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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

Hierarchy of mathematical models      4
History of finite elements      1
Houbolt method      774 804 809 811
Householder reduction to tridiagonal form      927
Hu — Washizu functional      270 297
Hydraulic network      82
Hyperbolic equation      106
Hyperelastic      582 592
Hypoelastic      582
Identity matrix      19
Identity vector      19
Imperfections (on structural model)      634
Implicit-explicit integration      783
Incompatible modes      262
Incompressibility      276
Incremental potential      561
Indefinite matrix      60 731 939 944
Indicial notation, definition      41
Indicial notation, use      41 499
Inf-sup condition for incompressible analysis derivation      304 312
Inf-sup condition for incompressible analysis general remarks      291
Inf-sup condition for structural/beam elements      330
Inf-sup test      322
Infinite eigenvalue      853
Initial calculations in central difference method      771
Initial calculations in Houbolt method      775
Initial calculations in Newmark method      781
Initial calculations in Wilson $\theta$ method      778
Initial stress load vector      164
Initial stress method      758
Initial value problems      110
Instability analysis of integration methods      806
Instability analysis of structural systems      630
Integration of dynamic equilibrium equations      see “Direct integration in”
Integration of finite element matrices      see “Numerical integration of finite element matrices”
Integration of stresses      see “Stress integration”
Interelement continuity conditions      see “Compatibility of elements/meshes”
Interpolant of solution      246
Interpolation functions      338 343 344 374
Inverse of matrix      27
Inviscid (acoustic) fluid      666
Inviscid flow      663
Isobands of stresses      255
Isoparametric formulations, computer program implementation      480
Isoparametric formulations, definition      345
Isoparametric formulations, interpolations      see “Interpolation functions”
Isoparametric formulations, introduction      338
Iteration      see “Gauss-Seidel iteration”; “Conjugate gradient method”; “Quasi — Newton methods”; “Eigenvalues and eigenvectors”
Jacobi eigensolution method      912
Jacobian operator      346
Jaumann stress rate tensor      591 617
Joining unlike elements      377
Jordan canonical form      808
Kernel definition      39
Kernel use in analysis of stability      318
Kinematic assumptions      399 420 437
Kirchhoff hypothesis      420
Kirchhoff stress tensor      515
Kronecker delta      45 46
Lagrange multipliers      144 270 286 626 744
Lagrangian formulations linearization      523 538
Lagrangian formulations, total Lagrangian (TL)      523 561 586
Lagrangian formulations, updated Lagrangian (UL)      523 565 586
Lagrangian formulations, updated Lagrangian Hencky (ULH)      614
Lagrangian interpolation      456
Lame constants      298 584
Lanczos method      945
Laplace equation      106 107
Large displacement/strain analysis      487 498
Latent heat      656
LDI/ factorization      705 (see also “Gauss elimination”)
Least squares averaging (smoothing)      256
Legendre polynomials      252
Length of vector      see “Euclidean vector norm”
Linear acceleration method      777 780
Linear dependency      36
Linear equations      see “Equations”
Linear form      228
Lipschitz continuity      757
Load operator      803
Load-displacement-constraint methods      761
Loads in analysis of heat transfer      652
Loads in analysis of structures      164
Loads in analysis of Tluid flows      678
Locking in (almost) incompressible analysis      283 303 308 317
Locking in structural analysis      275 332 404 408 424 444
Logarithmic strain tensor      512 614
Loss of orthogonality      952
Lumped force vectors      213
Lumped mass matrix      213
Mass matrix      165
Mass proportional damping      798
Master-slave solution      740
Materially-nonlinear-only analysis      487 540
Mathematical model accuracy      7
Mathematical model effectiveness      4 6
Mathematical model reliability      4
Mathematical model very-comprehensive      6
Matrix addition and subtraction      21
Matrix bandwidth      19 985
Matrix definition      18
Matrix deflation      906
Matrix determinant      31
Matrix identity matrix      19
Matrix inverse      27
Matrix multiplication by scalar      22
Matrix norms      68
Matrix partitioning      28
Matrix products      22
Matrix shifting      851 899 943 964
Matrix storage      20
Matrix symmetry      19
Matrix trace      30
Membrane locking      408 444
Mesh (from a sequence of meshes) compatible      377
Mesh (from a sequence of meshes) quasi-uniform      382 434
Mesh (from a sequence of meshes) regular      380
Mesh (from a sequence of meshes) uniform      243 245
Metric tensor      47
Mindlin (Reissner/Mindlin) plate theory      420
Minimax characterization of eigenvalues      63
Minimization of bandwidth      714 986
MITC elements error estimates      432
MITC elements plate elements      425
MITC elements shell elements      445 577
Mixed finite element formulations      268
Mixed interpolations for continuum elements      see “Displacement/pressure formulations”
Mixed interpolations for structural elements beam      274 330 406
Mixed interpolations for structural elements plate      424
Mixed interpolations for structural elements shell      444
Mode shape      786
Mode superposition with damping included      796
Mode superposition with damping neglected      789
Modeling constitutive relations      582
Modeling in dynamic analysis      813
Modeling linear/nonlinear conditions      487
Modeling type of problems      196
Modified Newton — Raphson iteration      759
Monotonic convergence      225 376
Mooney — Rivlin material model      592
Multiple eigenvalues convergence to      895 944 951 960
Multiple eigenvalues orthogonality of eigenvectors      55
Nanson’s formula      516
Natural coordinate system      339 342
Navier — Stokes equations      676 680
Newmark method      780 806 809 811
Newton identities      939
Newton — Raphson iterations      493 755
Nodal point information      981
Nodal point numbering      986

