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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
Marguerre shallow shell theory      133 247
Mass center of for beamshell      54 83
Mass center of for general body      16
mass density      12 86
Mass per unit area      56 167
Mass per unit length (in birod)      23
Mass surface of for axishell      163
Mass surface of for general shell      456
Material coordinate      14 269 407 423 447 448
Material failure      138
Material formulation      see “Lagrangian formulation”
Material homogeneous axishell      160 180 182 184 187 328
Material homogeneous beamshell      51 55 83—85 87 89 91 108 109 137 138 146
Material homogeneous birod      25
Material homogeneous general membrane      415
Material homogeneous general shell      454
Material homogeneous plate      487
Material reference surface      390
Material stability      21 28 37 85 86 182—184
Mean curvature      5 165 193 442 456n
Mean radius      218
Mechanical boundary conditions      see “Boundary condition mechanical”
Mechanical energy      36 81 178 414 474
Mechanical interpretation      483
Mechanical power, external axishell      169 324
Mechanical power, external beamshell      60 142 148
Mechanical power, external beamshell actual      142
Mechanical power, external birod      30
Mechanical power, external birod actual      31
Mechanical power, external general shell      463 471 473
Mechanical theory      5 147
Mechanical theory axishell      178 179 247
Mechanical theory beamshell      80 81
Mechanical theory birod      21 36—38
Mechanical theory general shells      4 473 474
Mechanical theory Kirchhoff      493 494
Mechanical variable      3 4 46
Mechanical work identity      4 30 36 46 60 169 184
Mechanical work identity axishell      169 178
Mechanical work identity beamshell      60 80n
Mechanical work identity birod      30 31
Mechanical work identity general membrane      401—403 414
Mechanical work identity general shell      453 463
Mechanical work identity Kirchhoff      481 484
Mechanical work identity reduced      479
Membrane      1 2 82 107 266—286
Membrane action      303
Membrane annular      218 221 274—277 279 440 446
Membrane assumption      259
Membrane axi-      180 199 205 252 259—280 296 297 344 435 446
Membrane beamshell      82 100 101 103
Membrane biologic(al)      1 261 264 272 273 389 419 442 447
Membrane cap      261 267 273
Membrane circular      215—221 273 274 412 440 446
Membrane conical      204 222 447
Membrane cylindrical      99 204 206—215 262 268—270 300 425 427—431 445 447
Membrane defonned shape      261 269 275 389 418 437
Membrane effect      146n
Membrane first integral      300
Membrane fluid-filled      99 247
Membrane force      287 303
Membrane fundamental state      310
Membrane general theory      5 389—452
Membrane hemispherical      277 278 418 419 436
Membrane inextensional model      5 99 102 252 253 277 278 418 419 435 445 446
Membrane large strain      205 261—264 268—275
Membrane linear      see “Linear membrane theory”
Membrane liquid-filled      273
Membrane orthotropic      276 415 427 434
Membrane panel      418
Membrane paraboloidal      274
Membrane pressure-loaded      221 245 252 253 261 265 267—273 275 389 390 399 412 416 427 435—439 441 442 445 446
Membrane pressure-loaded position dependent      413
Membrane rubberlike      199 261
Membrane shallow      442
Membrane spherical      204 229—249 270—273 447
Membrane spherical barrel      419 423n 435 436
Membrane spinning      205
Membrane stress resultant      see “Stress resultant general
Membrane toroidal      249—259 261
Membrane true      233 261 264 389 414—416 418 422 423 426 431 432 437 447 456 505 506
Membrane tubular      261
Membrane under point (concentrated) load      219 220 233 275 277 419 436
Membrane wrinkled      233 252 253 276—280 389 390 416 418 419 421 423 426 431—441 506 (see
Meridional inextensionality      354
Meridional section axishell      160—162 166 289 290
Meridional section axishell deformed      161
Meridional section curved tube      346 350
Meridionally incomplete tube      343 357
Metric      390 403 407 416 448
Metric coefficients, deformed      285 402 448 480
Metric components      285n 364 405n
Metric initial      434
Metric tensor deformed      343 397 444
Metric tensor three-dimensional      90 188
Metric time-dependent      448
Metric undeformed      261 402 423
Midcurve      55 165
