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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
Classical assumption in strain energy      198
Classical axishell      see “Axishell classical
Classical beamshell      82 85 108 109 148
Classical boundary condition      see “Boundary condition classical”
Classical differential geometry      403 405n 418 442
Classical flexural motion      105 106 111—113
Classical linear elasticity      316
Classical mechanics      11 31 32 61
Classical plate      315—317
Classical shell      185
Classical solution      28 173 178
Clausius — Duhem inequality      3 4 11 15 45 46 142 143 147 324 325
Codazzi equation      403 404 405n 434 435 445
Cold flux      15 323
Collapse of tube in bending      343 354—356
Compatibility (condition) axishell      159 177—179 192 196 197 199 200 202 203 226 296
Compatibility (condition) axishell buckling of      313 319
Compatibility (condition) beamshell      110 136
Compatibility (condition) bending      296
Compatibility (condition) birod      44
Compatibility (condition) circular cylindrical shell      319
Compatibility (condition) curved tube      345 349 352 354
Compatibility (condition) edge      296
Compatibility (condition) edge-interior      296
Compatibility (condition) Gauss      426
Compatibility (condition) general membrane      403—405 422 424—426
Compatibility (condition) general membrane wrinkling      439 440
Compatibility (condition) general shell      466—469 499 500 502
Compatibility (condition) general shell approximate      505
Compatibility (condition) general shell under Kirchhoff Hypothesis      477 478 493n 502
Compatibility (condition) helicoidal shell      372 376—379 381 382
Compatibility (condition) intrinsic form      177
Compatibility (condition) strain-rotation      177
Compatibility (condition) unishell      343
Complementary energy density      121 196 416—418 421
Complementary energy principle      42—44 118 121
Compliance tensor      418
Composite plate and shell      83 84 181 187
Compressible axiplate      190
Compressible material      191 263 264 420 439 487—489
Concentrated load      see “Load point”
Configuration deformed      122n 139 252 267 345 391 399
Configuration equilibrium      4 69 122 147 445
Configuration possible      126
Configuration referential      391 402 413 445
Configuration static      445
Configuration stressed      424
Configuration undeformed      119 122n 391 423
Conical shell      159 221—229
Conservation form      25
Conservation of energy      3—5 46 83 140 142 178 324
Conservation of mass      2 3
Conservation of mechanical energy      36 81 178 414 474
Constitutive relation (equation)      3—5 32 47 139 188
Constitutive relation (equation) axishell      163 165 168 179 180 183 196 197 199 245n 262—266 268 274 277 282 283 286 293—296 306—309 312 325—327
Constitutive relation (equation) axishell linear      184 266 327
Constitutive relation (equation) beamshell      51 54 55 66 81 89 96 99 105 110 116 117 119 132 140 141 143—145
Constitutive relation (equation) beamshell linear      113
Constitutive relation (equation) birod      26 48
Constitutive relation (equation) birod linear      48
Constitutive relation (equation) general membrane      391 414—422 424 425 434—436 440 444
Constitutive relation (equation) general shell      453 464 474 486 490 493 495 497 499 502
Constitutive relation (equation) three-dimensional      3 89 187 419 486
Constitutive relation (equation) unishell      343 349 372 376—380
Constraint      see “Constraint boundary edge”
Constraint boundary, edge      24 32 62 172 173 295 296 345 362 411 412 427
Constraint force of      34 61 62 170
Constraint general      32 170
Constraint geometrical      31 303
Constraint holonomic      33 36 61 114 171 290
Constraint homogeneous      34 68 409
Constraint independent      31 61 170
Constraint internal      415 416
Constraint kinematic      24 41 61 62 68 170 292 345 357 359 406 408 423 470 472
Constraint kinetic      423
Constraint matrix      67
Constraint nonholonomic      31 34 36 61 66 68 170 408 470
Constraint power of      32 61 170
Constraint proper (for true shell)      303
Constraint strain      478
Constraint time dependent      61
Constraint unilateral      61 63 170
Contact force      12 23 32 53 162 165 172
Continuum mechanics      2—4 11 12 32 46 71 80 121 179 401 463 468 490
Continuum one- or two-dimensions      2 21 24 140
Continuum three-dimensions      2 11 21 140 393 453 456
Contravariant components of a tensor      16 396 419 482 502
Contravariant components of a vector      406
Contravariant components vector      14 16 53 162n 292 397 461 476 479 494
