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Libai A., Simmonds J.G. — The Nonlinear Theory of Elastic Shells
Libai A., Simmonds J.G. — The Nonlinear Theory of Elastic Shells



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Название: The Nonlinear Theory of Elastic Shells

Авторы: Libai A., Simmonds J.G.

Аннотация:

Elastic shells are pervasive in everyday life. Examples of these thin-walled structures range from automobile hoods to basketballs, veins and arteries, and soft drink cans. This book provides the physical and mathematical basis for the quantitative analysis of the behavior of such shells and presents numerous applications. As a second edition, it not only brings all the material of the first edition entirely up to date; it also adds two entirely new chapters on general shell theory and general membrane theory. Aerospace, mechanical, and civil engineers, as well as applied mathematicians, will find this book a clearly written and thorough information source on shell theory.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1998

Количество страниц: 542

Добавлена в каталог: 19.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Functional form heat flux      48
Functional form strain-energy density: axishell      183 185 188 299 327
Functional form strain-energy density: beamshell      85 86
Functional form strain-energy density: birod      37
Functional general membrane      412
Functional general shell      473 481
Fundamental form first      364 390 398 402 407 448
Fundamental form second      365 398
Fundamental state      128 130—132 305 309 310
Fundamental theorem of calculus      25 166 395
Gauss surface equation      399 404 405n 426 434
Gauss — Mainardi — Codazzi condition      403 433
Gauss — Weingarten equation      398
Gaussian (surface) coordinates      see “Coordinate surface”
Gaussian curvature      see “Curvature Gaussian”
General cylinder      343n
General helicoid      343 365
General membrane      389—452
General shell      5 453—510
Generalized edge force      32 33 62 68 170 172
Generalized edge velocity      32 61—63 67
Geodesic      434
Geodesic curvature      407
Geometric discontinuity      389 426 454 506
Geometric imperfection      210 244
Geometric inhomogeneity      85 86 182
Geometric invariance      82 85 86
Geometric nonlinearities      82 100 102 262
Global symbols (in notation)      511—513
Green's function      204n
Green's function for shallow conical shell      227
Green's function for shallow spherical shell      237
Green's theorem      400 463
Gross curvature      350
Hamilton's principle for axishell      290 291
Hamilton's principle for beamshell      114 115
Hamilton's principle forbirod      40 41
Hamiltonian      299
Harmonic material      265 420 440
Heat      14 15 140
Heat flow      3 140 144n 148 326
Heat flux      4 15n 45 136 144 326
Heat influx      15 45 48 140
Heat influx resultant      140 141 327
Heat of three-dimensionality      31
Heat production (generation)      15 45 323
Heat production (generationinternal      329
Heating      14 141 147 323
Heating centerline      45
Helical tube      363
Helicoidal shell      5 363—385
Helicoidal shell cylindrical      385
Helicoidal shell pressurized      363 380
Helicoidal shell right      343 380—383
Helix, circular      343
Hellinger — Reissner variational principle      43 121
Hemispherical shell      247
Hinge angle      239 241
Hinge elastic      239 241 322
Hinge equation      238 241 242
Hinge function      239 240 242
Hinged edge      see “Boundary condition simple
Homogeneous material      see “Material homogeneous”
Hooke's law      83
Horizontal tangency (in toroidal shell)      252 254
Hu — Washizu functional      42
Hu — Washizu variational principle for axishell      292
Hu — Washizu variational principle for beamshell      116 117
Hu — Washizu variational principle for birod      42
Hu — Washizu variational principle for curved tubes      360
Imperfect beamshell      125 127
Imperfect boundary condition      318
Imperfect conical shell      229
Imperfect cylindrical shell      210 302
Imperfect inflatable      279
Imperfect plate      287n
Imperfect shell of revolution      318
Imperfect spherical cap      224
Imperfect spherical membrane      271
Imperfect spherical shell      320—322
Imperfect structure      127 317
Imperfection amplitude      127 319
Imperfection axisymmetric      318—320
Imperfection geometric      210
Imperfection insensitive      302
Imperfection sensitivity      317
Imperfection sinusoidal      320
Imperfection small      319
Imperfection unsymmetric      244 318 320
