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+<!-- source-page: 601 -->
+
+Load factor, 60, 210
+
+Load vector, 13, 24, 183, 188, 405
+
+Locking material, 30, 92
+
+Lumped mass matrix, 389, 392, 410
+
+Material properties, 37, 207, 281
+
+Mathematical theory of plasticity, 215
+
+Matrix inversion, 288
+
+Maxwell model, 117, 302, 305
+
+Mechanical sublayer method, 304
+
+Metal forming problems, 482
+
+Method of direct iteration, 14, 24, 40, 63
+
+Method of successive approximations, 14
+
+Midside nodal coordinate generation, 178, 341, 413
+
+Mindlin plates:
+Elastic expressions, 167
+
+Mindlin plates, elasto-plastic; 319
+
+Discretisation, 324
+
+Equilibrium equations, 321
+
+Mindlin plates, elasto-plastic layered; 326
+
+Nonlinear equilibrium equations, 327
+
+Program structure, 355
+
+Mindlin plates, elasto-plastic non-layered; 327
+
+Nonlinear equilibrium equations, 329
+
+Program structure, 331
+
+Mohr-Coulomb yield criterion, 219, 230, 234
+
+Newmark time stepping scheme, 432
+
+Newton-Raphson method, 15, 24, 40, 68
+
+No-tension model, 477
+
+Non-associated flow rule, 476
+
+Nonlinear elastic problems, 25, 74
+
+Non-Newtonian fluid flow, 482
+
+Normality condition, 224
+
+Notched bend specimen, 5
+
+Numerical integration, 174
+
+Octahedral shear stress, 218
+
+One-dimensional FORTRAN programs; 33
+
+Direct iteration of quasiharmonic problems, 63
+
+Elasto-plastic problems, 78
+
+Elasto-viscoplastic problems, 104
+
+Newton-Raphson solution of quasi-harmonic problems, 68
+
+Nonlinear elastic problems, 74
+
+One-dimensional nonlinear problems, 13
+
+Output of results, 58, 211, 258, 342, 363, 414
+
+Overlay method, 90, 304, 316
+
+Overlay simulation of: Four parameter viscous model, 309
+
+Three element viscous model, 309
+
+Visco-elastic model, 308
+
+Visco-elastic-plastic four parameter model, 309
+
+Pi plane, 217
+
+Piecewise linear strain hardening representation, 266
+
+Piola-Kirchhoff stresses, 386
+
+Plane Strain, elastic expressions, 164
+
+Plane Stress, elastic expressions, 162
+
+Plastic multiplier, 224
+
+Plastic potential, 224, 273
+
+Power law pseudoplastic, 483
+
+Prandtl-Reuss equations, 225
+
+Predictor-corrector algorithm, 434, 436
+
+Prescribed displacements in equation solution, 46
+
+Principal stress evaluation, 258
+
+Profile equation solver, 436, 440
+
+Program structure, 8, 34, 104, 134, 235, 281, 331, 355, 392, 440
+
+Programming notation, 10
+
+Pseudo-loads, viscoplastic, 100, 275
+
+Quasi-harmonic equation, 22, 63, 68
+
+Quasi-Newton method, 491
+
+Rayleigh damping, 391
+
+Residual forces, 15, 71, 76, 81, 102, 236, 249, 344, 364
+
+Sample input data and line printer output:
+
+Dynamic transient elasto-plastic explicit time integration example, 567
+
+Dynamic transient elasto-plastic implicit/explicit example, 578
+
+Elasto-plastic layered Timoshenko beam, 537
+
+Non-layered elasto-plastic Mindlin plate problem, 558
+
+One-dimensional direct iteration quasi harmonic example, 529
+
+One-dimensional elasto-plastic problem, 531
+
+<!-- source-page: 602 -->
+
+Sample input data—contd.
