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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
Temperature thickness distribution      141
Tension field      277—279 421 431 432 439 440 448
Tension-stretch      406
Tensor Cauchy — Green      420 447 486 487
Tensor compliance      418
Tensor components      421
Tensor couple-stress      160
Tensor curvature      see “Curvature tensor”
Tensor derivative      414n
Tensor elasticity      417 424
Tensor Eulerian strain      465
Tensor field      395n
Tensor first Piola — Kirchhoff      see “First Piola — Kirchhoff stress tensor”
Tensor geometrical      459 503
Tensor identity      17
Tensor invariant      184 202
Tensor Lagrangian strain      see “Strain Lagrangian
Tensor metric      see “Metric tensor”
Tensor moment of inertia      see “Moment of inertia tensor”
Tensor nonphysical components of      374n
Tensor norm      see “Norm general
Tensor notation      285n 292
Tensor notation complete      396
Tensor notation Euclidean direct-surface      396
Tensor permutation      185 405
Tensor physical components      90 188 379 381 503
Tensor product      184
Tensor proper orthogonal      see “Rotator”
Tensor representation      15 184 374n
Tensor second-order      15 187 464 481
Tensor second-order cofactor      405
Tensor second-order equation      405
Tensor second-order linear space      417
Tensor second-order surface      184 396
Tensor skew symmetric      462
Tensor strain      184 186 (see extensional
Tensor stress      421
Tensor stress couple      see “Stress couple tensor”
Tensor stress resultant      see “Stress resultant tensor”
Tensor stretch      464
Tensor unknown      503
Test function axishell      172 173
Test function beamshell      60 67 68
Test function birod      24 29 3 34 36 41
Test function general membrane      400 409 410
Test function general shell      471
Test velocity      400 462
thermal conductivity      48 145 327
Thermal damping      140
Thermal disturbance (effect, response)      2 24 36 80 81 140 170 178
Thermal equations axishell      322—328
Thermal equations beamshell      140—149
Thermal equations birod      45—48
Thermal expansion coefficient      48 146 327
Thermal variable      3 4 45 46 327
Thermodynamic stability      4 6 140 147—149
Thermodynamics      2 4 5
Thermodynamics first law      3 5 (see
Thermodynamics of axishell      178 322—328
Thermodynamics of beamshell      81 140—149
Thermodynamics of birod      36 45—48
Thermodynamics of continuum      14 15
Thermodynamics second law      3 11 (see
Thermoelastic axishell      324
Thermoelastic beamshell      142
Thermoelastic birod      46—48
Thermoelastic continuum      2
Thermoelastic shell      2
Thermoelasticity      2
Thermoelasticity coupled (in birod)      48
Thickness aximembrane constant      264
Thickness aximembrane deformed      271
Thickness aximembrane finite (large)      261
Thickness aximembrane undeformed      264n
Thickness aximembrane unknown distribution      273 274
Thickness aximembrane variable      264
Thickness axiplate constant      188
Thickness axiplate order of magnitude      287
Thickness axishell      182 186 205
Thickness axishell average      163
Thickness axishell cone      226
Thickness axishell constant      160 16S
Thickness axishell projected      224
Thickness axishell variable      160 161 204
Thickness axishell-to-mean radius      218
Thickness beamshell      82 83 86 137 138
Thickness beamshell average      54 92 140
Thickness beamshell constant      51 55 97
Thickness beamshell cover sheet      137
Thickness beamshell deformed      140
Thickness beamshell density weighted      84
Thickness beamshell direction      83 84 89 90 108 138 146
Thickness beamshell modulus weighted      84
Thickness beamshell of differential panel      54
Thickness beamshell total      82
Thickness beamshell variable      51 53 85
Thickness circular cylindrical shell      319
Thickness circular cylindrical shell variable      3
Thickness coordinate      2 4 140 391 453
Thickness curved tube, constant      344 345
Thickness deformed position distribution      see “Position current”
Thickness general membrane      414
Thickness general membrane base state      427
Thickness general membrane fixed      422
Thickness general membrane undeformed      415
Thickness general membrane vanishing      421
Thickness general membrane-stretch      420
Thickness general shell      2
Thickness general shell average      490
Thickness general shell constant      454
Thickness general shell of layer      454
Thickness general shell order of      476
Thickness general shell parameter      475
Thickness general shell reduction      493
Thickness general shell undeformed      487
Thickness general shell variable      453
Thickness general shell weighted integral      462
Thickness general shell-stretch      489
Thickness helicoidal shell, variable      363
Thickness strain distribution      see “Strain three-dimensional”
Thickness stress distribution      see “Stress three-dimensional”
Thickness temperature      141
Thinness, assumption, implication axishell      186 288
Thinness, assumption, implication axishell measure of      208
Thinness, assumption, implication beamshell      51 85—87 91
Three-dimensional continuum mechanics      see “Continuum mechanics three-dimensional”
Three-dimensional elasticity      1 54 118 140 230 316 453 476
Three-dimensional Euclidean space      11 364 390 394 403n 453
Three-dimensional strain-energy density      see “Strain-energy density three-dimensions”
Three-dimensional thermodynamics      144
Tonometry      247 273
torque      17 447 (see
Torque-rotation graph      441
Torsion      343
Torsion axishell      288—290
Torsion infinite tube      378—380
Torsional spring      69 131 308
Torsional wave      447
Torus      345
Transition (turning) point      249 251
Transition circle      279
Transition layer      322
Transition number (Reissner's)      208 209 225
Transition parameter (for toroidal shell)      251 254
Transition region spherical shell      322
