|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Antman S.S. — Nonlinear Problems of Elasticity |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Past history 18 417
Perturbation methods 33—42 166—170 511—521 528
Phase changes 529—530
Piola — Kirchhoff stress tensor first 404—408
Piola — Kirchhoff stress tensor reactive 427
Piola — Kirchhoff stress tensor second 406—407
Piola — Kirchhoff stress vectors 533 534
Piola — Kirchhoff traction vector 407
Plastic deformation and strain, permanent 605—606
Plastic loading 606
Plasticity 603—628
Plasticity, constitutive equations for 604—615 621—623
Plasticity, discrete models for 624—628
Plates see also “Shells”
Plates, buckling of 348—354 361—363 578—581
Poincare shooting method 41 680
Poincare, H. vii
Poisson's ratio 592
Polar decomposition theorem 394—396
Polyconvexity 464
Position field 386
Positive-definiteness 5 373
Post-buckling behavior, definition of 171
Potential energy for rods in space 313
Potential energy for rods in the plane 228 245—247
Potential energy for strings 21 44 46 64 82
Potential energy for three-dimensional bodies 171 458—459
Power 442 (also see “Virtual Power”)
Poynting effect 329
Prerequisites 1—2
Preservation of orientation see “Orientation”
Pressure 428 (also see “Hydrostatic pressure”)
Principal axes of strain 390
Principal invariants of a tensor 377
Principal planes of shear 390
Principal stretches 390
Projection of a linear operator 672
Prufer transformation 178
Puiseux series 681
Quadratic form of a tensor 373
Quasiconvexity 464
Quasilinearity 6
Radial motions of a string 77—78
Radial motions of an incompressible shell 523
Radial motions of an incompressible tube 521—522
Range of a function 3
Rank-one convexity 461
Rankine — Hugoniot jump conditions 29 634
Rarefaction 635—638
Rate independence, constitutive functions with 605—607
Rate-type, material of 419
Reactive stress 427 540
Reeken's problem for whirling strings 185—189
Reference configuration of a rod in space 261
Reference configuration of a rod in the plane 85
Reference configuration of a string 12
Reference configuration of a three-dimensional body 385
Reference configuration of a three-dimensional rod-like body 265 535
Reference configuration of a three-dimensional shell-like body 565—566
Reflexive Banach space 235 238 239 669
Regularity see “Bootstrap method”
Representation theorems for hemitropic and isotropic functions 438—441
Resultant couple see under “Couple”
Riemann invariants 631
Riemann problem 634—640
Riemann — Christoffel curvature tensor 393
Right Cauchy — Green deformation tensor 388
Right-handedness of basis 4
Rigid material 388 417 424
Rigid motions, invariance under see “Invariance”
Rings under hydrostatic pressure 101—116 218—222 253—256
Rivlin, R.S. vii
Rods, asymptotic theories of 559—564
Rods, Cosserat theories of 85—96 259—323 540—554 558—559
Rods, general theories of 322—323 531—554 558—559
Rods, induced theories of 531—554
Rods, intrinsic theories of 558—559
Rods, lateral buckling of 339—342
Rods, linear theories of 319—321
Rods, necking of 554—558
Rods, problems for 96—123 200—226 254—256 325—342 554—558
Rods, special Cosserat theories of 85—96 259—323
Rods, St. Venant's Principle for 559—564
Rods, theory of, in space 259—323 531—547
Rods, theory of, in the plane 85—96 318—319 548—554
Rods, under hydrostatic pressure 101—116 218—222 227—230 245—251 254—256
Rods, under terminal loads 96—101 125—131 160—166 168—170 197 215 337—339
Rods, validity of theories of 548
Rods, whirling of 116—123 222—226 251 253
Rotation tensor 394—396
Rotatory inertia, neglect of 319
Schauder fixed-point theorem 696
Second law of thermodynamics 444—445
Section of a rod, material 86 265 535