+
+One-dimensional elasto-viscoplastic problem, 535
+
+Two-dimensional elasto-plastic problem, 542
+
+Two-dimensional elasto-viscoplastic problem, 550
+
+Seismic analysis, 377, 399, 424
+
+Selective integration, 128, 325, 482
+
+Shape function derivatives:
+
+Cartesian, 171, 182
+
+Local, 171
+
+Shape function evaluation, 179, 346
+
+Shells, elasto-plastic and geometrically nonlinear, 488
+
+Singular points on the yield surface, 234
+
+Space diagonal, 217
+
+Sphere:
+
+Elasto-plastic, 267
+
+Elasto-viscoplastic, 315
+
+Spherical shell, dynamic example, 421, 458
+
+Starting algorithm for central difference scheme, 390
+
+Steady state conditions, 104, 109, 279, 297
+
+Stiffness matrix, 13, 24, 28, 100, 127, 142, 173, 244, 283, 348, 367, 439, 447
+
+Strain energy function, 25
+
+Strain hardening, 26, 222, 223
+
+Strain matrix, B, 172, 191
+
+Strain matrix, geometric nonlinear, 382, 395
+
+Strain softening, 223
+
+Stress intensity factor, 485
+
+Stress invariants, 216, 233
+
+Stress space, 217
+
+Subroutines, elasto-plastic (additional): DIMEN, 238
+
+FLOWPL, 243
+
+INVAR, 239
+
+LINEAR, 247
+
+Master segment, 260
+
+OUTPUT, 258
+
+RESIDU, 249
+
+STIFFP, 244
+
+YIELDF, 241
+
+ZERO, 238
+
+Subroutines, elasto-plastic layered Mindlin plates (additional):
+
+CHECK1, 360
+
+DEPMPA, 360
+
+Subroutines—contd.
+
+FEAM, 355
+
+LAYMPA, 360
+
+MDMPA, 362
+
+OUTMPA, 363
+
+RESMPA, 364
+
+STIMPA, 367
+
+STRMPA, 369
+
+Subroutines, elasto-plastic nonlayered Mindlin plates:
+
+CONVMP, 336
+
+DIMMP, 338
+
+FEMP, 334
+
+FLOWMP, 338
+
+GRADMP, 340
+
+INVMP, 340
+
+MINDPB, 341
+
+NODEXY, 341
+
+OUTMP, 342
+
+RESMP, 344
+
+SFR2, 346
+
+STIFMP, 348
+
+STRMP, 353
+
+SUBMP, 354
+
+VZERO, 354
+
+ZEROMP, 354
+
+Subroutines, elasto-plastic (standard):
+
+ALGOR, 209
+
+CONVER, 212
+
+INCREM, 210
+
+INPUT, 205
+
+Subroutines, elasto-viscoplastic (additional):
+
+FLOWVP, 294
+
+INVERT, 288
+
+Master segment, 299
+
+STEADY, 297
+
+STEPVP, 289
+
+STIFVP, 283
+
+STRESS, 295
+
+TANGVP, 286
+
+ZERO, 297
+
+Subroutines, elasto-viscoplastic transient dynamic analysis:
+
+BLARGE, 395
+
+CONTOL, 396
+
+DYNPAK, 392
+
+EXPLIT, 396
+
+FIXITY, 397
+
+FLOWVP, 398
+
+FUNCTA, 399
+
+FUNCTS, 399
+
+INPUTD, 399
+
+<!-- source-page: 603 -->
+
+Subroutines—contd.
