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| Ïîèñê ïî óêàçàòåëÿì |
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| Antman S.S. — Nonlinear Problems of Elasticity |
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| Ïðåäìåòíûé óêàçàòåëü |
Absolute continuity 8
Absolute temperature 443
Acceleration 387
Acoustic tensor 463
Active stress 427
Adjacent equilibrium, criterion of 171
Adjoint of a linear operator 669
Adjoint of a tensor 372
Adjugate tensor 464
Admissibility of shocks 639 645—649
Admissible functions in calculus of variations 229—230 235 478
Aeolotropic plates, buckling of 361—364
Aeolotropic plates, trivial states 355—361
Aeolotropy (Anisotropy) for plates 355—361
Aeolotropy (Anisotropy) for rods in space 292
Aeolotropy (Anisotropy) for three-dimensional bodies 436
Affine function 3
Algebraic multiplicity of eigenvalues 145 154—156 691
Almost everywhere, definition of 8
Alternating symbol 259
Alternative Theorems 373 670—671
Angular Impulse-Momentum Laws for rods 262 268 308—311
Angular Impulse-Momentum Laws for three-dimensional bodies 402 412
Angular momentum for rods 261—262 268
Angular momentum for shells 583
Angular momentum for three-dimensional bodies 402
Anisotropy see “Aeolotropy”
Annihilators 431 669
Antiplane problems, in elasticity 509—511
Antiplane problems, in plasticity 617—623
Antisymmetric tensor 372
Arches, buckling of 218—222 253—256
Arzela — Ascoli theorem 160—161
Asymptotic methods for shells 591—598
Asymptotic sequence 112
Asymptotic shape of inflated rings 110—116
Asymptotic shape of inflated shells 369
Asymptotic stability of motion 371
Asymptotics of large loads 208—215
Asymptotics of shock structure 655—658
Axial compression of an elastic body 477
Axial vector 372
Axisymmetric deformations of axisymmetric shells 343—370 572—578
Balance of Angular Momentum for three-dimensional bodies, vii 402 531 533 543 558 571
Balance of Linear Momentum for three-dimensional bodies 402 531 533 569
Ball's condition of polyconvexity 464
Banach spaces 10 140 665—667
Banach spaces, dual 237
Banach spaces, reflexive 235 238 239
Barrelling of a three-dimensional rod 514—517
bars see “Rods”
Base curve of a rod 86 535
Base surface of a shell 344 565
Basis, base vectors 4 371
Basis, dual 371
Basis, orthonormal 372
Beams see “Rods”
Bell's constraint 423 425 428 455
Bending couples (moments) see “Contact couple”
Bending couples (moments) for rods 90 263 549
Bending couples (moments) for shells 345 574
Bending strain see “Flexural strain”
Benjamin, T.B. 689
Bernoulli — Euler law 92 319 323
Bernoulli, Jas. vii
Bifurcation (Branching) 140
Bifurcation (Branching), global 140
Bifurcation (Branching), imperfect 140
Bifurcation (Branching), local 140
Bifurcation (Branching), multiparameter 151
Bifurcation (Branching), perfect 140
Bifurcation (Branching), secondary 146
Bifurcation (Branching), transcritical 368
Bifurcation diagram 128—131
Bifurcation point 140
Bifurcation problems for an incompressible body under normal traction 517—520
Bifurcation problems for barrelling of a three-dimensional rod 514 517
Bifurcation problems for circular arches and rings 101—110 218—222 253—256
Bifurcation problems for cylindrical shells 367—369
Bifurcation problems for lateral buckling of rods 339—342
Bifurcation problems for plates 348—354 361—363 578—581
Bifurcation problems for rods under terminal thrust and torque 337—339
Bifurcation problems for spherical shells 364—367
Bifurcation problems for the necking of a three-dimensional rod 514—517
Bifurcation problems for the necking of rods 554—558
Bifurcation problems for the planar buckling of rods 125—131 160—166 168—170 197—215
Bifurcation problems for whirling rods 222 226
Bifurcation problems for whirling strings 176—196
Bifurcation theory, and dynamical stability 170—172
Bifurcation theory, basic theorems of 151—160
Bifurcation theory, introduction to 125—172
Bifurcation theory, literature on mathematical aspects of 172
Bifurcation theory, mathematical concepts of 140—142
Bifurcation theory, mathematical examples of 142—150
Bifurcation theory, perturbation methods in 166—170 511—521