Semi-inverse problems of elasticity 470—511 521—527
Semicontinnity, lower 236—237
Semilinearity 6
Sets, basic definitions 7
Shear force for rods 90 101 263
Shear force for shells 345
Shear instability 135
Shear of an elastic block 480—488
Shear of an elastic cylinder 470 479
Shear strain for rods 88 261 272 275
Shear strain for three-dimensional bodies 388—389
Shear waves 525—527 649—658
Shear, principal planes of 390
Shear, simple 396—397
Shells, asymptotic theories of 591—598
Shells, circular plates 348—363
Shells, Cosserat theories of 568—572 581—589
Shells, cylindrical 367—368
Shells, general theories of 565—572
Shells, induced theories of 565—572
Shells, intrinsic theories of 581—589
Shells, Kirchhoff theory of 588—589
Shells, problems for 348—370 578—581
Shells, special Cosserat theories of 571—572 581—589
Shells, spherical 364—367
Shells, theory of, for axisymmetric deformations 343—347 572—578
Shells, under edge loads 348—363 367—368
Shells, under hydrostatic pressure 364—367 369
Shells, von Karman equations for plates 591—598
Shocks 632—640 645—649
Signorini, A. vii
Simple materials 418
Simple zero 163
Simultaneous zeros 366—367
Singularities of solutions of elasticity problems 529
Singularity theory 202—203 207—208 520—521 681
Skew tensor 372
Skw 373
Smoothness 4
snapping 138 362
Sobolev spaces 9 236 238 667
Solution branch 221
Solution pairs 61—62 128 152
Solution sheets 208—215
Spatial formulation 387 450—455
Spatial strain tensor 452
Special Cosserat theory of rods 259—323
Spectral representation of a symmetric tensor 375
Spectrum 152
Spherical coordinates, problems in 363—367 399 488—503 523
Spin tensor 452
springs 79—83
St. Venant's principle 530 559—564
Stability, adjacent equilibrium, criterion of 171
Stability, by the energy criterion 171
Stability, elastic 171
| Stability, in the sense of Lyapunov 170—171
Stability, infinitesimal 171
Statical determinacy and indeterminacy 215
Steady motions, definition of 453
Stokes theorem 382
Stored (internal, strain) energy for induced theories of rods 547 553
Stored (internal, strain) energy for membranes 590—591
Stored (internal, strain) energy for rods in space 282—283 296 312—313 559
Stored (internal, strain) energy for rods in the plane 92 117 205 227—230 235 245—247 250 254—256 643
Stored (internal, strain) energy for shells 586
Stored (internal, strain) energy for strings 21 44 78 81—82
Stored (internal, strain) energy for three-dimensional bodies 428 458 478 658
Strain energy see “Stored energy”
Strain rates for rods 272—275
Strains for axisymmetric shells 344
Strains for rods in space 260—261 272—275
Strains for rods in the plane 88
Strains for shells 583
Strains for three-dimensional bodies 387—394 451—452
Stress resultants also see “Contact force” “Contact
Stress resultants for induced theories of rods 537—538 542—547
Stress resultants for induced theories of shells 566—567 569—571 574
Stress tensor, active 427
Stress tensor, Cauchy 454
Stress tensor, dissipative part of 447
Stress tensor, engineering 407
Stress tensor, extra 427
Stress tensor, first Piola — Kirchhoff 404—408
Stress tensor, reactive 427 537 540
Stress tensor, second Piola — Kirchhoff 407—408
Stretch for rods 88 272 275
Stretch for strings 13
Stretch for three-dimensional bodies 388
Stretch, principal 390
Stretching tensor 452
Strings, elementary problems for 49—84
Strings, equations for 11—48
Strings, holding liquids 71—74
Strings, radial vibrations of 77—78
Strings, steady motions of 78—79
Strings, transverse motions of 32—33
Strings, under central forces 74—77
Strings, under normal loads 66—74
Strings, under vertical loads 50—66
Strings, whirling of 21
Strong convergence 238 665
Strong Ellipticity Condition 461—463 465—467 545—547
