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



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

Àâòîð: Crisfield M.A.

Àííîòàöèÿ:

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/.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/×èñëåííûå ìåòîäû/Êîíå÷íûå ýëåìåíòû/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1997

Êîëè÷åñòâî ñòðàíèö: 508

Äîáàâëåíà â êàòàëîã: 20.02.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
$F_eF_p$ approach for conventional rate form      312—315
$F_eF_p$ decomposition, based on final (current) configuration      324—326
$F_eF_p$ multiplicative decomposition      309
Additive rotation components      242—247
Additive rotation increments      200
Almansi strain      2—4 18 21
Anisotropic plasticity      99
Anisotropic plasticity, yield criteria for      122—128
Apex return      119 121—122
Applied loading      248—251
Arc-length methods      368—373
Arc-length methods, using relative variables      373—374
Asymmetric bifurcation      347—349
Asymmetric bifurcation, two-bar truss with      382—391
Augmented Lagrangian methods      426—431
Automatic time-stepping      468—470
Average acceleration method      448 452—453
Axial deformation      216
Axial strain      227
Axisymmetric membrane      70
B-bar method      76
Back stresses      159
Backward — Euler method      105 107—108 113—122
Backward — Euler return      129—132 134 144 168—169 185
Bauschinger effect      158
Bending dominant case      112
Bifurcation      355
Bifurcation points      343 347 356
Bifurcations      341
Biot strain      2—4 11 13 267
Biot stress      11 13 15 18 79 80 331 332
Bracketing techniques      356—358 383—389 393—394 396—397
Branch switching      355 359—362 389—391 394 397—398
Branch switching, using higher-order derivatives      361—362
Cartesian base vectors      35—36
Cauchy stress      11 13 21 22 48 313
Cauchy — Green tensor      64 94 322
Co-rotational approach for curved membrane using facet triangles      269—271
Co-rotational approach for curved membrane using quadrilaterals      271—272
Co-rotational approach for three-dimensional beam elements      213—226
Co-rotational approach for three-dimensional continua      266—269
Co-rotational approach for two-dimensional continua      262—266
Co-rotational approach large elastic strains in      300—301
Co-rotational elements      251
Co-rotational energy-conserving procedure for two-dimensional beams      461—465
Co-rotational facet shell formulation based on Morley’s triangle      276—280
Co-rotational formulation, extra internal variables      296—297
Co-rotational framework for semi-loof shells      283—285
Co-rotational framework for three-dimensional beams      285—287
Co-rotational shell formulation with three rotational degrees of freedom per node      273—276
Co-rotational shell formulation with two rotational degrees of freedom per node      280—283
Cohesive-frictional relationship      102
Comers, yield functions with      107—109
Compound rotations      195—197
Compressible neo-Hookean model      80—81 89
Computer program using truss elements      381—409
Concentrated moments      249—250
Concrete      135—136 151
Concrete, fixed and rotating crack models      140—142
Conjugate stress and strain measures      10—19
Consistency condition      161 163 173
Consistent linearisation      411
Consistent tangent      326—328
Consistent tangent matrix      184 434—435 437—438
Consistent tangent modular matrix      108 120—122 130—131 133
Consistent tangent modular tensor      172—173
Constitutive tensors      77
Constitutive tensors, transforming components of      37—38
Contact      411—446
Contact element, two-dimensional      412—413
Contact formulation, three-dimensional frictionless      431—435
Contact formulation, two-dimensional frictionless      412—416
Contact patch test      417—420
Contact, external forces      418—420
Contact, internal forces      417
Continua, finite element analysis      45—61
Continuum mechanics      1—25
Contravariant base vectors      41
Control parameter      357 358
Convected coordinates, and total, Lagrangian formulation      57—60
Convected curvilinear coordinates      38
