Lemm J.M. — Mathematical elasticity. Theory of shells :: Электронная библиотека попечительского совета мехмата МГУ

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Lemm J.M. — Mathematical elasticity. Theory of shells

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Название: Mathematical elasticity. Theory of shells

Автор: Lemm J.M.

Аннотация:

The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the "small" parameter.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 659

Добавлена в каталог: 06.02.2014

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Предметный указатель

Linearly elastic generalized membrane shell of the first kind      262 268 293
Linearly elastic generalized membrane shell of the second kind      262 283 293
Linearly elastic material      see "Linearized elasticity"
Linearly elastic membrane shell      199 246 466
Linearly elastic shallow shell      369
Lions (lemma of J.L. Lions)      42 105 119 218 256 279 376
Locking phenomenon      362 366
Lower face of a shell      148
Manifold      439 472 502 520 526 529 542 543
Marguerre — von Karman equations in curvilinear coordinates      552
Marguerre — von Karman shell theory      552
Mean curvature      82
Membrane locking      362 366 368
Membrane shell (linearly elastic membrane shell)      see "Linearly elastic elliptic membrane shell" "Linearly "Shell
Membrane theory      see "Planar membrane theory" "Shell
Membrane-dominated behavior      361
Method of formal asymptotic expansions      164 413
Metric tensor      18 55
Metric tensor on a surface      69
Middle surface of a shell      143
Middle surface of a shell with folds      76
Middle surface of a shell with little regularity      76 114 115 339 362 366
Middle surface of a shell with no boundary      143 234 292 297
Minimization of a functional      224 228 290 321 339 340 391 446 448 452 456 462 520 523 529 553
Minimizer of a three-dimensional energy      392
Minimizer of an energy      see "Minimization of a functional"
Mixed component of the curvature tensor on a surface      81
Mixed component of the metric tensor      57
Mixed components of the curvature tensor on a surface      81
Mixed components of the metric tensor      57
Multi-director shell theory      549
Multi-layered shell      368 371 454 550
Multiplicity of solutions      530
Naghdi's change of curvature tensor on a surface (linearized change of curvature tensor on a surface)      366
Naghdi's linear shell equations      365 376
Naghdi's linear shell equations for shells whose middle surface has little regularity      366
Naghdi's linearized change of curvature tensor      366
Naghdi's nonlinear shell theory      549
Natural curvilinear coordinates for a shell      14 145
Natural state      6 388
Nonhomogeneous elastic material      162 178 234 326 360 366
Nonhomogeneous elastic material (shell made with a nonhomogeneous elastic material)      162 178 234 326 360 366
Nonlinear Budiansky — Sanders shell theory      551
Nonlinear elasticity (three-dimensional nonlinear elasticity) in Cartesian coordinates      391
Nonlinear elasticity (three-dimensional nonlinear elasticity) in curvilinear coordinates      392
Nonlinear elasticity in Cartesian coordinates      391
Nonlinear elasticity in curvilinear coordinates      392
Nonlinear flexural shell theory      502 505 525
Nonlinear intrinsic shell theory      551
Nonlinear Koiter's shallow shell theory      553
Nonlinear Koiter's shell theory      547
Nonlinear membrane shell theory      439 451 463 464 505
Nonlinear Naghdi's shell theory with directors      549
Nonlinear planar membrane theory      451 453 454 460
Nonlinear shallow shell theory      552
Nonlinear shell theory      see "Shell theory"
Nonlinear shell theory based on the method of internal constraints      550
Nonlinearly elastic material      389 392 454
Nonlinearly elastic shallow shell      552
Nonuniqueness of solutions      530
Normal displacement of the middle surface      232 325
Not inhibited bending      325
Novozhilov shell theory      371
Novozhilov's shell theory      371
Numerical approximation of shell problems      362 363 368
Obstacle (shell lying on an obstacle)      555
One-director Cosserat surface      363 549
One-director shell theory      363 549
Parabolic middle surface (shells with parabolic middle surface)      296
Parabolic point      83
Parabolic point on a surface      83
Parabolic surface      296
Piola — Kirchhoff stress tensor (first Piola — Kirchhoff stress tensor)      388 403
Piola — Kirchhoff stress tensor (second Piola — Kirchhoff stress tensor)      387
Planar membrane theory (nonlinear planar membrane theory)      451 453 454 460
Planar point      82 132
Planar point on a surface      82 132
Plate      306 329 465 506
Plate Theory      152 326 358 370
Poisson ratio      389
Polyconvex stored energy function      392
Pressure load      455
Principal curvature      82
Principal direction      82
Principal radius of curvature      82
Principle of virtual work in Cartesian coordinates      388
Principle of virtual work in curvilinear coordinates      403
Quasiconvex envelope      459 462
Quasiconvex function      459
Radius of curvature      74
Reference configuration      6 386
Reference configuration of a shell      12 143
Regularity of solutions      60 122 235 341 373
Reissner — Mindlin plate theory      363 549
Riemann curvature tensor      136
Riemann curvature tensor on a surface      136
Rigid displacement lemma      see "Infinitesimal rigid displacement" "Infinitesimal
Rigidification of a surface      297
Rigidity of a surface      442
Scaled deformation      458
Scaled displacements      152 199 246 303 408 458
Scaled linearized strain      153
Scaled strain      410 see
Scaled three-dimensional elasticity tensor      154 410
Scaled three-dimensional elasticity tensor of a shell      154 410
Scaled three-dimensional equations for a linearly elastic shell      154 200 247 307
Scaled three-dimensional equations for a nonlinearly elastic shell      410
Scaled two-dimensional elasticity tensor of a shell      158 170 181 210 308 430 519
Scaled unknown      see "Scalings of displacements"
Scaled vector field      152 408
Scalings of deformations      458
Scalings of displacements      152 199 246 303 408 458
Scalings of stresses      237
Second fundamental form of a surface      81
Second order covariant derivative      94 345
Second Piola — Kirchhoff stress tensor      387 402
Sensitive variational problem      293 295 296
Shape optimization for shells      361
Shell      12 143 see
Shell becoming a plate      192 234 326 358 375
Shell made with a composite material      368 371