Nonaxisymmetric loading      209
Nonconforming elements      see “Compatibility of elements/meshes; Incompatible modes”
Nondimensionalized variables      676
Nonlinear analysis classification      487
Nonlinear analysis introduction to      485
Nonlinear analysis simple examples      488
Nonproportional damping      799
Nonsymmetric coefficient matrix      528 628 678 696 744 752
Norms of matrices      68
Norms of vectors      67
Numerical integration of finite element matrices composite formulas      459
Numerical integration of finite element matrices effect on order of convergence      469
Numerical integration of finite element matrices for quadrilateral elements      466
Numerical integration of finite element matrices for triangular elements      467
Numerical integration of finite element matrices Gauss quadrature      461
Numerical integration of finite element matrices in multiple dimensions      464
Numerical integration of finite element matrices Newton-Cotes formulas      457
Numerical integration of finite element matrices recommended (full) order      469
Numerical integration of finite element matrices Simpson rule      457
Numerical integration of finite element matrices trapezoidal rule      457
Ogden material model      592 594
Order of convergence of finite element discretizations      247 312 432 469
Order of convergence of Newton — Raphson iteration      757
Order of convergence of polynomial iteration      941
Order of convergence of Rayleigh quotient iteration      904
Order of convergence of subspace iteration      959
Order of convergence of vector iteration      895 898
Orthogonal matrices, definition      43
Orthogonal matrices, use      44 73 189 913 927 931
Orthogonal similarity transformation      53
Orthogonality of eigenspaces      55
Orthogonality of eigenvectors      54
Orthogonalization by Gram-Schmidt      907 952 956
Orthogonalization in Lanczos method      946
Orthogonalization in subspace iteration      958
Orthonormality      55
Ovalization      413
Overrelaxation      747
p - method of finite element refinement      251
Parabolic equation      106
Partitioning      see “Matrix partitioning”
Pascal triangle      246 380
Patch test      263
Peclet number      677
Penalty method connection to Timoshenko beam theory (and Reissner/Mindlin plate theory)      404
Penalty method, elementary concepts      144
Penalty method, relation to Lagrange multiplier method      147
Penalty method, to impose boundary conditions      190
Period elongation      811
Petrov — Galerkin method      687
Phantom frequencies/modes      472
Phase change      656
Pipe elements      413
Plane reflection matrix      73
Plane rotation matrix      43 913 932
Plane strain element      199 351
Plane stress element      170 199 351
Plasticity      597
Plate bending      200 205 420
Plate/shell boundary conditions      448
Poincare-Friedrichs inequality      237
Polar decomposition      508
Polynomial displacement fields      195 246 385
Polynomial iteration explicit iteration      938
Polynomial iteration implicit iteration      939
Positive definiteness      60 726
Positive semidefiniteness      60 726
Postbuckling response (postcollapse)      630 762
Potential incremental      561
Potential total      86 160 268
Prandtl number      677
Preconditioning      749
Pressure modes checkerboarding      319
Pressure modes physical      315
Pressure modes spurious      316 318 325
Principle of virtual displacements (or principle of virtual work) basic statement      125 156 499
Principle of virtual displacements (or principle of virtual work) derivation      126 157
Principle of virtual displacements (or principle of virtual work) linearization of continuum mechanics equations      523
Principle of virtual displacements (or principle of virtual work) linearization with respect to finite element variables      538
Principle of virtual displacements (or principle of virtual work) relation to stationarity of total potential      160
Principle of virtual temperatures, basic statement      644 678
Principle of virtual temperatures, derivation      645
Principle of virtual velocities      677
Products of matrices      see “Matrix products”
Projection operator      308
Proportional damping      796
QR iteration      931
Quadrature      see “Numerical integration of finite element matrices”
Quarter-point elements      370
Quasi-Newton methods      759
Quasi-uniform sequence of meshes      382 434
Radial return method      598
Radiation boundary conditions      644 658
Rank      39
Rate of convergence of finite element discretizations      244 247 312 432 469
Rate-of-deformation tensor      511
Rayleigh damping      797
Rayleigh quotient      60 868 904
Rayleigh quotient iteration      904
Rayleigh-Ritz analysis      868 960
Rayleigh’s minimum principle      63
Reaction calculations      188
Reduced order numerical integration      476
Reduction of matrix to diagonal form      57 (see also “Eigenvalues and eigenvectors”)
Reduction of matrix to upper triangular form      699 705
Reflection matrix      see “Plane reflection matrix”
Regular mesh      380
Reissner plate theory      420
Relative degrees of freedom      739 741
Reliability of finite element methods      12 296 303 469
Reliability of mathematical model      4
Residual vector in eigensolution      880
Residual vector in solution of equations      736
Resonance      793
Response history      see “Dynamic response calculations by”
Reynolds number      677
Rigid body modes      230 232 704 726
Ritz analysis      119 234
Robustness of finite element methods      12 296
Rotation matrix      see “Plane rotation matrix”
Rotation of axes      189
Rotation of director vectors, consistent/full linearization beams      570 579
Rotation of director vectors, consistent/full linearization shells      577 580
Round-off error      735
Row space of a matrix      39
Row-echelon form      38
Rubber elasticity      561 592
Schwarz inequality      238
Secant iteration      941
Second Piola — Kirchhoff stress tensor      515
Seepage      662
Selective integration      476
Shape functions      see “Interpolation functions”
Shear correction factor      399
Shear locking      275 332 404 408 424 444
Shell elements      200 207 437 575
Shifting of matrix      see “Matrix shifting”
Similarity transformation      53
Simpson’s rule      457
Single precision arithmetic      734
Singular matrix      27
Skew boundary displacement conditions      189
Skyline of matrix      708 986
Snap-through response      631
Sobolev norms      237
Solution of equations in dynamic analysis      768
Solution of equations in static analysis      695
Solvability of equations      313
Spaces       236
Spaces       239

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