Antman S.S. — Nonlinear Problems of Elasticity :: Электронная библиотека попечительского совета мехмата МГУ

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Antman S.S. — Nonlinear Problems of Elasticity

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Название: Nonlinear Problems of Elasticity

Автор: Antman S.S.

Аннотация:

Within the past few decades, there has been an accelerating development of methods for studying nonlinear equations. Nonlinear analysis offers exciting prospects for certain specific areas of nonlinear problems with continuum mechanics. The objective of this book is to carry out such studies for problems in nonlinear elasticity. This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems. The author's aim is to retain the orientation toward fascinating problems that characterizes the best engineering texts on structural stability while retaining the precision of modern continuum mechanics and employing powerful methods of nonlinear analysis. The author's approach is to lay down a general theory for each kind of elastic body, carefully formulate specific problems, introduce the pertinent mathematical methods, and then conduct rigorous analyses of the problems.

Язык:

Рубрика: Физика/Классическая физика/Упругие среды/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 750

Добавлена в каталог: 17.06.2005

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Предметный указатель

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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