Shell made with a nonhomogeneous material      162 234 326 360 366
Shell made with a soft material      464
Shell made with an anisotropic material      162 234 326 360 366 550
Shell theory of higher-order      550
Shell theory of the first order      550
Shell whose middle surface has little regularity      76 114 115 339 362 366
Shell whose middle surface has no boundary      143 234 292 297
Shell with folds      76 295 296 297
Shell with variable thickness      234 238 326 330 360
Simply supported shell      115 134 339 439 451 530
Singular perturbation problem      154
Sobolev spaces      41
Soft elastic material      464
Sphere      67 133 135 190 441
Spherical coordinates      15 67
St Venant — Kirchhoff elastic material      389 392 430 455
St Venant — Kirchhoff material      389 392 430
Stationary point of a functional      391 399 445 448 520 523
Stereographic coordinates      67
Stored energy function      391 392 451 455 463
Stored energy function of a nonlinearly elastic membrane shell (theory derived by $\Gamma$ -convergence)      463
Stored energy function of a St Venant — Kirchhoff material      391 455 459 464 467
Strain energy      see "Two-dimensional strain energy"
Strains in Cartesian coordinates      388
Strains in curvilinear coordinates      398
Stress couple      344 345
Stress resultant      224 229 344 345 450
Stresses in Cartesian coordinates      388
Stresses in curvilinear coordinates      402
Strongly clamped shell      503 504 525 530 548
Strongly elliptic system      236 373
Supplementary condition on L      123 236 373
surface      65
Surface force      see "Applied surface force"
Tangent space to a manifold      472 503 520
Tangential displacement of the middle surface      232 325
Term of order q in a formal asymptotic expansion      141
Theorema egregium      131 136
Theorema egregium of Gauss      131 136
Thickness of a shell      143
Third fundamental form of a surface      99
Three-dimensional affine Euclidean space      5
Three-dimensional constitutive equation      389
Three-dimensional elasticity tensor      11 32 392 396
Three-dimensional elasticity tensor in Cartesian coordinates      11 59 392
Three-dimensional elasticity tensor in curvilinear coordinates      32 50 59 182 396
Three-dimensional elasticity tensor of a shell      148
Three-dimensional energy in Cartesian coordinates      391
Three-dimensional energy in curvilinear coordinates      396
Three-dimensional equations for a linearly elastic shell      146
Three-dimensional equations for a nonlinearly elastic shell      406
Three-dimensional Euclidean space      5
Three-dimensional Korn's type (inequality of Korn's type) for a family of linearly elastic elliptic membrane shells      205 212 220 221
Three-dimensional Korn's type (inequality of Korn's type) for a family of linearly elastic shells      259 269 271 310
Three-dimensional linearized elasticity in Cartesian coordinates      8
Three-dimensional linearized elasticity in curvilinear coordinates      32
Three-dimensional nonlinear elasticity in Cartesian coordinates      391
Three-dimensional nonlinear elasticity in curvilinear coordinates      401
Time-dependent equations for a linearly elastic shell      234 326 347
Time-dependent equations for a nonlinearly elastic shell      550 551
Time-dependent Koiter's linear shell equations      347 361
Time-dependent shell theory      234 326 347 550 551
Time-dependent two-dimensional Koiter equations      347 361
Torus      66 133 292
Total curvature      82
Transverse variable      145 150
Two-dimensional boundary conditions of clamping      101 116 304 305 306 322 344
Two-dimensional boundary conditions of simple support      115 134 339 439 451 530
Two-dimensional boundary conditions of strong clamping      503 504 524 525 530 548
Two-dimensional boundary conditions of weak simple support      234
Two-dimensional constitutive equation      229 451
Two-dimensional constitutive equations for a linearly elastic elliptic membrane shell      229
