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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
Postbuckling Postbuckling oval shell      355
Postbuckling ring      132
Postbuckling shallow shell      133 312
Postbuckling shell of revolution      318 319
Postbuckling spherical cap      320—322
Postbuckling spherical shell      303 320 322
Potential      see “Load potential”
Potential energy approach (in buckling)      122
Potential energy functional      41 149 489
Potential energy incremental (in buckling)      126 127 303 305
Potential energy total      41
Prebuckling analysis      125 309 356
Prebuckling analysis linearized      125 356
Prebuckling deformation      125
Prebuckling path      123
Prebuckling solution      319
Prebuckling state      355 356
Pressure      see “Axishell Beamshell etc.”
Pressure gauge      249
Pressure potential      308 412 413
Principal curvature      182 186 268 346 426
Principal strain      416 417 434
Principle of conservation of energy      see “Thermo-dynamics first
Principle of equipresence      47 144 326
Principle of mechanical boundary conditions axishell      170
Principle of mechanical boundary conditions beamshell      61 63 67
Principle of mechanical boundary conditions birod      32 33 35
Principle stationary total potential energy axishell      239 273 291 292
Principle stationary total potential energy beamshell      115 116 126 133
Principle stationary total potential energy birod      41 42
Principle stationary total potential energy curved tube      358 359
Principle virtual work      see “Virtual work principle
Proper orthogonal tensor      see “Rotator”
Properly constrained (supported) shell      303 311
Pseudo constitutive relation (in a wrinkled membrane)      276
Pseudo plane      439 440
Pseudo strain      434
Pseudo surface of a wrinkled membrane      276 277 432—436 448
Pseudo surface ruled      277 434
Pseudo-elastic      265
Quasi-linear algebraic equation      67
Quasi-linear differential equation ordinary      266 267 378
Quasi-linear differential equation partial      105 110 200 282 284
Quasi-linear process      122n
Quasi-shallow shell theory      5 311 317n 453 503 505
Radius of curvature      see “Curvature”
Rankine — Timoshenko beam theory      96
Rates (local, objective)      464
Rational normal      59
Rational rotation vector      468—470
Rayleigh quotient      126
Rayleigh — Ritz method      273 320
Red blood cell      273
Reduced equation of energy balance      46 142 324 326
Reference curve deformed      54 58 59 77 78 91 97 99 135 138
Reference curve influence on strain energy      88
Reference curve initial (undeformed)      53—55 58 82 86 109 133 183
Reference curve state      145 327 402
Reference curve undeformed      55 56 58
Reference frame      see “Basis”
Reference meridian      164 165 168 205 253 296
Reference pressure      100
Reference shape      1 3—5 11 16 19 21 48 53 56 82 86 87 90 138 160 365 366 403 453 455
Reference surface deformed axishell      159 174 261 268 285n 288 290 316
Reference surface deformed general membrane      391 398 402 403 405n 406
Reference surface deformed general shell      480 492
Reference surface deformed unishell      346 358 360
Reference surface initial (undeformed)      146 167 192 193 369
Reference surface initial (undeformed) axishell      161 163—165 168 170 174 184 186 188 197 260 268 276 289 31In 317
Reference surface initial (undeformed)general membrane      391—396 402 403
Reference surface initial (undeformed)general shell      453 454 456—458 460 461 474 475 481 482 486 493 503 506
Reference surface initial (undeformed)unishell      343 363 365 366 370 376
Reference surface material      390
Reference surface toroidal      252 254 345
Referential coordinate      14
Reissner — Meissner — Reissner (RMR) equations (of Koiter)      181 201 202 204
Reissner's equations      199
Reissner's equations simplified      200—259 296 300 301 313 318 389
Rigid ball      171
Rigid base      418
Rigid body      1 17—19 31 32 64 280
Rigid body displacement      262n 299 374
Rigid body dynamics      457 462
Rigid body formula      462
Rigid body motion      16 61 132n 159 343 351 402 464
Rigid body movement      207 211 374
Rigid boundary      346
Rigid constraint      427
Rigid disk      272 273
Rigid hole      218
Rigid hub      218 247 275 440
Rigid inclusion      273 454
Rigid indenter      247
Rigid plate      247 272 279 363 435