Contravariant form      374
Contravariant surface base vector      397
Contravariant vector      397 403n
Coordinate axial      269
Coordinate Cartesian      14—16 21 72 97 100 413 487
Coordinate circular cylindrical      160 188 316 345 346 412 427
Coordinate circumferential      323n
Coordinate convected      14 447
Coordinate curve (line)      346 365 433—435 453 454
Coordinate curve (line) deformed      368
Coordinate curvilinear      14 433
Coordinate Gaussian      346 396 461
Coordinate general      16
Coordinate Lagrangian      14 346 447
Coordinate material      14 269 407 423 447 448
Coordinate midsurface      187 453
Coordinate plane polar      320
Coordinate radial      15n 296
Coordinate rectangular      103
Coordinate referential      14
Coordinate shell      51 82n 85 160 182 453 487
Coordinate surface      319 343 364 365 368 390 395 397 405 433 453 464 474
Coordinate thickness      2 4 140 391 453
Coordinate transformation      182 183
Coordinate transverse      146
Coordinate-bound      402 404
Coordinate-free      395n 396 402 403 460 461 467 469 470 478
Core (of a sandwich shell)      89 137 138
Cosserat continuum, thermodynamics of      144
Cosserat hypothesis      453
Cosserat model      486
Couple-stress theory      160
Covariant base vector      365
Covariant derivative operator      397
Covariant differentiation      397 480
Covariant tensor component bending strain      482 497
Covariant tensor component curvature      365 405n 475
Covariant tensor component deformed metric      397 448 480
Covariant tensor component Lagrangian strain      402 414 424 444
Covariant tensor component undeformed metric      364 405n 448
Covariant vector      466 468
Covariant vector component      410 466 468
Critical (equilibrium) state      126 128 130
Critical frequency      137
Critical load      126 302
Critical load for circular cylindrical shell (tube)      132 210 319
Critical load for conical shell      222 224 225 228
Critical load for plate      314
Critical load for spherical cap      244
Critical moment (for tube)      356
Critical point      124 127 271
Critical pressure for aximembrane      269
Critical pressure for closed spherical shell      302
Critical pressure for tube      131 302
Critical stress for a beamshell column      302
Critical stress for an axially compressed cylindrical shell (tube)      302 355
Critical stress for an edge-loaded plate      302
Cross of tube      347
Cross of tube arbitrary      343 350n
Cross of tube closed      343 344 347
Cross of tube distortion      356
Cross of tube elliptic      355
Cross of tube end      351
Cross of tube moment      358
Cross of tube open      343 347
Cross of tube ovalization      344
Cross of tube rotation      346 358
Cross of tube symmetric      351
Cross of tube unsymmetric      354
Cross of tube wrinkled      438
Cross section      21 22 25 37 53
Cross section bisymmetric      4 24
Cross section deformed      139
Cross section meridional      166 346 350
Cross section modulus-weighted      181
Cross section rectangular      85
Cross toroidal circular      249 251 252
Cross toroidal concentric circles      436
Cross toroidal convex      252
Cross toroidal deformed      252
Cross toroidal degenerate      436
Cross toroidal flat      252
Cross toroidal general      249—259
Cross toroidal tilted      261
CROSS variable      113 163
Crown      159 249 252—254 261 269 389
Curvature      44 183 433
Curvature change of      113 389 418
Curvature component      186 364
Curvature deformed      99 268 284—287 356 404 407
Curvature double      5 159
Curvature effect      21 51 101 102 328 439
Curvature effect on strain energy      87 181
Curvature effect on stress distribution      138n 139
Curvature function      428 429
Curvature Gaussian      5 159 165 311 384 403 405 456n
Curvature generating function      285
Curvature geodesic      407
Curvature gross      350
Curvature longitudinal      437—439
Curvature mean      5 165 193 442 456n
Curvature meridional      193 356
Curvature norm      186
Curvature of curve      55 57 78 82 86 87 99 101 133 137 406 408
Curvature of deformed plate      344 357
Curvature of reference surface      184 186 188 260
Curvature principal      182 186 268 346 426
Curvature tensor      184 343 365 384 395 403 405
Curvature weak      133 425
Curved tube      see “Tube curved”
Cylindrical motion      53 56
Cylindrical motion differential equations of      59 60
Cylindrical motion integral equations of      53—57
Cylindrical shell      210 302 303 318—320
Dead load      see “Load dead”
Deep shell      see “Shell deep”
Deformation gradient (surface)      397
