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Bathe K.-J. — Finite element procedures

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Название: Finite element procedures

Автор: Bathe K.-J.

Аннотация:

A text for upper-level undergraduate and graduate courses on finite element analysis or for self-study by engineers and scientists, developed from the author's earlier Finite Element Procedures in Engineering Analysis (Prentice-Hall, 1982). It does not present a survey of finite element methods, but concentrates only on certain procedures, namely on techniques that are useful in engineering practice and that will likely be employed for many years to come. The emphasis is on reliability and on finite element procedures that are general and reliable for engineering analysis. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Язык:

Рубрика: Математика/Численные методы/Конечные элементы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 1037

Добавлена в каталог: 19.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$C^{m-1}$ problem      235
space      236
Accuracy of calculations      227 (see also “Errors in solution”)
Acoustic fluid      666
Almansi strain tensor      585
Alpha $(\alpha)$ integration method in heat transfer analysis      830
Alpha $(\alpha)$ 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 $\alpha$ 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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