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 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 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 # 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