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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
Edge condition      see “Boundary condition”
Edge curve      406
Edge decay axishell      218
Edge decay beamshell      96 102
Edge decay curved tube      346 355n
Edge decay cylindrical membrane or shell      429 431—433
Edge deformed      406 410 501
Edge displacement      206 221 483
Edge displacement generalized      473
Edge disturbance      344 346 430 431
Edge effect      3 355 356 431
Edge effect degenerate      2
Edge effect simple      2
Edge effect three-dimensional      476
Edge elastically restrained      279
Edge extension      406 407
Edge fictitious      470n
Edge finite rotation vector      483
Edge fixed      64—66 273 275 406 412
Edge force (membrane)      406
Edge free      64 65 205 229 231 232 243 380 382 411 426 470
Edge hinged      66 69
Edge kinematic conditions      297
Edge kinematic variables      482
Edge kinematic vector      61 114 170 290 291
Edge load axial      205 207 211 262
Edge load deformation independent      308
Edge load generalized      32 33 62 68 170 172
Edge load inclined      263
Edge load radial      204 211 218 221 261 269
Edge load rate of work (power)      61 69 70 170 483 493
Edge load self-equilibrating      2 429
Edge load shear      276
Edge load tensile      276 435
Edge load traction (membrane)      411
Edge load vector      61 63 67 115 170 173 291 471
Edge load vertical      217 261
Edge load virtual work      291
Edge loaded axishell      249
Edge loaded beamshell      51 119 120
Edge loaded conical shell      318
Edge loaded cylindrical shell      263 318
Edge loaded membrane      422
Edge loaded plate      301 318
Edge loaded spherical shell      249 318
Edge moment      172 206 230 232 261 345 351 472 481
Edge potential      see “Load potential edge”
Edge rotation      261 482 501
Edge shear stress      276 411
Edge shell      453
Edge simple support      64
Edge spin      483
Edge stress      206
Edge stress couple      290
Edge stress effective Kirchhoff      484
Edge stress pseudo      483
Edge stress resultant      290 294 313 345
Edge support      66
Edge thrust      217
Edge torque      380
Edge track      409
Edge vector of test functions      177
Edge velocity vector      65 69
Edge velocity, generalized      32 61—63 67
Edge zone      96 102 277 310 476 506 507
Eigenfunction      272
Eigenvalue      315—317 426 447
Eigenvalue problem      132 319
Elastic      1
Elastic axishell      179
Elastic beamshell      81—94
Elastic birod      36
Elastic hinge      239 241 322
Elastic isotropy axishell      180 181 184—187 245n 251 252 263 264 313 345
Elastic isotropy beamshell      83 91 113 478
Elastic isotropy general membrane      416 418—420 424 426 430 434 438 441 447
Elastic isotropy general shell      485 486 489 506
Elastic isotropy unishell      345 363
Elastic modulus      see “Young's modulus”
Elastic-plastic      123 359
Elastica      94
Elastica heavy      98
Elastica inextensional (classical)      82 97 99 102 104 132
Elastica linearly extensible      102
Elasticity tensor      417 424
Elastodynamics of axishell      280—290 (see
Elastodynamics of beamshell      105—114 (see
Elastostatics aximembrane      259—280
Elastostatics axishell      196—200
Elastostatics beamshell      94—105
Elastostatics general membrane      421—427
Elastostatics general shell      498—502
Elastostatics unishell      343—388
Elliptic integral, function      99 100 105 132 287 435
End couple (curved tube)      343—345 351 352 354 355 360
End couple (curved tube) effect      352
End force (curved tube)      343 350 357 359 378
Energy balance      148
Energy balance differential (local) equation      46—48 142 325
Energy balance reduced      46 142 324 326
Energy balance thermodynamic foundation of      125 147—149
Energy criterion (for buckling)      125 126 130 136
Energy integral      103 105 120 131n 300
entropy      15
Entropy density      323
Entropy density couple      142 335
Entropy density resultant      4 45 140 323
Entropy flux      4 45 141
Entropy flux deviation      327
Entropy inequality      3
Entropy influx resultant      140 141 323
Entropy supply      45 48 141 323 324
Equation of motion      4
Equation of motion classical flexure      110 111
Equation of motion classical solution      21 28 29 34 35 60 168 169