Transition region toroidal shell      251
Transition section      249
Transverse normal strain      77n 146 487
Transverse normal stress      91
Transverse shear compliance      200
Transverse shear stress      91 138 490
Transverse stress resultant      see “Stress resultant transverse
Transversely homogeneous layer      85 182
Trefftz criterion      126
True membrane      see “Membrane true”
True shell      159 301—303
Tube      1 5 343—363 cylindrical; general cylindrical”)
Tube bent, wrinkled      437—439
Tube buckling of      131 302 355 356
Tube circular      131 251 269 344
Tube curved      344—363 378
Tube curved classical theory      353
Tube curved shallow      356
Tube finite      344
Tube helical      363
Tube infinite      378
Tube inflated      265 276
Tube long      355 356
Tube open      343 357
Tube pressurized      343—356 359 360 378
Tube rubberlike      269 288
Tube shearable      345 349 353 357
Tube slender      353
Tube straight      348 349 361
Tube toroidal      249
Tube variational principle      357—363
Tube wrinkling      276
Twist(ing)      343
Twist(ing) aximembrane      275
Twist(ing) axishell      275 288—290
Twist(ing) circular cylindrical membrane      277 447
Twist(ing) circular membrane      440 441
Twist(ing) right helicoidal shell      380—383
Unishell      343—388
Unishell definition      5
Unit normal to curve      57 64
Unit normal to deformed string      408
Unit normal to meridian      168
Unit normal to shock      392 459
Unit normal to surface      174 365 390 396 412 448 456n 475
Unit outward normal to boundary      390 395 403 406 407 410 456 466
Unit outward normal to face      13
Unit outward normal to side of triangle      394
Unit outward normal to surface      12 21 53
Unit tangent to boundary      403 410 460
Unit tangent to curve      57 62 64 78
Unit tangent to deformed string      408
Unit tangent to meridian      168 290
Unit vector      130 167 345 348 371 413 470 (see orthonormal”)
Unit vector axis of rotation      364 468
Universal equation      212
Universal function (solution)      212 265
Unshearable      see also “Kirchhoff Hypothesis”
Unshearable beamshell      96 100
Unshearable edge beam      470
Unshearable materia]      104
Unshearable ring      132
Unstable buckling      317
Varga material      420 438 439
Variation      39 41 74 159 189n 281 291 299 358 359 368 369 376
Variation second      232
Variational equilibrium equation      see also “Equilibrium equation variational”
Variational equilibrium equation solution      360
Variational formulation, principles      5 6 121 311
Variational formulation, principles for axishell      290—301
Variational formulation, principles for axishell elastostatics      291
Variational formulation, principles for axishell extended      292 296
Variational formulation, principles for beamshell      114—121
Variational formulation, principles for beamshell elastostatics      115
Variational formulation, principles for beamshell extended      116
Variational formulation, principles for birod      21 38—44
Variational formulation, principles for birod extended      42
Variational formulation, principles for curved tube      343 357—363
Variational formulation, principles for curved tube extended      360
Variational formulation, principles in continuum mechanics      121
Variational formulation, principles mixed, of Reissner      296
Variational formulation, principles with stress and rotation      122
Vector space      39 64 67 73 175 417
Vector space theory of      67
Velocity angular      362
Velocity axishell      167 169
Velocity axishell angular      174 205
Velocity axishell axial      287
Velocity axishell boundary condition      286
Velocity beamshell      56 66 109
Velocity beamshell angular      69
Velocity beamshell components      105
Velocity beamshell edge vector      63 67
Velocity birod      24 30 38
Velocity birod shock      26
Velocity birod wavefront      25
Velocity curved tube      358
Velocity curved tube angular      358
Velocity general membrane      400 401 443
Velocity general membrane angular      444
Velocity general membrane components      443
Velocity general membrane test      400
Velocity general shell      461 463
Velocity general shell angular      464
Velocity general shell test      462
Velocity three-dimensional continuum      12
Vibration      54 69 112 140 260 280 288 445 446
Virtual work      368 463
Virtual work external      369
Virtual work internal      369 376
Virtual work, principle of      4n 6 39 41
Virtual work, principle of for axishell      172 173 267 281
Virtual work, principle of for beamshell      67—69 115
Virtual work, principle of for birod      21 24 33—36
Virtual work, principle of for general membrane      290 293 410
Virtual work, principle of for general shell      463 471
Virtual work, principle of for unishell      358 359 368
Volume controlled deformation      270
von Kdrman equations      246 287 405 503 (see
Wave acceleration (stress)      447
Wave buckling      354
Wave circumferential      244 321
Wave fiexural-extensional      113
Wave finite amplitude      447
Wave flexural      89 114
Wave inextensional      114
Wave inflation (fluid)      447
Wave longitudinal      37 113 447
Wave motion      113
Wave shear      89 447
Wave shock      21 26 448
Wave shock solitary      114
Wave shock symmetric      447
Wave shock torsional      447
Wave shock transverse      447
Wavefront      11 25 26 447
Wavefront velocity      25
Wavelength of deformation pattern      133 189 487 503 506
Wavelength short      260
Wavelength typical      426
Weak curvature approximation      425
Weak solution      see “Equation of motion weak
Winkler approximation      138n
Wrinkle strain      276 440
Wrinkled region      253 276—278 436 440
Wrinkles (in collapse of tube)      355 356
Wrinkling      5 233 252 253 261 (see wrinkled”)
Yield stress      137
Yield stress modified      137n
Young's modulus      25 37 82 83 111 145 180 182 188 191 415 476 485 504 506
1 2 3 4 5 6 7 8
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