Rigid plug      229
Rigid post      407n
Rigid ring      269 277 279
Rigid rotation      364 464
Rigid rotation in curved tube      346
Rigid structure      470
Rigid surface      99
Rigid table      243
Rigid tube      412 413
Rigid wall      32 119 275 406
Ring      103 105 106 111 120 122 125 130 132 206 218 269 277 279 308 314n
Rise-to-thickness ratio      231n 232
Rivlin — Saunders material      274
Rivlin — Saunders strain-energy      232 275 420 514
Rod (bisymmetric)      see “Birod”
Roller support      65
Rotary inertia      96n 478
Rotation axishell      159 168 177 179 199 220 229 284 291 294 309 311
Rotation axishell edge      261
Rotation axishell finite (large)      194 253 266 288
Rotation axishell function      218
Rotation axishell linearized      195
Rotation axishell-stress resultant system      280 287n
Rotation beamshell      64 97 98 105 109 118 119 140
Rotation beamshell finite (large)      102 113
Rotation curved tube      347 357 359 362
Rotation curved tube circumferential      346
Rotation curved tube cross section      358
Rotation curved tube end      352
Rotation curved tube finite (large)      353 372
Rotation curved tube vector      358
Rotation general membrane      405 418
Rotation general membrane finite (large)      416 423 425 502 503
Rotation general membrane linear      399 411 446
Rotation general shell      474 499n
Rotation general shell edge      482
Rotation general shell linearized      482
Rotation general shell vector      468—471 478 482 495 499—502
Rotation general shell vector edge      483
Rotation helicoidal shell      364 383
Rotation helicoidal shell vector      369—371
Rotation linearized      195 201
Rotation moderate      see “Moderate rotation theory”
Rotation rigid      see “Rigid rotation”
Rotation unishell      343
Rotator      364 369—371 462 466
Rotator elementary      371
Rubber balloon      261 270 271
Rubberlike      see “axishell rubberlike etc.”
Ruled surface      434
Schwerin's solution      219
Second law of thermodynamics      3 11 15 (see
Self-weight      69n 112 173 197 267 286
Semi-inverse approach      345 346 351 380
Semi-membrane theory      3 356 503
Series expansion      2 4 217 355 (see
Shallow membrane      442
Shallow quasi-      5 311 317n 453 503 505
Shallow shell      see “Arch Axishell etc.”
Shallow shell hinge      see “Hinge”
Shallow shell solution      235 238
Shallow spherical shell (cap)      237 239 242 250—252 256 261 308 318 320 321
Shallow(ness)      100 125 133—135 298 311 312 318 356 442
Shallow(ness) buckling mode      133 309 311 312
Shallow(ness) parameter      231 243 246
Shape initial      435 446 448 (see shape”)
Shape-adjustable      262
Shear coefficient      316 490
Shear constant      92
Shear deformation in axishell      285n 292 301 307n 310 312 313
Shear deformation in beamshell      56 66 96 105 112 132 133 136 138 139
Shear deformation in curved tube      353
Shear deformation in general shell      475 476 478
shear modulus      89 139 191 487
Shear transverse      438 (see
Shear wave      89
Shearable axishell      285n 310 312
Shearable beamshell      66 81 96 122 136
Shearable plate      313 316
Shearable shallow shell      133
Shearable tube      345 349 353 357
Shell      see also “Axishell; Beamshell; Unishell”
Shell approaches ascending      6
Shell approaches derived      2
Shell approaches direct      2
Shell approaches mechanical (isothermal)      5
Shell approaches mixed      3
Shell biologic      1 226
Shell classical theory      185 476
Shell conical      159 221—229
Shell coordinate      51 82n 85 160 182 453 487
Shell cylindrical      see “Axishell cylindrical;Beamshell”
Shell deep      236 241 242 247 249 261 318
Shell domelike      244
Shell edge      453
Shell effect (in plate dynamics)      287
Shell face      see “Face”
Shell fluid-filled      99 247
Shell general      453—510
Shell general cylindrical      210 302 303 318—320
Shell helicoidal      see “Helicoidal shell”
Shell hemispherical      247
Shell of revolution      see “Axishell and Postbuckling”
Shell of weak curvature      133 425
Shell orthotropic      89 181
Shell orthotropic polar      see “Polar orthotropic”
Shell preloaded      287 288
Shell quasi-shallow      5 311 317n 453 503 505
Shell reference surface      see “Reference surface”
Shell rubberlike      1 5 261
Shell sandwich      89
Shell shallow      see “Axishell shallow etc.”