Deformation planar      439
Deformation potential      106 113
Deformation power      30 60 76 169 180 192 402 414 463
Deformation power density      76 80n 159 160n 175 176 196 482
Deformation small, superimposed      399 421—423 427 448
Deformation tensor      420 447 486 487
Deformed (current) state      448
Deformed angle      266
Deformed base vector      16
Deformed basis      see “Basis deformed”
Deformed curvature      see “Curvature deformed”
Deformed image      11 13 16 22 53 54 58 139 163 174 366 367 390 397 406 412 483
Deformed meridian      259 262 279 285 349 360n
Deformed metric coefficient      285 402 448 480
Deformed position      see “Position current”
Deformed radius      270
Deformed shape      261 269 275 389 418 437
Deformed thickness      271
Degree of freedom      171
Degree of nonlinearity in buckling analysis      128 304
Degree of nonlinearity in membrane model      269
Delta function      3 227 237
Derived approach      2
Deviation      see “Base-reference deviation”
Diaphragm      1
Diaphragm support extrinsic      65 66
Diaphragm support intrinsic      65 66
Dimple (dimpling)      235 237 242 260 322
Direct (tensor) product      184 364 395
Direct approach      2 137 138 40 389 390n 416 417 419
Director      2 486
Dislocation      466
Displacement, admissible      41 42 126 127 303
Displacement, admissible axishell      192
Displacement, admissible axishell ahorizontal      288 299
Displacement, admissible axishell axial      267 308
Displacement, admissible axishell normal      224
Displacement, admissible axishell radial      207 221 228 229 233 234 307 319
Displacement, admissible axishell tangential      224 262n
Displacement, admissible axishell transverse      270 287
Displacement, admissible axishell twisted      288
Displacement, admissible axishell vertical      233 249 253 288 316
Displacement, admissible beamshell      64 77 121
Displacement, admissible beamshell axial      64
Displacement, admissible beamshell end      40
Displacement, admissible beamshell eneralized      125
Displacement, admissible beamshell horizontal      80
Displacement, admissible beamshell incremental      126
Displacement, admissible beamshell norm      123 125 147
Displacement, admissible beamshell normal      80
Displacement, admissible beamshell parameter      100
Displacement, admissible beamshell tangential      80
Displacement, admissible beamshell transverse      64
Displacement, admissible beamshell vertical      80
Displacement, admissible birod      24 37
Displacement, admissible boundary conditions      see “Boundary condition displacement”
Displacement, admissible edge      see “Edge displacement”
Displacement, admissible equation of motion      see “Equation of motion form”
Displacement, admissible general membrane      391 399
Displacement, admissible general membrane bending      438
Displacement, admissible general membrane Cartesian component      413
Displacement, admissible general membrane continuity      423 440
Displacement, admissible general membrane gradient      399
Displacement, admissible general membrane normal      391 446
Displacement, admissible general membrane tangent      391 446
Displacement, admissible general shell      470 478 479 494 495
Displacement, admissible general shell alternative components      496
Displacement, admissible general shell decomposition      504
Displacement, admissible general shell derivative      479
Displacement, admissible general shell partial differential equations for      497
Displacement, admissible general shell radial      506
Displacement, admissible general shell rational function of      481
Displacement, admissible in variational principle      40 43 44 117 121 126 357
Displacement, admissible midsurface, radial      241
Displacement, admissible norm      123 125
Displacement, admissible rigid body      262n 299 374
Displacement, admissible unishell      343
Displacement, admissible virtual      410
Displacement, admissible weighted average      24
Divergence theorem      141 167 367 368 395 403 409 460 480 481
DMV theory      5 133 311 425 503
Donnell approximation      133
Donnell nonlinear shell equations      312 319
Donnell — Mushtari — Vlasov theory      5 133 311 425 503
Dyad      15
Dynamic consistency condition      55 84 91—93 366 164 457 487 489 491 492
Dynamics of membrane      443—448 (see
EDGE      1 2
Edge angle      211 231 262
Edge angular discontinuity      261 430
Edge beam      470
Edge clamped      65 66 243 245
Edge common      407
Edge compatibility      296
1 2 3 4 5 6 7 8
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