Equation of motion differential (local) axishell      166—168
Equation of motion differential (local) beamshell      59 60
Equation of motion differential (local) birod      24 25
Equation of motion differential (local) general membrane      395—400
Equation of motion differential (local) general shell      460 461
Equation of motion differential (local) plate      287
Equation of motion differential (local) three-dimensional continuum      3 14 19
Equation of motion displacement form birod      37 38
Equation of motion displacement form general shell      496
Equation of motion displacement-shear strain form axishell      280 281
Equation of motion displacement-shear strain form beamshell      106—109
Equation of motion first integral      19
Equation of motion first-order system axishell      282—284
Equation of motion first-order system beamshell      105 109 110
Equation of motion gross      16—20
Equation of motion hybrid general membrane      396—398
Equation of motion hybrid general shell      461
Equation of motion integral (-impulse)      3 4n
Equation of motion integral (-impulse) axishell      161—167 169
Equation of motion integral (-impulse) beamshell      53—57 59 60
Equation of motion integral (-impulse) birod      4 21—24 26 28 29 46
Equation of motion integral (-impulse) general membrane      390 401
Equation of motion integral (-impulse) general shell      455—457 463 466 479
Equation of motion integral (-impulse) helicoidal shell      369
Equation of motion integral (-impulse) three-dimensional continuum      11 12 140 393
Equation of motion intrinsic form      21 37 38 284—287 421 422 444 502
Equation of motion rotation-stress resultant form      109 280 282—283 287n
Equation of motion second-order system (axishell)      282
Equation of motion twisted axishell      289
Equation of motion weak form      28—30 33 41 60 114 169 172 290 400 401 409 461—463 471
Equation of motion weak solution      21 28 29 34 35 40 68 169
Equilibrium configuration      4 69 123 147
Equilibrium equation (wrinkled) pseudo-surface      277 278 432—434 439 440
Equilibrium equation axial      267
Equilibrium equation axishell      196 251 260 275 306 312
Equilibrium equation beamshell      94 95 103 126 131 133
Equilibrium equation curved tube      348 349 350n
Equilibrium equation force axishell      196 296 297 311
Equilibrium equation force beamshell      119 120 129 130
Equilibrium equation force general shell      498 499
Equilibrium equation force helicoidal shell      365—368 375 382
Equilibrium equation general membrane      421—427 443
Equilibrium equation general membrane intrinsic form      421
Equilibrium equation general membrane isotropic stress      442
Equilibrium equation general shell      499n
Equilibrium equation horizontal      196
Equilibrium equation incremental (in buckling)      129 130 305 306
Equilibrium equation moment axishell      196 197 199 201—203 295 296
Equilibrium equation moment beamshell      119 120 129 131 134
Equilibrium equation moment general shell      477 498 499
Equilibrium equation moment helicoidal shell      365—368 375—378 380 382
Equilibrium equation normal      233
Equilibrium equation radial (cylindrical shell)      319
Equilibrium equation string      406 407
Equilibrium equation three-dimensional      91 138
Equilibrium equation variational axishell      291 293 294—296 298 299
Equilibrium equation variational beamshell      116—118 127
Equilibrium equation variational curved tube      359 361—363
Equilibrium equation vertical      177 197 199 233
Equilibrium integral      102 131n 374
Equilibrium neutral      122 126
Equilibrium path axisymmetric      303 318
Equilibrium path bifurcation      244
Equilibrium path fundamental      123 126 135 136 303 318
Equilibrium path secondary      123—126 135 306n 317 318
Equilibrium path straight      123
Equilibrium point      126
Equilibrium solution, fundamental      122
Equilibrium state      126
Equilibrium state adjacent      126
Equilibrium state critical      126
Equilibrium state fundamental      130
Equilibrium state neighboring      123
Equilibrium temperature      148
Euler angle      371
Euler parameter      364 370 371
Euler — Bemoulli theory      64 96n 97 100 113 138n
Euler — Lagrange equations      120 268 299 305
Eversion cylindrical shell      208
Eversion hemispherical shell      230
Eversion spherical cap      230
