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Villaggio P. — Mathematical models for elastic structures
Villaggio P. — Mathematical models for elastic structures



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Название: Mathematical models for elastic structures

Автор: Villaggio P.

Аннотация:

During the seventeenth century, several useful theories of elastic structures emerged, with applications to civil and mechanical engineering problems. Recent and improved mathematical tools have extended applications into new areas such as mathematical physics, geomechanics, and biomechanics. This book offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures that are used to solve practical problems with particular emphasis on nonlinear problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 688

Добавлена в каталог: 26.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Shock, conditions in continua      18
Shock, contact discontinuities in strings      339
Shock, Herrmann — Mindlin three-dimensional theory      59
Shock, influence of inertia on      53
Shock, Pochhammer — Chree's extension      57
Shock, Saint-Venant's dynamical theory      54—57
Shooting method in buckling of rods      280
Shooting method in membrane theory      372
Shooting method in rod theory      280
Signorini's method in elasticity      35
Signorini, A.      35 664
Simmonds, J.G.      90 91 129 199 530 600 602 629 658 659 661 662 664
Simple materials, definition of      8 9 21
Simpson, A.      312 315 664
Simulation in science      viii
Slack regions in networks      390
Slack variables in a rectangular membrane over an obstacle      401
Slack variables in optimizing reinforced plates      487 490
Slack variables in rod optimization      235
Slipping of a tape or a cylinder      361
Snapping of a membrane      415
Snyder, J.M.      193 195 666
Sobolev embedding theorem in membrane theory      404
Sobolev embedding theorem in shell theory      576
Sobolev spaces, $L^{p}, W^{1, p}, W^{2, p}$, in nonlinear elasticity      36 37
Sobolev spaces, $W^{1, 4}$, in treating Foeppl — Karman equations      516
Sobolev spaces, $W^{1, \alpha}$ in rod theory      277
Sobolev, S.L.      277
Sodhi, D.S.      596 598 664
Solids, definition of crystalline      23
Solids, definition of isotropic      23
Sommerfeld, A.      3 664
Spaghetti problem and its reverse      199
Spatial description      8
Stability of a bubble      419—420
Stability of a circular plate      532—535
Stability of a membrane      415
Stability, infinitesional of a beam      219 288
Stability, neutral of a beam      288
Stampacchia, G.      402 403 404 661
Starosel'skii, L.A.      135 655
Statically admissible stress field in the rod theory      74 126
Steele, C.R.      561 664
Stephen, N.G.      88 664
Sternberg, E.      73 75 664
Stevin, S.      303 664
Stoker, J.J.      265 404 532 567 656 664
Stokes, G.G.      3 20 30 100 664
Strain energy function for a developable surface      596
Strain energy function for the helical strip      594
Strain energy function in a nonlinear spring      341
Strain energy function in Berger's plate      522
Strain energy function in cables      196
Strain energy function in cables under hydrodynamic forces      312 313
Strain energy function in continua      27
Strain energy function in curved rods      132
Strain energy function in membranes      381
Strain energy function in rods      124—137
Strain energy function in shells      626 629 650
Strain energy function in strings      348
Strain energy function in taut cables      311
Strain energy function, nonconvex in bars      285—288
Strain tensor in Foeppl — Karman's theory      503
Strain tensor in Kirchhoff's theory of rods      167 168
Strain tensor in membranes      380 400 405 416
Strain tensor in nonlinearly elastic plates      539
Strain tensor in plates      455
Strain tensor in Reissner's plate      471
Strain tensor in rods      129 165
Strain tensor in shells      550 551 560 633 642
Strain tensor in strings      304
Strain tensor in the director rod theory      165
Strain tensor in the three-dimensional theory of shells      556
Strain tensor, Cauchy — Green, right and left      22 25 649
Strain tensor, extensional in shells      623 648
Strain tensor, Green — Saint-Venant's      161
Strain tensor, infinitesimal      26
Stress function in plane elasticity      102
Stress function in the suturing of membranes      431
Stress principle of Cauchy in continua      8
Stress principle of Cauchy in rods      165
Stress resultants for nonlinearly elastic rods      70
Stress resultants for thin walled beams      96
Stress resultants in cables      304
Stress resultants in linearly elastic rods      70—72 78—81 88—91
Stress resultants in membranes      366
Stress resultants in networks      386
Stress resultants in nonlinearly elastic plates      541
Stress resultants in plane plates      451 452
Stress resultants in pretwisted beams      124
Stress resultants in Reissner's plates      471
Stress resultants in rods      66 67
Stress resultants in shells      548 633
Stress resultants in the director theory of rods      165
Stress resultants in the presence of large strains      143
Stress tensor of Cauchy in continua      17
Stress tensor of Lagrange in membranes      381
Stress tensor of Piola — Kirchhoff      28
Stress tensor of Piola — Kirchhoff in shells      561 589 631 644
Stress tensor of Piola — Kirchhoff's in plates      541