Midsurface axishell      181 182 187 234 319
Midsurface beamshell      104 137
Midsurface general membrane      415
Midsurface general shell      453 454 492
Midsurface helicoidal shell      366 377 384
Minimal surface      442 443
Mixed approach      3
Mixed load potential      118 121 294 362
Mixed-energy density for axishell      180 196—198 203 259 282 293 296
Mixed-energy density for axishell quadratic      181 199—202 265 300 312
Mixed-energy density for beamshell      82 96 117
Mixed-energy density for beamshell quadratic      85 103 105 110 134 135
Mixed-energy density for general shell      475—478 485 497 499 500 502 505
Mixed-energy density for unishell      349 361 380 382
Mixed-energy density for unishell quadratic      349 352 353
Mixed-energy density modified      197 301 361
Moderate rotation theory of axishell      202n 205 218 251 275 298 318
Moderate rotation theory of beamshell      133
Moderate rotation theory of membrane      275
Modified stress couple      76n 493 499
Moment beamshell      56 57 99 116 118 128
Moment beamshell arm      138
Moment beamshell conjugate      78 106
Moment beamshell modified      79
Moment curved tube arm      352
Moment curved tube cross-sectional      358
Moment curved tube end      344 345 351
Moment higher      80n 492
Moment of inertia per unit area axishell      166
Moment of inertia per unit area beamshell      56
Moment of inertia tensor general body, initial, instantaneous      17
Moment of inertia tensor general shell (per unit area), initial, instantaneous      462
Momentum rotational      4 12 17 19 56 108 109 165 457 461 462
Momentum rotational balance of      2 3 4n 11 14 16 23 24 108 112 164 165 176 179 180 280 282 283 391 396 401 457 459 461—463 479 480 498
Momentum rotational vector      4 453
Momentum translational      12 17 23 109 163 391 456 460 461
Momentum translational balance of      2 3 4n 11 14 16 23 24 106 107 111 164 176 179 280 282 283 390 392 393 395 400 456 459 460 462 463 479 496 498
Mooney ( — Rivlin) material      96 252 269 271 272 275 277 288 420 438 514n
Mooney — Rivlin strain-energy density      239
Motion      11 22
Motion classical flexural      105 106 111—113
Motion cylindrical      51—157
Motion first integral      19
Motion longitudinal      24 37 38
Motion torsionless      159—196 280—288 290 291
Motion wave      37 113 447
Natural boundary condition      see “Boundary condition natural”
Natural initial condition      see “Initial condition natural”
Nearly inextensional deformation      81 109 159 389 476 499n 506
Neo — Hookean material      93 139 189 191 252 269 271 275 288 420 436 514n
Neo — Hookean strain-energy density      258 447 486 492 493
Neutral equilibrium, equations of      122 126
Nonaxisymmetric bifurcation      see “Bifurcation unsymmetric”
Norm(||.||)      39
Norm(||.||) axishell strain bending      187
Norm(||.||) axishell strain total      184 328
Norm(||.||) beamshell displacement      123 125 147
Norm(||.||) beamshell incremental temperature      147
Norm(||.||) beamshell strain      87—89
Norm(||.||) beamshell temperature gradient      148
Norm(||.||) beamshell velocity      147
Norm(||.||) general membrane tensor extensional strain      417
Norm(||.||) general membrane tensor stress      426
Norm(||.||) general shell tensor curvature      492 503
Norm(||.||) general shell tensor general      503 504
Norm(||.||) general shell tensor strain (extensional, bending)      475 485—487 492
Normal bending stiffness      200
Normal bending strain      159 176 178 184 201
notations      511—513
Null space      32 35 61 67 170 472
Ogden material      436 439
Ogden strain-energy density      271 272 514
One-dimensional state of strain      343—388
Operator      39
Operator Bessel      227 229 237
Operator biharmonic      319 426
Operator constant coefficient      204n
Operator del      395n 397
Operator derivative      39
Operator derivative surface, covariant      397
Operator differential      222 233
Operator initial-stress (membrane)      426
Operator integral      229
Operator linear      15
Operator linear membrane      411 426
Operator load      72 73 173
Operator numerical-valued (functional)      39
Operator symmetric      73 417 473
Orthononnal vectors      51 57 67 160 168 427
Orthotropic      see “Membrane or Shell orthotropic”
Oscillation of air-filled membrane      445
Oscillation of annular plate      287
Oscillation of circular membrane      446
Oscillation of circular plate      287