Blowup in three-dimensional hyperelasticity 658—664
body 265 385—386 400
Body couple for rods 89 261 543
Body couple for shells 345 571
Body force for rods 89 261 542
Body force for shells 345 570
Body force for strings 14—15
Bootstrap method 31 242—245 247—250
Boundary conditions for rods in space 301—307
Boundary conditions for rods in the plane 93
Boundary conditions for strings 14
Boundary conditions for three-dimensional bodies 408—411 534
Boundary conditions, in sense of trace see “Trace”
Bounded (continuous) linear functional 237 668
Bounded (continuous) linear operator 668
Branch of solution pairs 129
Branching see “Bifurcation”
Brouwer degree see under “Degree of a mapping”
Brouwer fixed-point theorem 689—690
Brouwer index see under “Index”
Buckling of arches 218—222
Buckling of circular arches 218—222
Buckling of cylindrical shells 367—369
Buckling of frameworks 216
Buckling of plates 348—354 361—363 578—581 587
Buckling of rings 101—110 253—256
Buckling of rods under terminal thrust and torque 337—339
Buckling of spherical caps 136—138
Buckling of spherical shells 364—367
Buckling of whirling rods 222—226
Buckling, lateral of beams 339—342
Buckling, literature on 139—140 256—257
Buckling, load 125 132
Buckling, planar of rods 125—131 160—166 168—170 197—215 254—256
Buckling, problems of elasticity, survey of 125—140
Buckling, under follower loads 317—318
Calculus of variations, direct methods of 234—253
Calculus of variations, Fundamental Lemma of 21 244
Calculus of variations, literature on 256
Calculus of variations, Minimization Theorem of 239
Calculus of variations, Multiplier Rule of 230—234
Calculus of variations, normality in 250—251
Calculus of variations, semicontinuity in 236—237
Cardan joint 305
Catastrophe theory 203
Catenary problem 49—64 84
Cauchy Decomposition Theorem 395
Cauchy deformation tensor 451
Cauchy sequence 666
Cauchy stress tensor 454
Cauchy — Bunyakovskii — Schwarz inequality 9
Cauchy — Green deformation tensors 388 452
Cauchy's Polar Decomposition Theorem 394—396
Cauchy's Representation Theorem for hemitropic functions 284—285
Cauchy's Stress Theorem 404—405 584—586
| Cauchy, A.L. vii
Cauchy-elastic material 458
Cavitation 477 494—499
Cayley — Hamilton theorem 377
Center — Manifold Theorem 563
Chain rule 380
Characteristic equation for a tensor 377
Characteristic value 141
Characteristics 631
Christoffel symbols 383
Classical solution 12
Clausius — Duhem inequality 444 610—611
Clausius — Planck Inequality 445
Coercivity conditions see “Growth and coercivity conditions”
Cofactor tensor 379
Coleman — Noll condition 463
Coleman — Noll Entropy Principle 445
Compact Embedding Theorem 239
Compact operator 156 239 693
Compact set in Euclidean space 7
Compact support 3
Compatibility for antiplane motions 510 618
Compatibility for elastoplastic loading 608
Compatibility of boundary and initial conditions 14
Compatibility of strains 391—394
Components of vectors and tensors 375
Components of vectors and tensors, contravariant 383
Components of vectors and tensors, covariant 383
Components of vectors and tensors, mixed 383
Components of vectors and tensors, physical 383
Compression of a fiber in a body 388
Compression of a string 16
Compression of an elastic ball 492—494
Compression, total, preclusion of 642—644
Concavity methods 658
Cone in a linear space 387
Configuration of a rod in space 260—261 558
Configuration of a rod in the plane 86
Configuration of a shell 582
Configuration of a string 12—3
Configuration of a three-dimensional body 385
Configuration of an axisymmetric shell 343
Configuration, reference see “Reference configuration”
Conjugate energy for elastic rods in space 290 315 330
Conjugate energy for elastic rods in the plane 93 117 251
Conjugate energy for elastic strings 54
Connected component 156
Connected set 149 156
Conservation of energy (Energy equation) for elastic strings 21 78 82
Conservation of energy (Energy equation) for rods 335 643
Conservation of energy (Energy equation) for three-dimensional bodies 443 522 659 663
Conservation of energy (Energy equation) for viscoelastic rods 643