Corner regions      148 416
Corner return      121—122
Corrector      460—461
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      365—366
Cotter — Rivlin rate      21
Coulomb sliding friction      422—424 429
Coulomb sliding friction in three dimensions      438—439
Covariant components      33—34 39 40
Cracking      135—138
Crushable foam model      104
Curvature      204—211 228
Curvature without nodal triads      207—211
Curvature, expressions directly using nodel triads      204
Curved quadrilateral membrane      271—272
Curved triangular membrane      269—271
Cylindrical arc-length method      364—365
Cylindrical arc-length method, choice of root      374—376
Cylindrical arc-length method, corrector using      361
Cylindrical arc-length method, line-searches with      370—373
Damage function      149—150
Damage mechanics      148—152
Damage relationship      151
Deformation gradient      35—36 93
Deformation theory      142—143
Degrees of freedom      214 273—276 280—283 382 392
Deviatoric stresses      101
Deviatoric term      65
Displacement control at specified variable      363—364
Displacement control, corrector using      361
Displacement derivative matrix      93
Displacement nodes      294
Dorkin et al. formulation      239—240
Double cantilever beam      374
Drucker — Prager relationship      131
Drucker — Prager return      119
Drucker — Prager yield criterion      101—104 133—134 148
Dynamic equilibrium equations      455 456—458
Dynamic equilibrium with rotations      470—472
Dynamic relaxation algorithm      376
Effective tangent stiffness matrix      74
Eigenvector expansion      134—135
Elastic damage model      139
Elastic-plastic damage model      139
Elasto-plastic stiffnesses      178
Element formulation      57—59
Energy conserving total Lagrangian formulation      458—461
Energy function, examples      89—95
Energy functional      338 426
Energy-conserving algorithms      455
Energy-conserving co-rotational procedures      480—483
Energy-conserving isoparametric formulations      483—485
Energy-conserving procedure for two-dimensional beams      466—468
Enhanced deformation gradient      298
Enhanced F formulations      301—304
Enhanced strains      291—293
Equilibrium equations      456
Equilibrium states      135—140
Equivalent plastic strain rate      146
Euler parameters      196 198—199
Euler theorem      193
Euler — Bernoulli element      251
Eulerian coordinate systems      85
Eulerian formulation      45—46 78—79
Eulerian formulation, extra internal variables      298—300
Eulerian formulation, internal force vector for      47—48
Eulerian formulation, key equations      46—47
Eulerian formulation, transformation of tangent constitutive relationship      84
Eulerian strain rate      10
Eulerian triad      13 20 84
Explicit co-rotational procedure for beams      473—474
Explicit dynamics code      308
Explicit dynamics code, rate form with      315—316
Explicit solution procedure      450—452
Facet approximations      269—271
Faceted dealisation      416
Fibre yield      112
Finite element analysis of continua      45—61
Flow rules      104—105 123—124 183 326
Flow theory      144—148
Flow vector      129
Follower loads      248—251
Forward — Euler method      105
Fracturing      135—148
Friction      411—446
Galerkin-type procedure      73
Gauss points      146 207 210 226 227 229 246 331 477
Gaussian elimination      74
General predictors using higher-order derivatives      362—365
Geometric stiffness matrix      72 221 223 237
Global rotational forces      275
Gravity loading      251
Green strain      2—4 8 18 26 35—37 39 40 45 47 58 66—72 76 78 80 81—84 235 458
Green strain, truss element using      350—351
Green — Nagdhi rate      20 21 95 314
Gurson’s model      104
Hardening      158—187
Hardening models      174—181
Hencky model      90—91 93—95
Higher-order correctors      400—402
Higher-order derivatives for truss elements      349—352
Higher-order derivatives, branch switching using      361—362
Higher-order derivatives, correctors using      365—366
Higher-order derivatives, general predictors using      362—365
Higher-order predictor      398—400