Stuart's problem for whirling strings 189—190
Sturm — Liouville problem 162 178
Sturmian theory 162 178 181
Summation convention 259 371
Support of a function 3
Suspension bridge problem 49—52 64—66
SYM 373
Symmetric tensor 5 372
Symmetry conditions for constitutive equations for rods and shells 97 296 349 551—554 577—578
Symmetry group of a material 437
Symmetry of the stress tensor 406 533
Symmetry transformation 437
Temperature 443
Tension for rods 90 263
Tension for strings 16
Tensors 4 371—383
Tensors of higher order 375
Tensors, adjoint of 372
Tensors, adjugate of 464
Tensors, antisymmetric 372
Tensors, cofactor of 379
Tensors, components of 375 383
Tensors, identity 5 373 383
Tensors, indefinite 373
Tensors, invariants of 377 438—441
Tensors, invertible 373
Tensors, matrix of 375
Tensors, negative-definite 373
Tensors, nonsingular 373
Tensors, orthogonal 373—374
Tensors, positive-definite 5 373
Tensors, product of 372
Tensors, proper-orthogonal 374
Tensors, quadratic form of 373
Tensors, semidefinite 373
Tensors, skew 372
Tensors, spectral representation of 375
Tensors, symmetric 5 372
Tensors, transpose of 372
Tensors, zero 5 373
Test functions 20
Thermoelasticity, constitutive equations of, for strings 17
Thermoelasticity, constitutive equations of, for three-dimensional bodies 448—449
Thermomechanical process 445
Thermomechanics 441—149
Thermoplastic loading 610—611
Thermoplasticity 610—612
Thermoviscoelasticity, constitutive equations of 446—448
Torsion of an elastic block 480—488
Torsion of an elastic cylinder 474—476 479
Torsional strain of a rod 261 272—273 275
Total energy of a membrane 590—591
Total energy of a rod 313
Total energy of a spring-mass system 82
Total energy of a string 21 42
Total energy of a three-dimensional body 443
tr 374
Trace of a tensor 374
Trace, boundary and initial conditions in sense of 14 23—24 410—411
Transport theorem 453
Transpose of a tensor 372
Transverse isotropy see under “Isotropy”
Transverse motions of a string 32
Travelling waves and shock structure 645—649
Travelling waves in rods 334—337
Travelling waves in strings 33
Travelling waves in viscoelastic media 651—658
Triangle inequality 665
Trivial solution pairs 129 152 355—361
Truesdell, C. vii
Twist 307
Twisting couple (moment) for rods 263
Uniform rods 97 298—299
Uniform strings 18
Union of sets 7
Uniqueness of solutions in elasticity 460
Universal deformations 506—509
Universal joint 305
Universal motions 523—525
Unshearability 92 102
Variation first see under “Derivatives and differentials”
Variation second 253—256
Variational characterization of equations for elastic strings 42—46
Variational characterization of equations for hyperelastic elastic rods 227—230 312—313
Variational characterization of equations for hyperelastic membranes 590—591
Variational characterization of equations for three-dimensional hyperelastic bodies 458—459
Vector space 665
Vectors 4—6 371—372 665
Vectors, axial 372—373
Velaria problem 49
Velocity 387
Vertical shear 101
Virtual displacements and velocities 20
Virtual Power (Work), Principle of, for rods 244 308—311 313
Virtual Power (Work), Principle of, for strings 20 22 24—28
Virtual Power (Work), Principle of, for three-dimensional bodies 411—417 533—534 593
Viscoelasticity, constitutive equations of, for longitudinal motion of rods 640—642
Viscoelasticity, constitutive equations of, for rods in space 264 283—285
Viscoelasticity, constitutive equations of, for strings 18
Viscoelasticity, constitutive equations of, for three-dimensional bodies 418—419 649—650
von Karman equations for plates 591—598
Vorticity 452
Wave equation, linear 34—35
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå