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Crisfield M.A. Ч Non-Linear Finite Element Analysis of Solids and Structures. Vol. 2: Advanced Topics
Crisfield M.A. Ч Non-Linear Finite Element Analysis of Solids and Structures. Vol. 2: Advanced Topics

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Ќазвание: Non-Linear Finite Element Analysis of Solids and Structures. Vol. 2: Advanced Topics

јвтор: Crisfield M.A.


Non-linear Finite Element Analysis of Solids and Structures Volume 2: Advanced Topics M. A. Crisfield Imperial College of Science, Technology and Medicine, London, UK In such fields as aeronautical, civil, mechanical and structural engineering, non-linear analysis techniques are becoming widely used for the solution of practical engineering problems. Taking an engineering rather than a mathematical bias, this comprehensive book builds on the fundamental ideas explained in Volume One, introducing the reader to more detailed, advanced topics. Large strains and large rotations, plasticity with a range of yield criteria and hardening rules, stability theory and advanced solution procedures including branch-switching techniques, contact and friction, and nonlinear dynamics, are covered in depth. Examples from a non-linear finite element computer program incorporating the advanced solution procedures are included. The computer program is available on the Internet via anonymous ftp, using the URL ftp://ftp.cc.ic.ac.uk/pub/depts/aero/nonlin2/.

язык: en

–убрика: ћатематика/„исленные методы/ онечные элементы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1997

 оличество страниц: 508

ƒобавлена в каталог: 20.02.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
$F_eF_p$ approach for conventional rate form      312Ч315
$F_eF_p$ decomposition, based on final (current) configuration      324Ч326
$F_eF_p$ multiplicative decomposition      309
Additive rotation components      242Ч247
Additive rotation increments      200
Almansi strain      2Ч4 18 21
Anisotropic plasticity      99
Anisotropic plasticity, yield criteria for      122Ч128
Apex return      119 121Ч122
Applied loading      248Ч251
Arc-length methods      368Ч373
Arc-length methods, using relative variables      373Ч374
Asymmetric bifurcation      347Ч349
Asymmetric bifurcation, two-bar truss with      382Ч391
Augmented Lagrangian methods      426Ч431
Automatic time-stepping      468Ч470
Average acceleration method      448 452Ч453
Axial deformation      216
Axial strain      227
Axisymmetric membrane      70
B-bar method      76
Back stresses      159
Backward Ч Euler method      105 107Ч108 113Ч122
Backward Ч Euler return      129Ч132 134 144 168Ч169 185
Bauschinger effect      158
Bending dominant case      112
Bifurcation      355
Bifurcation points      343 347 356
Bifurcations      341
Biot strain      2Ч4 11 13 267
Biot stress      11 13 15 18 79 80 331 332
Bracketing techniques      356Ч358 383Ч389 393Ч394 396Ч397
Branch switching      355 359Ч362 389Ч391 394 397Ч398
Branch switching, using higher-order derivatives      361Ч362
Cartesian base vectors      35Ч36
Cauchy stress      11 13 21 22 48 313
Cauchy Ч Green tensor      64 94 322
Co-rotational approach for curved membrane using facet triangles      269Ч271
Co-rotational approach for curved membrane using quadrilaterals      271Ч272
Co-rotational approach for three-dimensional beam elements      213Ч226
Co-rotational approach for three-dimensional continua      266Ч269
Co-rotational approach for two-dimensional continua      262Ч266
Co-rotational approach large elastic strains in      300Ч301
Co-rotational elements      251
Co-rotational energy-conserving procedure for two-dimensional beams      461Ч465
Co-rotational facet shell formulation based on MorleyТs triangle      276Ч280
Co-rotational formulation, extra internal variables      296Ч297
Co-rotational framework for semi-loof shells      283Ч285
Co-rotational framework for three-dimensional beams      285Ч287
Co-rotational shell formulation with three rotational degrees of freedom per node      273Ч276
Co-rotational shell formulation with two rotational degrees of freedom per node      280Ч283
Cohesive-frictional relationship      102
Comers, yield functions with      107Ч109
Compound rotations      195Ч197
Compressible neo-Hookean model      80Ч81 89
Computer program using truss elements      381Ч409
Concentrated moments      249Ч250
Concrete      135Ч136 151
Concrete, fixed and rotating crack models      140Ч142
Conjugate stress and strain measures      10Ч19
Consistency condition      161 163 173
Consistent linearisation      411
Consistent tangent      326Ч328
Consistent tangent matrix      184 434Ч435 437Ч438
Consistent tangent modular matrix      108 120Ч122 130Ч131 133
Consistent tangent modular tensor      172Ч173
Constitutive tensors      77
Constitutive tensors, transforming components of      37Ч38
Contact      411Ч446
Contact element, two-dimensional      412Ч413
Contact formulation, three-dimensional frictionless      431Ч435
Contact formulation, two-dimensional frictionless      412Ч416
Contact patch test      417Ч420
Contact, external forces      418Ч420
Contact, internal forces      417
Continua, finite element analysis      45Ч61
Continuum mechanics      1Ч25
Contravariant base vectors      41
Control parameter      357 358
Convected coordinates, and total, Lagrangian formulation      57Ч60
Convected curvilinear coordinates      38
Corner regions      148 416
Corner return      121Ч122
Corrector      460Ч461
Corrector, based on linearised arc-length method      360
Corrector, using cylindrical arc-length method      361
Corrector, using displacement control      361
Corrector, using higher-order derivatives      365Ч366
Cotter Ч Rivlin rate      21
Coulomb sliding friction      422Ч424 429
Coulomb sliding friction in three dimensions      438Ч439
Covariant components      33Ч34 39 40
Cracking      135Ч138
Crushable foam model      104
Curvature      204Ч211 228
Curvature without nodal triads      207Ч211
Curvature, expressions directly using nodel triads      204
Curved quadrilateral membrane      271Ч272
Curved triangular membrane      269Ч271
Cylindrical arc-length method      364Ч365
Cylindrical arc-length method, choice of root      374Ч376
Cylindrical arc-length method, corrector using      361
Cylindrical arc-length method, line-searches with      370Ч373
Damage function      149Ч150
Damage mechanics      148Ч152
Damage relationship      151
Deformation gradient      35Ч36 93
Deformation theory      142Ч143
Degrees of freedom      214 273Ч276 280Ч283 382 392
Deviatoric stresses      101
Deviatoric term      65
Displacement control at specified variable      363Ч364
Displacement control, corrector using      361
Displacement derivative matrix      93
Displacement nodes      294
Dorkin et al. formulation      239Ч240
Double cantilever beam      374
Drucker Ч Prager relationship      131
Drucker Ч Prager return      119
Drucker Ч Prager yield criterion      101Ч104 133Ч134 148
Dynamic equilibrium equations      455 456Ч458
Dynamic equilibrium with rotations      470Ч472
Dynamic relaxation algorithm      376
Effective tangent stiffness matrix      74
Eigenvector expansion      134Ч135
Elastic damage model      139
Elastic-plastic damage model      139
Elasto-plastic stiffnesses      178
Element formulation      57Ч59
Energy conserving total Lagrangian formulation      458Ч461
Energy function, examples      89Ч95
Energy functional      338 426
Energy-conserving algorithms      455
Energy-conserving co-rotational procedures      480Ч483
Energy-conserving isoparametric formulations      483Ч485
Energy-conserving procedure for two-dimensional beams      466Ч468
Enhanced deformation gradient      298
Enhanced F formulations      301Ч304
Enhanced strains      291Ч293
Equilibrium equations      456