Imperfection-sensitive bifurcation      327
Imperfection-sensitive buckling      323
Imperfection-sensitive cylindrical shell      302 303 319
Imperfection-sensitive increase      302
Imperfection-sensitive ring      132
Imperfection-sensitive spherical cap      321
Imperfection-sensitive structure      125
In-plane bending of tube      344—356 363 438
In-plane components, stress tensor      439
In-plane deformation      346
In-plane restraint      279
In-plane strain      487 489 491
In-plane stretching      277
In-plane traction      279
Incompressibility      191 263 416 421
Incompressibility condition      90
Incompressible body      89 189 487
Incompressible material      104 188 251 264 271 279 288 420 486 488 489 513
Incremental stress function      307
Inelastic behavior      122 290 344
Inertial frame      12 18 23 53 113 161 389 455
Inextensional airbag      419
Inextensional approximation      246 248n 249
Inextensional axishell      303 383
Inextensional beamshell      see “beamshell inextensional”
Inextensional bending      2 5 208 260n 499 502
Inextensional constitutive relation      419
Inextensional deformation axishell      159 241 303
Inextensional deformation beamshell      96 102 103
Inextensional deformation cylindrical helicoidal shell      385
Inextensional deformation general shell      468
Inextensional deformation helicoidal shell      383—385
Inextensional deformation near      81 159 389 476 499n 506
Inextensional deformation right helicoidal shell      385
Inextensional deformation split shell of revolution      383—385
Inextensional deformation unishell      344
Inextensional dimpling      322
Inextensional elastica      82 97 99 102 104 132
Inextensional membrane      see “Membrane inextensional
Inextensional model      100 102
Inextensional motion      105
Inextensional shell      470
Inextensional string      409 410
Inextensional wave      114
Inextensionality      96 125 159 410 435 445
Inextensionality condition      113 279 446
Inextensionality meridional      354
Infinite cylindrical shell      see “Beamshell”
Inflatable      261 389
Inflatable cylindrical      270
Inflatable imperfection      279
Inflatable spherical      279 419 421
Inflation of a membrane cylindrical      269 438
Inflation of a membrane flat, circular      273 274
Inflation of a membrane spherical      265 270—273
Inflation of a membrane toroidal      252
Inflation of a membrane tube      265
Inflation of a straight tube      251 343 378—380
Inflation of a toroidal shell      251
Inflation wave      447
Influence coefficient      249
Initial basis      57 168 196 469
Initial condition      5
Initial condition essential birod      24 35
Initial condition essential general membrane      392
Initial condition natural axishell      167 172
Initial condition natural beamshell      56 68
Initial condition natural birod      24 33—35
Initial condition natural general membrane      391 409
Initial condition natural general shell      457 472
Initial curve      see “Reference curve initial”
Initial mass density      264
Initial metric      434
Initial moment of inertia      17 462
Initial position      21 23 53 188 395
Initial postbuckling analysis      133 136 321 355
Initial reference curve      see “Reference curve initial”
Initial shape      435 446 448 (see shape”)
Initial spin      167
Initial stress      37 224 416 437 485
Initial tension      406
Initial value problem      21 38 41 61 168
Initial velocity      24 167
Instability      see “Stability”
Integral edge condition (for a curved tube)      345
Integral equation      204 221 227 229 236 237 246
Integral equation of motion      see “Equation of motion integral”
Integral weighted (average)      3 4 21 23 453 462
Integral-impulse form      see “Equation of motion integral”
Integro-differential equation      246
Interior approximation (to shell equations)      259 261
Interior contribution      96
Interior failure      138
Interior layer (or zone)      254 256 257 260 261 354n
Interior of membrane      277 430
Interior shell equations      2 3
Interior solution      217 218 233 245
Intermediate variable      220 256
Internal energy      36 40 46 80 81 142 178 179 324 473 474
Internal energy density      46 142 324
Intrinsic diaphragm support      see “Diaphragm support”
Intrinsic dynamics      see “Equation of motion intrinsic
Intrinsic form      42
Intrinsic strain compatibility      177
Invariant elastic coefficient      475
Invariant in strain-energy density      419 420 486
Invariant of couple-stress tensor      160
Invariant of second-order tensor      184