Shell spherical      229—249 302 303 318 320—322
Shell thermoelastic      2 4
Shell toroidal      249—259
Shell true      159 301—303
Shell tubular      261
Shell unishell      5 343—388
Shell-membrane      389 415 422 426n 431 503 505—507
Shock axishell      168 184
Shock axishell line      168
Shock axishell speed      184
Shock beamshell      68
Shock beamshell condition      58
Shock beamshell line      58 59
Shock beamshell speed      59
Shock birod      28 29 34
Shock birod condition (relation)      6 29 30 34
Shock birod front      27
Shock birod speed      28
Shock birod velocity      26
Shock birod wave      21 26
Shock general membrane      392 393 410
Shock general membrane geometry      393
Shock general membrane speed      392
Shock general membrane wave      448
Shock general shell      458 459
Shock general shell relation      459
Shock general shell speed      458
Simple support      see “Boundary condition simple
Simplified Reissner equations      see “Reissner's equations simplified”
Singular behavior      182
Singular matrix      409
Singular nature of neo-Hookean material      252
Singular perturbation      97 208 209 217 236
Singular point      186 236
Singular solution (membrane)      218 223
Singular stress-free state (membrane)      427
Slack      448
Slack region      435
Small strain      see “Strain small”
Smoothness assumption (condition, restriction, requirement)      4
Smoothness assumption (condition, restriction, requirement) axishell      166 167 169 173 260 291 292 294 303 325
Smoothness assumption (condition, restriction, requirement) beamshell      53 59 60 68 85 87 88 91 116 118 120 142 143 148
Smoothness assumption (condition, restriction, requirement) birod      27—29 33—35 38 40—43 46
Smoothness assumption (condition, restriction, requirement) curved tube      359 361 362
Smoothness assumption (condition, restriction, requirement) general membrane      390—392 395 396 400 402 403 409 410 417 423n 448
Smoothness assumption (condition, restriction, requirement) general shell      454 458 460 462 466 472 477
Smoothness assumption (condition, restriction, requirement) helicoidal shell      364 365 367 369
Snap-buckling (snapping)      123n 124 125 127 135 136 230 232 244 279 302 309 318 320 321
Snapback (of spherical cap)      232
Soap film      441—443
Specific heat at constant volume      48 146 149 327
Specific heat matrix      149
Spherical barrel      419 423n 435 436
Sphericity, loss of      271 272
Spin      16 56 166 169 358 462—465 469 470 482
Spin apparent      461
Spin basis      see “Basis spin”
Spin edge      483
Spin effective      19
Spin gross      17
Spin minimizing      18
Spin test      462
St. Venant dispersion      431
St. Venant Principle      346
St. Venant solution      346
Stability      5 69 (see
Stability approximate analysis      130 306
Stability at bifurcation point      124 321
Stability at critical state      126
Stability at limit point      123
Stability axishell      243 270—272 301—322
Stability axishell everted      216
Stability axishell inflatable      279
Stability axishell point-loaded spherical shell      243
Stability axishell solution: cylindrical shell      208
Stability axishell spherical cap      244 321
Stability beamshell      122—136 147 149 301 303
Stability beamshell arch and ring      122—125 130 132 135 136
Stability curved tube, buckling point      355
Stability discrete system      122
Stability dynamic      122 125
Stability general membrane      389 432
Stability infinitesimal analysis      123
Stability loss of      123
Stability material      21 28 37 85 86 182—184
Stability neutral      231
Stability nonconservative      122
Stability postbuckled plate      276
Stability potential energy approach      122 306
Stability thermodynamic      4 6 140 147—149
Stability two types      122 123
State variable      4 145
Static-geometric duality      79 159 177 195 199 267 303 354 370 499n
strain      76 77 175 176 347 373 464—466
1 2 3 4 5 6 7 8
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