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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
Non-orthogonal curvilinear coordinates      26—27
Non-symmetric stiffness matrix      244
Normalised quaternions      196
Normalised quaternions from rotation matrix      199
Numerical performances      295—296
Off-diagonal shear components      83
Ogden energy function      91—93
Ogden model      62
Oldroyd rate      21
One-dimensional case      109—112
Orthogonal unit base vectors      38
Overlay model      174—180
Patch test      287 289 417—420
Penalty approaches      412—416 431—435
Penalty/barrier method for contact      439—440
Perzyna model      183
Petrov — Galerkin procedure      458 459
Piola — Kirchhoff stress tensor      57
Piola — Kirchhoff stresses      4 9 11 18 26 36—37 45—47 58—59 66—72 76 78 80 81 90 236 312 457 458 459
Plain strain      69
Plane stress      170—172
Plane stress with incompressibility      69—71
Plane stress, kinematic hardening      164—166
Plane-stress hypothesis      70
Plane-stress plasticity      135
Plastic model      139
Plastic slopes      162 163
Plastic strain rate multiplier      146
Plasticity      99—187
Point loads      248—249
Polar decomposition      3 21 89 267
Power/unit initial volume      19
Prager evolution law      161 165
Predictor      460
Predictor-corrector technique      449—450 455
Pressure connection matrix      79
Pressure displacement relationship      73
Principal directions      81—84
Principal log strains      90—91
Principal stresses      101 142
Principal stretch ratios      63—65 79—86 84 85 88
Pseudo-vector      191 194—196 199—201 218—220
Pseudo-vector from rotation matrix      197—198
Quaternions      198—199
Radial-return procedure      166—168
Rankine yield criterion      142
Rate equations      316—320
Rate form with explicit dynamics code      315—316
Rate form, $F_eF_p$ approach      312—315
Rayleigh damping      376
Rayleigh quotient      469
Reissner theory      227
Reverse strain profile      110
Rigid-body motion      5
Riks — Wempner algorithm      360
Riks — Wempner linear arc-length method      368
Rodrigues formula      191—194 209 210 217 274 276
Rotating crack model      141 142—143
Rotation matrix      94
Rotation matrix for large rotations      191—194
Rotation matrix, alternative forms      194—195
Rotation matrix, approximations      195
Rotation matrix, associated with additive and non—additive increments      200
Rotation matrix, derivative      202
Rotation matrix, exponential form      194
Rotation matrix, normalised quaternion from      199
Rotation matrix, pseudo-vector from      197—198
Rotational displacements      468
Rotational equilibrium equations      274 472
Rotational local forces      274
Rotational variables and triads      277
Rotational velocities and accelerations      474—476
Scalar coefficients      31
Second-order tensors in non-orthogonal coordinates      30
Second-order tensors, transforming components to new set of base vectors      30—31
Semi-direct bracketing      358
Shape functions      26 38 72 231 251 290 477
Shear locking in bending      288
Shear strain      227
Shells, yield functions for      109—115
Simo and Vu-Quoc formulation      226—233
Single-vector return      119 120
Singular points      342
Singular points, classification      346—349
Singular points, direct computation      366—368
Singular points, indirect computation      355—359
Skew coordinates      38—42
Skew-symmetric matrix      202 206 470
Sliding friction      422—424 429
Sliding friction, Coulomb, in three dimensions      438—439
Small rotations      188—191
Small strain equations      314
Smallest rotation      202—204
Softening materials      135—148
Spin matrix      268
Spin vector      266
Spurrier’s algorithm      199
Square yield criterion      142—148
Stability      452—455
Stability coefficients      352
Stability test      301—304
Stability theory      338—353
Stable symmetric bifurcation      341
Static internal force vector      468
Static/dynamic solution procedures      376—378
Sticking friction      420—422
Sticking friction in three dimensions      435—438
Stiffness parameter      415
Strain energy      415
Strain energy function      7 64
Strain measures and structures      1—4 17—18
Strain profile      110
Strain ratios      112 128
Strain sampling points      294
Stress intensities      112
Stress invariants      101
Stress profile      110
Stress resultants      109—115
Stress-strain relationship      66 111 143 162 167 176
Substitute functions      293—295
Symmetric bifurcations      347
Symmetry and non-symmetry      240—243
Symmetry at equilibrium      243—247
Tangent constitutive relationships, transformation for Eulerian formulation      84
Tangent modulus      150
Tangent stiffness equations      79 232
Tangent stiffness matrix      47 59 221—223 229—231 237—239 266 424 468
Tangent stiffness matrix in relation to Truesdell rate of Kirchhoff stress      49
Tangent stiffness matrix, alternative derivation      54 56
Tangent stiffness matrix, continuum derivation      49—51
Tangent stiffness matrix, discretised derivation      51—53
Tangent stiffness matrix, using Jaumann rate of Cauchy stress      55
Tangent stiffness matrix, using Jaumann rate of Kirchhoff stress      53—54
Tangent stiffnesses      178
Tangential constitutive matrix      83
Tangential constitutive relationships      70
Tangential gap      420 422 436
Tangential modular matrix      151
Taylor series      2 74 108 129 133 134 147 168 184 297 338 344 426 449 450 456 461
Test functions      356 357 358 458
Three-dimensional arch truss      405—407
Three-dimensional beams, co-rotation technique      213—226
Three-dimensional beams, co-rotational framework      285—287
Three-dimensional beams, isoparametric formulation      477—478
Three-dimensional continua, co-rotational approach      266—269
Three-dimensional dome      395—404
Three-dimensional formulations for beams and rods      212—259
Three-dimensional model      151
Three-dimensional plasticity      161
Total Lagrangian finite element formulation      71—76
Trace operation      32
Trapezoidal rule      448 452 453
Tresca yield criterion      101—102 106
Triad rotation      202—204
Truesdell rate of Kirchhoff stress      8—10 20 21 49 54 77 79 84 87 90 327
Truss elements, computer program using      381—409
Truss elements, higher-order derivatives for      349—352
Truss elements, using Green’s strain      350—351
Truss elements, using rotated engineering strain      351
Two-bar truss with asymmetric bifurcation      382—391
Two-dimensional beams      286—287
Two-dimensional beams, co-rotational energy-conserving procedure for      461—465
Two-dimensional beams, energy-conserving procedure for      466—468
Two-dimensional case      112—113
Two-dimensional circular arch      407
Two-dimensional continua, co-rotational approach for      262—266
Two-vectored return      118—119 121 148
Uniaxial case      110 111
Unstable symmetric bifurcation      341
Unsymmetric bifurcation      341
Valanis — Landel hypothesis      89
Vector components, transforming to new set of base vectors      28—29
Virtual work      229 236
Viscoplasticity      182—185
Volumetric term      65
von Mises truss      392—395
von Mises yield criterion      99 104 122 123 131 135 148 158 161 162 164 169 173
Work terms      32
Yield criteria      180
Yield criteria for anisotropic plasticity      122—128
Yield functions      171 313
Yield functions for shells      109—115
Yield functions with corners      107—109
Yield surfaces      107—108 114—115 159
Ziegler model      161
Ziegler rule      165
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