Ex Libris                        Wanted                           
blank

       
blank

blank
blank
blank
blank
Antman S.S. Nonlinear Problems of Elasticity
Antman S.S.  Nonlinear Problems of Elasticity









?
Ctrl+Enter


: Nonlinear Problems of Elasticity

: Antman S.S.

:

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.


: en

: / / /

:

ed2k: ed2k stats

: 1995

: 750

: 17.06.2005

: | | ID
blank
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 645649
Admissible functions in calculus of variations      229230 235 478
Aeolotropic plates, buckling of      361364
Aeolotropic plates, trivial states      355361
Aeolotropy (Anisotropy) for plates      355361
Aeolotropy (Anisotropy) for rods in space      292
Aeolotropy (Anisotropy) for three-dimensional bodies      436
Affine function      3
Algebraic multiplicity of eigenvalues      145 154156 691
Almost everywhere, definition of      8
Alternating symbol      259
Alternative Theorems      373 670671
Angular Impulse-Momentum Laws for rods      262 268 308311
Angular Impulse-Momentum Laws for three-dimensional bodies      402 412
Angular momentum for rods      261262 268
Angular momentum for shells      583
Angular momentum for three-dimensional bodies      402
Anisotropy      see Aeolotropy
Annihilators      431 669
Antiplane problems, in elasticity      509511
Antiplane problems, in plasticity      617623
Antisymmetric tensor      372
Arches, buckling of      218222 253256
Arzela Ascoli theorem      160161
Asymptotic methods for shells      591598
Asymptotic sequence      112
Asymptotic shape of inflated rings      110116
Asymptotic shape of inflated shells      369
Asymptotic stability of motion      371
Asymptotics of large loads      208215
Asymptotics of shock structure      655658
Axial compression of an elastic body      477
Axial vector      372
Axisymmetric deformations of axisymmetric shells      343370 572578
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 665667
Banach spaces, dual      237
Banach spaces, reflexive      235 238 239
Barrelling of a three-dimensional rod      514517
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      128131
Bifurcation point      140
Bifurcation problems for an incompressible body under normal traction      517520
Bifurcation problems for barrelling of a three-dimensional rod      514 517
Bifurcation problems for circular arches and rings      101110 218222 253256
Bifurcation problems for cylindrical shells      367369
Bifurcation problems for lateral buckling of rods      339342
Bifurcation problems for plates      348354 361363 578581
Bifurcation problems for rods under terminal thrust and torque      337339
Bifurcation problems for spherical shells      364367
Bifurcation problems for the necking of a three-dimensional rod      514517
Bifurcation problems for the necking of rods      554558
Bifurcation problems for the planar buckling of rods      125131 160166 168170 197215
Bifurcation problems for whirling rods      222 226
Bifurcation problems for whirling strings      176196
Bifurcation theory, and dynamical stability      170172
Bifurcation theory, basic theorems of      151160
Bifurcation theory, introduction to      125172
Bifurcation theory, literature on mathematical aspects of      172
Bifurcation theory, mathematical concepts of      140142
Bifurcation theory, mathematical examples of      142150
Bifurcation theory, perturbation methods in      166170 511521
Blowup in three-dimensional hyperelasticity      658664
body      265 385386 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      1415
Bootstrap method      31 242245 247250
Boundary conditions for rods in space      301307
Boundary conditions for rods in the plane      93
Boundary conditions for strings      14
Boundary conditions for three-dimensional bodies      408411 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      689690
Brouwer index      see under Index
Buckling of arches      218222
Buckling of circular arches      218222
Buckling of cylindrical shells      367369
Buckling of frameworks      216
Buckling of plates      348354 361363 578581 587
Buckling of rings      101110 253256
Buckling of rods under terminal thrust and torque      337339
Buckling of spherical caps      136138
Buckling of spherical shells      364367
Buckling of whirling rods      222226
Buckling, lateral of beams      339342
Buckling, literature on      139140 256257
Buckling, load      125 132
Buckling, planar of rods      125131 160166 168170 197215 254256
Buckling, problems of elasticity, survey of      125140
Buckling, under follower loads      317318
Calculus of variations, direct methods of      234253
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      230234
Calculus of variations, normality in      250251
Calculus of variations, semicontinuity in      236237
Cardan joint      305
Catastrophe theory      203
Catenary problem      4964 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      394396
Cauchy's Representation Theorem for hemitropic functions      284285
Cauchy's Stress Theorem      404405 584586
Cauchy, A.L.      vii
Cauchy-elastic material      458
Cavitation      477 494499
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 610611
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      391394
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      492494
Compression, total, preclusion of      642644
Concavity methods      658
Cone in a linear space      387
Configuration of a rod in space      260261 558
Configuration of a rod in the plane      86
Configuration of a shell      582
Configuration of a string      123
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      400401 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      1520
Constitutive functions and equations, generalities for three-dimensional bodies      417419
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      430432
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      317318
Constraints, generating rod theories      269271 535537 541
Constraints, generating shell theories      424 429 434136 566 568
Constraints, in calculus of variations      228235
Constraints, internal      see Material constraints
Constraints, isoperimetric      228
Constraints, Kirchhoff's      424 429 433
Contact couple for rods      8990 261263 543
Contact couple for shells      345 571 576 583
Contact force for rods      8990 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      385455
Contraction mapping principle      675S76
Contravariant components      383
Controllable deformations      506 523
Convergence, strong      238 665666
Convergence, weak      237238
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      529530
Curl      381
Curve      6
Curvilinear coordinates formulation of continuum mechanics in      532534
Cylindrical coordinates, problems in      343363 367368 397399 470485 504505 521523
Deformation for induced theories of rods      535537 541542 548549
Deformation for induced theories of shells      565566 568 572574 582583
Deformation gradient      387
Deformation of a rod in space      260261 272280 558559
Deformation of a rod in the plane      8688
Deformation of a shell      343345 582583
Deformation of a string      1314
Deformation of a three-dimensional body      385399 450452
Deformation of an axisymmetric shell      343345
Deformation tensors      388 451452
Degree of a mapping      683698
Degree of a mapping, Brouwei      5859 683693
Degree of a mapping, homotopy invariance of      688 696
Degree of a mapping, Leray Schauder      693696
Degree of a mapping, literature on      696
Density of mass      14 400401 453
Derivatives and differentials, Frechet      5 142 378380
Derivatives and differentials, Gateaux      5 43 142 243 378380
DET      5
Determinant      5 377
Determinant, derivative of      379380
Determinism, principle of      see Constraint Principle
Differential equations, basic definitions      67
Differential type, materials of      419
Dilatation of an elastic ball      494
Dilatation of an elastic block      480488
Dilatation of an elastic cylinder      478
Dilatational strain of a rod in space      261 272 275
Directors for axisymmetric shells      343344
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      300301
Discretization      4648
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
1 2 3 4
blank
blank
blank
HR
@Mail.ru
       © , 2004-2019
   | Valid HTML 4.01! | Valid CSS!