Two-dimensional constitutive equations for a nonlinearly elastic membrane shell (theory derived by formal analysis)      451
Two-dimensional elasticity tensor of a shell      101 117 190 228 291 322 338 344 365 450 524 527
Two-dimensional energy of a linearly elastic elliptic membrane shell      224 229
Two-dimensional energy of a linearly elastic flexural shell      322
Two-dimensional energy of a linearly elastic generalized membrane shell      290
Two-dimensional energy of a linearly elastic shallow shell      370
Two-dimensional energy of a nonlinearly elastic flexural shell      524 530
Two-dimensional energy of a nonlinearly elastic membrane shell (theory derived by $\Gamma$ -convergence)      463
Two-dimensional energy of a nonlinearly elastic membrane shell (theory derived by formal analysis)      445 446 450
Two-dimensional energy of a nonlinearly elastic shallow shell      553 554
Two-dimensional equations for a linearly elastic elliptic membrane shell      117 126 210 223 227
Two-dimensional equations for a linearly elastic flexural shell      101 309 318 320 321
Two-dimensional equations for a linearly elastic generalized membrane shell      268 283
Two-dimensional equations for a nonlinearly elastic flexural shell      518 530
Two-dimensional equations for a nonlinearly elastic membrane shell (theory derived by $\Gamma$ -convergence)      463
Two-dimensional equations for a nonlinearly elastic membrane shell (theory derived by formal analysis)      444 450
Two-dimensional equations of a linearly elastic elliptic membrane shell      117 126 210 223 227 359
Two-dimensional equations of a linearly elastic flexural shell      101 309 318 320 359
Two-dimensional equations of a linearly elastic generalized membrane shell      268 283 359
Two-dimensional equations of a nonlinearly elastic flexural shell      518 522 523
Two-dimensional equations of a nonlinearly elastic membrane shell (theory derived by formal analysis)      444 448 450
Two-dimensional equations of equilibrium      229 451
Two-dimensional equilibrium equations for a linearly elastic elliptic membrane shell      229
Two-dimensional equilibrium equations for a nonlinearly elastic membrane shell (theory derived by formal analysis)      451
Two-dimensional Koiter energy of a linearly elastic shell      344
Two-dimensional Koiter energy of a nonlinearly elastic shell      548
Two-dimensional Koiter equations for a linearly elastic shell      100 111 115 337 339 341 344 360 373 375
Two-dimensional Koiter equations for a nonlinearly elastic shell      547
Two-dimensional Koiter strain energy of a linearly elastic shell      344
Two-dimensional Koiter strain energy of a nonlinearly elastic shell      548
Two-dimensional strain energy      see also "Two-dimensional Koiter strain energy"
Two-dimensional strain energy of a linearly elastic elliptic membrane shell      229 344 361
Two-dimensional strain energy of a linearly elastic flexural shell      322 344 361
Two-dimensional strain energy of a linearly elastic generalized membrane shell      290
Two-dimensional strain energy of a nonlinearly elastic flexural shell      524 548
Two-dimensional strain energy of a nonlinearly elastic membrane shell (theory derived by $\Gamma$ -convergence)      463
Two-dimensional strain energy of a nonlinearly elastic membrane shell (theory derived by formal analysis)      450 548
Umbilical point      82 133
Umbilical point on a surface      82 133
Uniformly elliptic system      123 236 237 373
Unilateral eigenvalue problems for shells      555
Uniqueness of solutions      52 101 111 115 122 124 126 223 317 338 340 366 367 376 530
Upper face of a shell      148
Volume element      18
Weak lower semi-continuity of a functional      431 452 536
Weakly simply supported shell      234
Weingarten (formula of Weingarten)      88
Well-inhibited bending      232
Young modulus      389

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