Conservation of mass 400—401 453
Constitutive functions and equations, generalities for induced theories of rods 539
Constitutive functions and equations, generalities for rods in space 264
Constitutive functions and equations, generalities for strings 15—20
Constitutive functions and equations, generalities for three-dimensional bodies 417—419
Constitutive functions and equations, specific forms see under “Elasticity” “Plasticity” “Thermoelasticity” “Thermoplasticity” “Viscoelasticity”
Constitutive principles see “Coercivity” “Dissipativity” “Entropy” “Invariance “Isotropy” “Monotonicity “Order”
Constraint Principle, Global 430—432
Constraint Principle, Local 427
Constraints of incompressibility 423 428 455
Constraints of inextensibility 314 423 428 433
Constraints of unshearability 92 102 314
Constraints, Bell's 423 425 428 455
Constraints, Ericksen's 423 428 455
Constraints, external for rods 317—318
Constraints, generating rod theories 269—271 535—537 541
Constraints, generating shell theories 424 429 434—136 566 568
Constraints, in calculus of variations 228—235
Constraints, internal see “Material constraints”
Constraints, isoperimetric 228
Constraints, Kirchhoff's 424 429 433
Contact couple for rods 89—90 261—263 543
Contact couple for shells 345 571 576 583
Contact force for rods 89—90 261 345 542
Contact force for shells 345 569 583
Contact force for strings 14
Contact force for three-dimensional bodies 404
Contact problems 529
Contact torque for rods 89 261
Contact torque for shells 583
Continuity equation, material form of 401
Continuity equation, spatial form of 453
Continuous and continuously differentiable functions, spaces of 9 666
Continuum mechanics, general principles of 385—455
Contraction mapping principle 675—S76
Contravariant components 383
Controllable deformations 506 523
Convergence, strong 238 665—666
Convergence, weak 237—238
Convexity of energy for rods in space 290
Cosserat theory of plates see under “Shells”
Cosserat theory of rods see under “Rods”
Cosserat theory of shells see under “Shells”
Coulomb friction 625
Couple, bending for rods 263
Couple, on a body 401
Couple, twisting for rods 263
Covariant components 383
Covariant derivatives 383
Cramer's rule 379
Cross product 4 371
Cross section of a rod 86 265 535
Crystals 529—530
Curl 381
Curve 6
Curvilinear coordinates formulation of continuum mechanics in 532—534
Cylindrical coordinates, problems in 343—363 367—368 397—399 470—485 504—505 521—523
Deformation for induced theories of rods 535—537 541—542 548—549
Deformation for induced theories of shells 565—566 568 572—574 582—583
Deformation gradient 387
Deformation of a rod in space 260—261 272—280 558—559
Deformation of a rod in the plane 86—88
Deformation of a shell 343—345 582—583
Deformation of a string 13—14
Deformation of a three-dimensional body 385—399 450—452
Deformation of an axisymmetric shell 343—345
Deformation tensors 388 451—452
Degree of a mapping 683—698
Degree of a mapping, Brouwei 58—59 683—693
Degree of a mapping, homotopy invariance of 688 696
Degree of a mapping, Leray — Schauder 693—696
Degree of a mapping, literature on 696
Density of mass 14 400—401 453
Derivatives and differentials, Frechet 5 142 378—380
Derivatives and differentials, Gateaux 5 43 142 243 378—380
DET 5
Determinant 5 377
Determinant, derivative of 379—380
Determinism, principle of see “Constraint Principle”
Differential equations, basic definitions 6—7
Differential type, materials of 419
Dilatation of an elastic ball 494
Dilatation of an elastic block 480—488
Dilatation of an elastic cylinder 478
Dilatational strain of a rod in space 261 272 275
Directors for axisymmetric shells 343—344
Directors for rods in space 260 322 540
Directors for rods in the plane 86
Directors for shells 558 568 582
Directors, representation in terms of Euler angles 300—301
Discretization 46—48
Dislocation of an elastic body 477
Dissipation inequality 448
Dissipativity for longitudinal motions of rods 640
Dissipativity for strings 19
Dissipativity for three-dimensional bodies 448
div 381
Divergence 381
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