Higher-order terms      344—346
Hilbert — Hughes — Taylor method      455—456
Hill yield criterion      122—128
Hill yield criterion with plane stress      126—128
Hill yield criterion, hardening with      124—126
Hoffman yield criterion      131—133
Hookean stress strain relationships      8
Hughes — Winget algorithm      319
Hybrid formulation      74—76
Hyperelastic material      20
Hyperelastic models, examples      86—89
Hyperelastic relationship      10
Hyperelasticity      7—8 62—68
Hypoelastic material      20
Hypoelastic relationship      10
Ilyushin yield criterion      99
Ilyushin yield function      113—115
Implicit co-rotational formulation      476—477 479—480
Implicit solution procedure      449—450
In-plane dominant strain profile      110
Incompatible modes      287—290
Incompressibility condition      69—71 75
Incompressible locking      288
Incompressible material      76
Indentation problem      303
Intermediate configuration, $F_eF_p$ decomposition      320—324
Internal force vector      46—48 229
Inverse Jacobian      34
Isoparametric degenerate-continuum beam element      234
Isoparametric formulation      231—233
Isoparametric formulation for three-dimensional beams      477—478
Isoparametric Timoshenko beam approach      233—240
Isotropic conditions      10—13
Isotropic hardening      159
Isotropic yield criteria      99—107
Jacobian matrix      33—34 41 48
Jaumann rate of Cauchy stress      4—7 20 21 46 53—54 55 312 314—315 327 452
Jaumann rate of Kirchhoff stress      77—79 91
Joints      252—256
Kinematic hardening      159 160 180
Kinematic hardening stresses      167
Kinematic hardening, plane stress      164—166
Kirchhoff stress      7 9 11 13 15 20—22 48 49 53—54 80 88 301 312 313 321 323 324 327 329
Kirchhoff stress tensor      94
Kuhn — Tucker conditions      425
Lagrange multiplier      71
Lagrangian coordinate systems      85
Lagrangian formulation      233—240 457—461
Lagrangian formulation, total      57—60 71—76
Lagrangian frame      2 83
Lagrangian measures      21
Lagrangian methods, augmented      426—431
Lagrangian multipliers      424—426
Lagrangian system      45
Lagrangian triad      11 13 15—16 82 87
Lam constants      7
Lankford anisotropy coefficient      127
Large rotations      188—212
Large rotations, non-vectorial      188
Large rotations, rotation matrix for      191—194
Large strains      308—337
Large strains in co-rotational approach      300—301
Large strains in finite element formulation      328—332
Large-strain analysis      4—7
Large-strain elaso-plastic analysis      4
Limit points      339 343 346—347 356
Line-searches      402—403
Line-searches with arc-length and similar methods      368
Line-searches with cylindrical arc-length method      370—373
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      216—218
Local reciprocal basis      27
Locked solutions      455
Locking behaviour      288
Log strain      2 3
Master-slave approach      252—256
Material imperfection      139
Matrix      105—107
Mean value theorem      65
Mesh dependency      135—140
Mesh distortion tests      295
Metric tensor      31—32
Mixed formulation      72—73
Mixed hardening      159 163—164
Mixed linear hardening      166—167 168—169 170—172
Mohr — Coulomb yield criterion      99 102—103 106 115—122
Mohr’s circle      128 144
Mooney — Rivlin energy function      64 66 69 76 78 92
Mooney — Rivlin material      71 303
Mooney — Rivlin relationship      65
Morley’s triangle      276—280
Mroz model      180
Multidimensional scalar damage      151
Multiple bifurcation      357
Multiplicative $F_eF_p$ approach      309—311
Natural coordinates      33—34
Neo — Hookean energy function      64 76
Neo — Hookean law      66
Newmark formula      468
Newmark methods      446—447
Newton — Raphson iterations      74 135 167 169 254 269 323 359 366 368 378 428 434 450 456 478
Nodal triads      204—207 216 223
Non-additive rotation increments      200
Non-linear dynamics      446—488
Non-linear hardening      167—168
Non-linearity      99—187
Non-local continuum approach      140
Non-orthogonal coordinates, second-order tensors in      30
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