+
+INTIME, 401
+
+INVAR, 403
+
+JACOBD, 404
+
+LINGNL, 404
+
+LOADPL, 405
+
+LUMASS, 410
+
+MODPS, 413
+
+NODXYR, 413
+
+OUTDYN, 414
+
+PREVOS, 416
+
+RESVPL, 417
+
+YIELDF, 419
+
+Subroutines, implicit/explicit transient dynamic analysis (additional):
+
+ADDBAN, 444
+
+ADDRES, 444
+
+COLMHT, 445
+
+DECOMP, 445
+
+DINTOB, 446
+
+GEOMST, 446
+
+GSTIFF, 447
+
+IMPEXP, 449
+
+ITRATE, 451
+
+LINKIN, 452
+
+MIXDYN, 442
+
+MULTPY, 454
+
+REDBAK, 455
+
+RESEPL, 456
+
+Subroutines, one-dimensional:
+
+ASSEMB, 49
+
+ASTIF1, 70
+
+BAKSUB, 54
+
+CONUND, 72
+
+CONVP, 109
+
+DATA, 35
+
+GREDUC, 51
+
+INCLOD, 60, 110
+
+INCVP, 107
+
+INITAL, 59
+
+Master segment, 61
+
+Master segment (viscoplasticity), 111
+
+MONITR, 65
+
+NONAL, 40
+
+REFOR1, 71
+
+REFOR2, 76
+
+REFOR3, 81
+
+RESOLV, 57
+
+RESULT, 58
+
+STIFF1, 63
+
+STIFF2, 75
+
+STIFF3, 78
+
+STUNVP, 106
+
+Subroutines, Timoshenko beam analysis:
+
+BEAM, 135
+
+BEAML, 144
+
+LAYER, 147
+
+REFORB, 137
+
+RFORBL, 146
+
+STIFBL, 145
+
+STIFFB, 136
+
+Subroutines, two-dimensional (elastic):
+
+BMATPB, 191
+
+BMATPS, 191
+
+CHECK1,200
+
+CHECK2, 202
+
+DBE, 194
+
+ECHO, 201
+
+FRONT, 194
+
+GAUSSQ, 179
+
+JACOB2, 181
+
+LOADPB, 188
+
+LOADPS, 183
+
+MODPB, 193
+
+MODPS, 192
+
+NODEXY, 178
+
+SFR2, 179
+
+Substructuring, 493
+
+Subterranean cavity, viscoplastic, 314
+
+Tangent modulus, 26, 225
+
+Tangential stiffness, 20, 26, 28, 236, 275, 327, 329
+
+Tangential stiffness method, 20, 40, 206
+
+Theorem of minimum total potential energy, 44
+
+Time-step limitations:
+
+Dynamic transient, 391, 426, 437
+
+Elasto-viscoplastic, 102, 276
+
+Timoshenko beam analysis; 121
+
+Basic assumptions, 122
+
+Element stress resultants, 128
+
+Finite element idealisation, 125
+
+Formulation of the stiffness matrix, 127, 142
+
+Layered approach, 122, 141
+
+Non-layered approach, 121, 122
+
+Solution of nonlinear equations, 132, 143
+
+Timoshenko layered beam program, TIMLAY, 144
+
+Timoshenko non-layered beam program, TIMOSH, 135
+
+Tolerance value, 65, 72, 298
+
+Tresca yield criterion, 217, 230, 234
+
+<!-- source-page: 604 -->
+
+# SUBJECT INDEX
+
+Unconditional stability, 276, 302, 437
+
+Uniaxial yield stress, 26, 219
+
+Uniaxial tension test, 26, 225
+
+Virtual work, 124, 162
+
+Viscoelastic behaviour, 305, 308
+
+Viscoplastic:
+
+Strain increment, 273
+
+Stress increment, 274, 295
+
+Viscoplastic computational procedure:
+
+One dimension, 103
+
+Two dimensions, 278
+
+Viscoplastic element stiffness formulation, 283
+
+Viscoplastic flow function, 273, 286
+
+Viscoplastic strain rate, 100, 272, 294, 398
+
+Viscoplastic strain rate derivative matrix, 274, 279
+
+Viscoplasticity, basic theoretical response:
+
+Dynamic application, 381
+
+One dimension, 98
+
+Two dimensions, 272
+
+Viscoplasticity in two dimensions, 271
+
+Viscoplasticity in one dimension, 95
+
+Viscosity coefficient, 97
+
+Volume, elemental, 172
+
+Von Mises yield criterion, 218, 230
+
+Weighting functions, 23
+
+Winkler foundation, 151, 372
+
+Work hardening, 222, 223, 228
+
+Yield criterion, 26, 216, 272, 326, 328
+
+Yield function constants, 231, 234, 235
+
+Yield moment, 129
+
+Yield surface, 217