finite element discretization 254
Convergence criteria in for iterative processes using norms 67
Convergence criteria in Gauss-Seidel iteration 747
Convergence criteria in mode superposition solution 795
Convergence criteria in nonlinear analysis 764
Convergence of, conjugate gradient iteration 750
Convergence of, finite element discretization 225 376
Convergence of, Gauss-Seidel iteration 747
Convergence of, Jacobi iteration 914 920
Convergence of, Lanczos method 949 953
Convergence of, mode superposition solution 795 814
Convergence of, Newton-Raphson iteration 756
Convergence of, QR iteration 935
Convergence of, Rayleigh quotient iteration 904
Convergence of, subspace iteration 959 963
Convergence of, vector forward iteration 897
Convergence of, vector inverse iteration 892
Coordinate interpolation 342
Coordinate systems area 371
Coordinate systems Cartesian 40
Coordinate systems global 154
Coordinate systems local 154 161
Coordinate systems natural 339 342 372
Coordinate systems skew 189
Coordinate systems volume 373
Coulomb’s law of friction 624
Coupling of different integration operators 782
Covariant base vectors 46
Covariant basis 46
creep 606
Critical time step for use of  integration method 831
Critical time step for use of central difference method 772 808 817
Cyclic symmetry 192
Damping 165 796
Damping ratio 796 802
Dc network 83
Deflation of matrix 906
Deflation of polynomial 942 945
Deflation of vectors 907
Deformation dependent loading 527
Deformation gradient 502
| Degree of freedom 161 172 273 286 329 345 413 981
Determinant calculation of 31
Determinant of associated constraint problems 729 850
Determinant of deformation gradient 503
Determinant of Jacobian operator 347 389
Determinant search algorithm 938
Digital computer arithmetic 734
Dimension of space 36
Dimension of sub’space 37
Direct integration in dynamic stress analysis 769 824
Direct integration in fluid flow analysis 680 835
Direct integration in heat transfer analysis 830
Direct stiffness method 80 151 165
Director vectors 409 438 570 576
Displacement interpolation 161 195
Displacement method of analysis 149
Displacement/pressure formulations basic considerations 276
Displacement/pressure formulations Displacement/pressure formulations elements 292 329
Displacement/pressure formulations u/p formulation 287
Displacement/pressure formulations u/p-c formulation 287
Distortion of elements (effect on convergence) 382 469
Divergence of iterations 758 761 764
Divergence theorem 158
Double precision arithmetic 739
Drucker — Prager yield condition 604
Duhamel integral 789 796
Dyad 44
Dyadic 44
Dynamic buckling 636
Dynamic load factor 793
Dynamic response calculations by mode superposition solution 785
Dynamic response calculations by step-by-step integration 769
d’Alembert’s principle 134 165 402
Effective creep strain 607
Effective plastic strain 599
Effective stiffness matrix 775 778 781
Effective stress 599
Effective-stress-function algorithm 600 609 611 616
Eigenpair 52
Eigenproblem in buckling analysis 92 632 839
Eigenproblem in heat transfer analysis 105 836 840
Eigenproblem in vibration mode superposition analysis 786 839
Eigenspace 56
Eigensystem 52
Eigenvalue problem 51
Eigenvalue separation property 63 728 846
Eigenvalues and eigenvectors, basic definitions 52
Eigenvalues and eigenvectors, calculation of 52 887
Eigenvalues and eigenvectors, of associated constraint problems 64
Electric conduction analysis 83 662
Electro-static field analysis 662
Element matrices, definitions in displacement-based formulations 164 347 540
Element matrices, definitions in displacement/pressure formulations 286 388 561
Element matrices, definitions in field problems 661
Element matrices, definitions in general mixed formulations 272
Element matrices, definitions in heat transfer analysis 651
Element matrices, definitions in incompressible fluid flow 677
Elliptic equation 106
Ellipticity condition 304
Ellipticity of a bilinear form 237
Energy norm 237
Energy-conjugate (work-conjugate) stresses and strains 515
Engineering strain 155 486
Equations of finite elements assemblage 185 983
Equations of finite elements in heat transfer analysis 651
Equations of finite elements in incompressible fluid flow analysis 678
Equations of finite elements in linear dynamic analysis 165
Equations of finite elements in linear static analysis 164
Equations of finite elements in nonlinear dynamic analysis 540
Equations of finite elements in nonlinear static analysis 491 540
Equilibrium iteration 493 526 754
Equilibrium on differential level 160 175
Equilibrium on element level 177
Equivalency of norms 67 238
Error bounds in eigenvalue solution 880 884 949
Error estimates for displacement-based elements 246 380 469
Error estimates for displacement/pressure elements 312
Error estimates for MITC plate elements 432
Error measures in eigenvalue solution 884 892
Error measures in finite element analysis 254
Error measures in mode superposition solution 795
Errors in solution 227
Euclidean vector norm 67
Euler backward method 602 831 834
Euler forward method 831 834
Euler integration method, use in creep, plasticity 607
Euler integration method, use in heat transfer 831
Eulerian formulation 498 672
Existence of inverse matrix 27
Explicit integration 770
Explicit-implicit integration 783
Exponential scheme of upwinding 686
Field problems 661
Finite difference method approximations 132
Finite difference method differential formulation 129
Finite difference method energy formulation 135
Finite difference method in dynamic response calculation 769
Finite elements an overview of use 2
Finite elements elementary examples 79 124 149 166
Finite elements history 1
Finite strip method 209
First Piola — Kirchhoff stress tensor 515
Fluid flow analysis incompressible viscous flow 671
Fluid flow analysis irrotational (potential) flow 663
Fluid-structure interactions 668 672
Folded plate structure 208
Forced vibration analysis see “Dynamic response calculations by”
Forms bilinear 228
Forms linear 228
Fracture mechanics elements 369
Free vibration conditions 95 786
Friction see “Coulomb’s law of friction”
Frontal solution method 725
Full Newton-Raphson iteration 756 834
Full numerical integration 469
Functionals 110 115
Galerkin least squares method 688
Galerkin method 118 126
Gauss elimination a computer program 715
Gauss elimination computational errors in 734
Gauss elimination introduction to 697
Gauss elimination number of operations 714
Gauss elimination physical interpretation 699
Gauss quadrature 461
Gauss-Seidel iteration 747
Generalized coordinates 171 195
Generalized displacements, see “Generalized coordinates”
Generalized eigenproblems see also “Eigenproblem in”)
Generalized eigenproblems, definition 53
Generalized eigenproblems, various problems 839
Generalized formulation 125
Generalized Jacobi method 919
Ghost frequencies see “Phantom frequencies”
GMRes (Generalized minimal residual) method 752
Gram-Schmidt orthogonalization 907 952 956
Green-Lagrange strain tensor 50 512
Guyan reduction 875 960
h- method of finite element refinement 251
h/p method of finite element refinement 253
Half-bandwidth see “Bandwidth of matrix”
Hardening in creep 607
Hardening in plasticity 599
Hardening in viscoplasticity 610
Hat function 131 692
Heat capacity matrix 89 655
Heat conduction equation 106 107 643
Heat transfer analysis 80 89 642
Hellinger — Reissner functional 274 285 297 477
Hencky (logarithmic) strain tensor 512 614
Hierarchical functions 252 260 692
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