Equilibrium states      135Ч140
Equivalent plastic strain rate      146
Euler parameters      196 198Ч199
Euler theorem      193
Euler Ч Bernoulli element      251
Eulerian coordinate systems      85
Eulerian formulation      45Ч46 78Ч79
Eulerian formulation, extra internal variables      298Ч300
Eulerian formulation, internal force vector for      47Ч48
Eulerian formulation, key equations      46Ч47
Eulerian formulation, transformation of tangent constitutive relationship      84
Eulerian strain rate      10
Eulerian triad      13 20 84
Explicit co-rotational procedure for beams      473Ч474
Explicit dynamics code      308
Explicit dynamics code, rate form with      315Ч316
Explicit solution procedure      450Ч452
Facet approximations      269Ч271
Faceted dealisation      416
Fibre yield      112
Finite element analysis of continua      45Ч61
Flow rules      104Ч105 123Ч124 183 326
Flow theory      144Ч148
Flow vector      129
Follower loads      248Ч251
Forward Ч Euler method      105
Fracturing      135Ч148
Friction      411Ч446
Galerkin-type procedure      73
Gauss points      146 207 210 226 227 229 246 331 477
Gaussian elimination      74
General predictors using higher-order derivatives      362Ч365
Geometric stiffness matrix      72 221 223 237
Global rotational forces      275
Gravity loading      251
Green strain      2Ч4 8 18 26 35Ч37 39 40 45 47 58 66Ч72 76 78 80 81Ч84 235 458
Green strain, truss element using      350Ч351
Green Ч Nagdhi rate      20 21 95 314
GursonТs model      104
Hardening      158Ч187
Hardening models      174Ч181
Hencky model      90Ч91 93Ч95
Higher-order correctors      400Ч402
Higher-order derivatives for truss elements      349Ч352
Higher-order derivatives, branch switching using      361Ч362
Higher-order derivatives, correctors using      365Ч366
Higher-order derivatives, general predictors using      362Ч365
Higher-order predictor      398Ч400
Higher-order terms      344Ч346
Hilbert Ч Hughes Ч Taylor method      455Ч456
Hill yield criterion      122Ч128
Hill yield criterion with plane stress      126Ч128
Hill yield criterion, hardening with      124Ч126
Hoffman yield criterion      131Ч133
Hookean stress strain relationships      8
Hughes Ч Winget algorithm      319
Hybrid formulation      74Ч76
Hyperelastic material      20
Hyperelastic models, examples      86Ч89
Hyperelastic relationship      10
Hyperelasticity      7Ч8 62Ч68
Hypoelastic material      20
Hypoelastic relationship      10
Ilyushin yield criterion      99
Ilyushin yield function      113Ч115
Implicit co-rotational formulation      476Ч477 479Ч480
Implicit solution procedure      449Ч450
In-plane dominant strain profile      110
Incompatible modes      287Ч290
Incompressibility condition      69Ч71 75
Incompressible locking      288
Incompressible material      76
Indentation problem      303
Intermediate configuration, $F_eF_p$ decomposition      320Ч324
Internal force vector      46Ч48 229
Inverse Jacobian      34
Isoparametric degenerate-continuum beam element      234
Isoparametric formulation      231Ч233
Isoparametric formulation for three-dimensional beams      477Ч478
Isoparametric Timoshenko beam approach      233Ч240
Isotropic conditions      10Ч13
Isotropic hardening      159
Isotropic yield criteria      99Ч107
Jacobian matrix      33Ч34 41 48
Jaumann rate of Cauchy stress      4Ч7 20 21 46 53Ч54 55 312 314Ч315 327 452
Jaumann rate of Kirchhoff stress      77Ч79 91
Joints      252Ч256
Kinematic hardening      159 160 180
Kinematic hardening stresses      167
Kinematic hardening, plane stress      164Ч166
Kirchhoff stress      7 9 11 13 15 20Ч22 48 49 53Ч54 80 88 301 312 313 321 323 324 327 329
Kirchhoff stress tensor      94
Kuhn Ч Tucker conditions      425
Lagrange multiplier      71
Lagrangian coordinate systems      85
Lagrangian formulation      233Ч240 457Ч461
Lagrangian formulation, total      57Ч60 71Ч76
Lagrangian frame      2 83
Lagrangian measures      21
Lagrangian methods, augmented      426Ч431
Lagrangian multipliers      424Ч426
Lagrangian system      45
Lagrangian triad      11 13 15Ч16 82 87
Lam constants      7
Lankford anisotropy coefficient      127
Large rotations      188Ч212
Large rotations, non-vectorial      188
Large rotations, rotation matrix for      191Ч194
Large strains      308Ч337
Large strains in co-rotational approach      300Ч301
Large strains in finite element formulation      328Ч332
Large-strain analysis      4Ч7
Large-strain elaso-plastic analysis      4
Limit points      339 343 346Ч347 356
Line-searches      402Ч403
Line-searches with arc-length and similar methods      368
Line-searches with cylindrical arc-length method      370Ч373
Linear strain vector      59
Linearised arc-length method, corrector, based on      360
Load control      363
Load/pressure variable coupling vector      73
Local base vectors      27
Local displacements      216Ч218
Local reciprocal basis      27
Locked solutions      455
Locking behaviour      288
Log strain      2 3
Master-slave approach      252Ч256
Material imperfection      139
Matrix      105Ч107
Mean value theorem      65
Mesh dependency      135Ч140
Mesh distortion tests      295
Metric tensor      31Ч32
Mixed formulation      72Ч73
Mixed hardening      159 163Ч164
Mixed linear hardening      166Ч167 168Ч169 170Ч172
Mohr Ч Coulomb yield criterion      99 102Ч103 106 115Ч122
MohrТs circle      128 144
Mooney Ч Rivlin energy function      64 66 69 76 78 92
Mooney Ч Rivlin material      71 303
Mooney Ч Rivlin relationship      65
MorleyТs triangle      276Ч280
Mroz model      180
Multidimensional scalar damage      151
Multiple bifurcation      357
Multiplicative $F_eF_p$ approach      309Ч311
Natural coordinates      33Ч34
Neo Ч Hookean energy function      64 76
Neo Ч Hookean law      66
Newmark formula      468
Newmark methods      446Ч447
Newton Ч Raphson iterations      74 135 167 169 254 269 323 359 366 368 378 428 434 450 456 478
Nodal triads      204Ч207 216 223
Non-additive rotation increments      200
Non-linear dynamics      446Ч488
Non-linear hardening      167Ч168
Non-linearity      99Ч187
Non-local continuum approach      140
Non-orthogonal coordinates, second-order tensors in      30
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