Oscillation of circular tube      288
Oscillation of spherical shell      288
Outer limit      422
Outer region      257
Outer solution      252 256
Outer space      140
Outward normal      see “Unit outward normal”
Ovalization      344 355
Panel arbitrary      376
Panel curvilinear      162 165 368
Panel cylindrical      302 418
Panel differential      54
Panel skewed      367
Panel thin-walled      51
Panel truncated      53
Paper (as a structure)      62 99 112 113
parameter list      143 325
Particle axiplate      188
Particle axishell      163
Particle beamshell      53 137 140
Particle birod      21
Particle general membrane      390 391 400 413
Particle general shell      453 455 456
Particle helicoidal shell      366 367
Particle three-dimensional continuum      11 12 14 15
Periodicity as boundary condition      132 349 350 359
Periodicity in structure      343
Periodicity of response      343
Periodicity of solution      41 319 345 351
Perturbation analysis      127 306
Perturbation method      249
Perturbation of perfect shape      125
Perturbation series, expansion      96 230 252 255 287
Perturbation singular      97 208 209 217 236
Perturbation superimposed      88 251 319 427
Perturbation theory (for buckling)      318
Physical components      90 188 379 381 423
pipe      344
Pipe bending      344
Pipe circular      344 345
Pipe elbow      344
Pipkin's first integral      268 300
Planar motion      see “Cylindrical motion”
Plane of curvature (of a curved tube)      344 357
Plane strain      85 146 279 405
Plane stress      see also “Stress plane”
Plane stress approximate      94
Plastic effect      356
Plastic perfect      123n
Plate      1 5 179
Plate annular      216—218 225 287
Plate buckling      303 313—318
Plate circular      187 188—191 199 215—222 226 279 287 492
Plate composite      83 84 181 187
Plate compressible      190
Plate end      33
Plate equation of motion      287
Plate heated      144 146 147 326
Plate intrinsic form      38
Plate linear theory      247
Plate plane stress      see “Stress plane”
Plate pressure loaded      216
Plate rectangular      276 482
Plate rigid      247 272 279 363 435
Plate shearable      313 316
Plate square      301
Plate strain-energy density      181n 187—191 197 485 486 490—493
Plate stretching      493
Plate three-dimensional      90 93 476 487
Plate three-dimensional attachment      470n
Plate under point (concentrated) load      314—317
Plate von Karman theory      246 287 405 503
Plate von Karman theory wrinkling      431
Plateau's problem      442
Point load      see “Load point”
Poisson's problem      442
Poisson's ratio      83 85 180 191 202 204 218 234 434 485 506 514
Poisson's variable      438
Polar coordinate      320
Polar orthotropic layer      181
Polar orthotropic material      218 345
Ponding      270 278
Ponding collapse      278
Position (vector) current (deformed, weighted) axishell      163 198 266 291 297 299 324
Position (vector) current (deformed, weighted) beamshell      51 54 90 97 100 115 118 121 133 139 141 146
Position (vector) current (deformed, weighted) curved tube      346 358 359 362
Position (vector) current (deformed, weighted) general membrane      390 410 412 413 419 447
Position (vector) current (deformed, weighted) general shell      4 453 455 466 486 487 501
Position (vector) current (deformed, weighted) helicoidal shell      368
Position (vector) current (deformed, weighted) three-dimensional body      2 11 16 142
Position (vector) given      414
Position (vector) initial (undeformed) axishell      179 262 263 286 308
Position (vector) initial (undeformed) beamshell      71 121 147
Position (vector) initial (undeformed) birod      21
Position (vector) initial (undeformed) curved tube      346
Position (vector) initial (undeformed) general membrane      390 391 395
Position (vector) initial (undeformed) general shell      453—455
Position (vector) initial (undeformed) helicoidal shell      367
Position (vector) initial (undeformed) three—dimensional body      11 13
Position (vector) vector      4 21
Postbuckling      see also “Membrane wrinkled”
Postbuckling arch      136
Postbuckling axishell      317—322
Postbuckling beam      125
Postbuckling beamshell      127 128 132
Postbuckling circular cylindrical shell      303 319
Postbuckling column      122 125 302
Postbuckling plate      217 276 303
1 2 3 4 5 6 7 8
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