Invariant of strain-energy density      86 182 183 185 475
Invariant of vector      185
Invariant scalar      184 185
Invariant stress      418
Invariant tensorially      202
Inverse problem      273
Isometric bending      418
Isothermal deformation (theory)      2 4 5 147 149 327
Isotropic      see also “Elastic isotropy”
Isotropic material      54 91 160 251 264 313 363 438
Isotropic stress      441
Jump (condition) axishell      168 169 176 179 183 184 214 237
Jump (condition) axishell infinitesimal      184
Jump (condition) beamshell      58 59 77
Jump (condition) beamshell infinitesimal      86
Jump (condition) birod      25—30
Jump (condition) general membrane      392 393 447
Jump (condition) general shell      458 459 466
Kinetic energy axishell      169
Kinetic energy beamshell      60
Kinetic energy beamshell rotational      56
Kinetic energy beamshell variation      114
Kinetic energy birod      31
Kinetic energy birodreduced      30 40
Kinetic energy general membrane      402
Kinetic energy general shell      463
Kinetic energy general shell rotational      462
Kinetic energy three-dimensional continuum      18
Kinetic energy three-dimensional continuum reduced      19
Kirchhoff boundary conditions      470 501
Kirchhoff hypothesis      5 77n 311 476 512n
Kirchhoff hypothesis axishell      257 288 314
Kirchhoff hypothesis beamshell      82 100 133
Kirchhoff hypothesis general shell      453 468—470 475—494 496 497 499—502
Kirchhoff hypothesis helicoidal shell      380
Kirchhoff motion      66 77n 188
Kirchhoff motion reduced      77n
Kirchhoff theory      502
Lagrange multiplier for axishell      159 172 179 180 198 200 292—295 327
Lagrange multiplier for beamshell      68 116 119
Lagrange multiplier for birod      34 42
Lagrange multiplier for general membrane      409 410
Lagrange multiplier for general shell      471—473
Lagrange multiplier for unishell      361
Lagrange's equations of motion      32
Lagrangian coordinate      14 346 447
Lagrangian description (formulation)      3 391 392 458
Lagrangian strain      see “Strain Lagrangian”
Lagrangian total components      121
Lagrangian viewpoint      21
Layered plates and shells      51 83 84 160 181 454
Legendre ( — Fenchel) transformation      43 82 103 179 197 377 417 475
Legendre function      234
Legendre polynomial      272
Limit point instability      123 125 133 135 136 226 229 270 278 318 354 355 360
Linear bending theory axiplate      316
Linear bending theory cylindrical shell      214 431
Linear bending theory toroidal axishell      251
Linear membrane operator      426
Linear membrane paradox (for toroidal shell)      250
Linear membrane theory      222 233 245 249 252 254 256 257 266 298 355 426 427 430
Liouville transformation      255
Lip (on a hemispherical shell)      230
Load      1—3
Load apex      278
Load buckling axishell      317
Load buckling beamshell      137
Load buckling cylindrical shell      210 319
Load buckling plate      314 315 317
Load buckling spherical shell      244
Load centrifugal      69 174 251 412
Load critical      see “Critical load”
Load dead      44 69 118n 128 136 295n 305 308 363 412
Load deformation-independent      128 129 131 305 308 309
Load edge      see “Edge load”
Load follower      74 406
Load gravity      69n 112 173 197 267 286
Load hydrostatic      70 99 174 413 488
Load impulsive      3
Load incremental      147 429
Load limit-point      226 229
Load line      87 418 423
Load point (concentrated)      3 97 104 123 125 132 136 182 220 230 232—244 247 249 275 277 309 314—318 320—322 419 436 484
Load potential      5 19 40 51 69 71 76 77 83 118 173 296 364 472 473 489
Load potential complementary      43
Load potential edge      70 130 170 308 411 445 474 481
Load potentialmixed      118 121 294 362
Load pressure      see “Axishell pressure pressure
Load thermal      2
Load-deflection curve (relation) for beamshell      104 106
Load-deflection curve (relation) for membrane circular      275
Load-deflection curve (relation) for membrane liquid-filled      273
Load-deflection curve (relation) shallow conical shell      229
Load-deflection curve (relation) shell of revolution      318
Load-deflection curve (relation) spherical cap      232
Load-deflection curve (relation) spherical shell      235 241 243 244
Local buckling mode      320 356
Locality      85 86 182
Locality in buckling      320 356
Logarithmic singularity (in plate buckling)      316
Love — Kirchhoff hypothesis      311 476
Lyapunov functional      147 149
Mainardi — Codazzi formula      403 404 405n 434 435 445
1 2 3 4 5 6 7 8
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