Eversion tubular membrane      262
Exact equations axishell      178 182 324
Exact equations beamshell      56 80 134 142
Exact equations birod      46
Exact equations shell      3 453 456 464 496 502 505
Exact equations toroidal membrane      251
Exact solution aximembrane      273
Exact solution axishell      233 245
Exact solution beamshell      96 100 101 105
Exact solution curved tube      345
Exact static-geometric duality      196
Exact strain-energy density      485
Exact two-dimensional theory      2
Extension of a circular cylindrical membrane      269 270 277
Extension of a right helicoidal shell      380—383
Extension of a tube      251 343 378—380
Extensional strain      see “Strain extensional”
Extensional strain vector      304 328 369—371 376
External couple per unit area axishell      166
External couple per unit area beamshell      56
External couple per unit area general shell      457
External couple per unit area helicoidal shell      367
External force per unit area axishell      164
External force per unit area axishell twisted      289
External force per unit area beamshell      55
External force per unit area general membrane      390
External force per unit area general shell      456
External force per unit area helicoidal shell      366
External force per unit length, birod      23 45
External mechanical power      see “Mechanical power external”
External torque      17
External virtual work      369
Extreme fiber stress formula      137
Face axishell      160 162 163 323
Face beamshell      51 53 54 82n
Face general shell      453
Face plate      144 326 490
Failure analysis (direct approach)      137 138
Failure bifurcation      356
Failure catastrophic      123 276
Failure criteria      136—140
Failure envelope      137—139
Failure global      137
Failure in bending      344
Failure limit point      356
Failure local      137
Failure material      138
Failure mode of      278 344
Finite element      5 33 41 105 121 241 287 311 434 444 447
Finite rotation vector      358 364 468—470
Finite rotation vector rational      468 469 482 495 499—501
Finite rotation vector rational edge      483
First integral axishell      178
First integral beamshell      97 102
First integral curved tube      354
First integral cylindrical membrane      268 269 300
First integral cylindrical shell      211 213 215 268 299
First integral helicoidal shell      367 372 376
First integral hinge function      239 242
First integral motion      19
First law of thermodynamics      see “Conservation of energy”
First Piola — Kirchhoff stress tensor      14—16 53 139 162n 393 460
First-approximation shell theory      190 201 202 281 283—285 380n 382
Fixed edge      see “Boundary condition”
Flange      211 351
Fluid drop      99 100
Fluid-solid interaction      443
Foeppl theory (for membranes)      220 221 247 275
Foeppl — Karman equations      215—218 279
Follower force      74 406
Force of constraint      34 61 62 170
Force, beamshell, internal      55 (see beamshell”)
Force-kinematic relation      119 295 363
Force-momentum vector      25
Frame      see “Basis”
Frechet derivative      39 73
Free edec      2
Free edec axishell      207 211 216 218 229—232 249 269
Free edec beamshell      65 97 119 120
Free edec curved tube      359
Free edec general membrane      411 426n
Free edec general shell      470
Free edec helicoidal shell      380 382
Free-energy density      2
Free-energy density axishell      324 326 327
Free-energy density axishell modified      326
Free-energy density axishell quadratic      327
Free-energy density beamshell      142 144
Free-energy density beamshell modified      143
Free-energy density beamshell quadratic      146
Free-energy density birod      46 47
Free-energy density birod quadratic      48
Frenet formulas (for a curve)      365 406
Frequency critical      137
Frequency low      54 280 287
Frequency natural      137 239 287 446
Friction coefficient      62 172
Functional      see also “Hu — Washizu functional”; “Load functional”; “Lyapunov functional”; “Potential energy functional”)
Functional analogy      68 69 246
Functional analysis      71 73
Functional axishell      172 291 294—297
Functional beamshell      69 80 115 116 120 126 149
Functional birod      24 33—36 39 41 44
Functional curved tube      360
1 2 3 4 5 6 7 8
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