Stress tensor, converted in rods      64
Stress tensor, material or second of Piola — Kirchhoff      21 37
Stress vector, Cauchy's in rods      65 147
Stress vector, Piola — Kirchhoff's in rods      65 66 147
Stretching tensor in continua      27
Strings in large strains      322—326
Strings under hydrostatic loads      312 313 331
Strings, equilibrium equations for      306—308
Strings, existence theory of      324
Strings, optimization of      331—333
Strings, peeling and slipping of      357—365
Strings, rotating      348—352
Strings, stiff or soft      351 352
Strong ellipticity condition for plates      543
Strong ellipticity condition for shells      565 645
Strong ellipticity condition in three-dimensional elasticity      33
Structure, incorrect theories of      x
Structure, model of      ix
Sturm theorem of comparison      180 375
Sturm, C.      180
Substantial particle, notion of      7
Suturing of plane membranes      429—433
Synge and Prager's method in beams      129
Synge, J.L.      129 600 663 664
Szabo, L      3 53 54 459 577 664
Szeri, A.J.      643 664
Tabarrok, B.      312 315 664
Tachau, H.      210 658
Tadjbakhsh, I.      230 240 664
Tait, P.G.      3 28 660
Tamai, T.      225 664
Tang, Y.K.      582
Tarski, A.      vii 664
Taylor, B.      546
Tchebychev nets, theory of      385
Tchebychev polynomials in the treatment of elastica      184
Tchebychev, P.L.      183 385 665
Telega, J.J.      484 661
Temperature, notion of      7
Tevendran, V.      334 665
Thermodynamics, first law of      19
Thermoelastic materials, general      22
Thermoelastic materials, linear      31
Thin-walled beams, Vlasov's hypothesis      95
Thin-walled beams, Vlasov's integrodifferential equations for      99
Thin-walled beams, Vlasov's theory of      5 93—100
Third fundamental form in shell theory      561
Thurston, G.A.      606 665
Tie-rods      204 205
Tielking, J.T.      399 659 665
Timoshenko, S.      81 665
Ting, L.      428 665
Todhunter, I.      27 665
Toepliz, O.      581
Tolke, F.      435 665
Torsion-flexure axes in a beam      108 141 164
Torsional rigidity of a rod      72
Torsional rigidity, generalized      135
Total energy of a beam      74
Total energy of a cable      312
Total energy of a membrane      423
Total energy of a spherical shell      652
Total potential energy in a beam      74 119
Total potential energy in a cable      312
Total potential energy in a hyperelastic body      36
Total potential energy in a pretwisted beam      119
Total potential energy in a taut cable      312
Total potential energy in Berger's plate      522
Total potential energy of a buckled rod      173
Total potential energy of a buckled shell      617
Total potential energy of a hyperelastic shell      642
Total potential energy of a plate with variable thickness      480
Total potential energy of a shallow membrane      416
Total potential energy of a thick plate      475
Total potential energy of an inflated membrane      401 423
Toupin, R.A.      9 164 165 665
Transport theorem in continua      13
Transport theorem in the presence of a singular surface      14
Trosch, A.      245 665
Truesdell, C.      4 5 9 11 20 30 61 64 135 164 165 303 555 665
Truskinovkii, L.      285 656
Trusses, Michell's theory of      5
Tsien, H.S.      415 418 419
Tutek, Z.      161 657
Twists, initial twists in beams      117—125 154
Unilateral constraints in membranes      392—404
Unilateral constraints in networks      390
Unilateral constraints in strings      336—339
Unimodular transformation      23
v. der Waals, J.D.      288
Vailati, G.      5 6
Variational derivation of the dynamical equations of a beam      253 254
Velaria, problem of      303
Velocity, definition of      9
Velocity, transport velocity, in dynamical peeling      363
Venkateswara, G.R.      181
Verma, G.R.      331 665
Vielsack, P.      224 605
Virga, E.      8 662
Viscosity criterion      347
Vlasov, V.Z.      5 93 95 98 555 556 558 574 665
Vogehus, M.      472 482 662
Voigt, W.      73 665
Volterra integral equation, with singular kernel      284
Volterra, V.      284
Volume, element of      11
Vorovich, I.I.      573 665
Wang, C.-Y.      176 177 208 255 256 665
Wang, C.M.      334 665
Wang, S.F.      177 659
Warping function in beams      118 139
Watson, L.T.      208 256 665
Waves of rarefaction      346
Waves, definition of      11
Waves, longitudinal      346
Waves, Riemann's problem for      347
Weak formulation of a boundary value problem      38
Weakly closed functional in rod theory      277
Weakly lower semicontinuous functional in plate theory      492
Weakly lower semicontinuous functional in rod theory      277
Weinberger, H.F.      3 292 308 368 369 370 371 445 662 663 666
Weiss, P.      663
Wempner, G.      110 666
Wilkes, E.      x
Williams, K.A.J.      617 660
Wilson, J.M.      193 195 666
wires      210—218
Wires, bird-cage condition for      212
Wires, theory of suspended      204
Wittgenstein, L.      1
Worch, G.      81 102 112 583 666
Work consistent displacements      91
Work, done by the inertial forces      249
Wrinkled states of plates      532—535
Wu, C.H.      429 433 666
Yabuta, T.      195 198 666
Yang, W.H.      392 399 659 666
Yoshizawa, N.      195 198 666
Young's modulus      31
Young, A.E.      204
Young, T.      31
Zachman, D.      243 666
Zerna, W.      582 659
Ziegler, H.      259 666
Zveriaev, E.M.      563 666
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