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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
Elasticity, "rari constant" theory of      5
Elasticity, existence theorems in      31—44
Elasticity, Navier's equations of      5
Eliseyev, V.V.      248 250 658
Elishakov, I.      259 661
Elliptic integrals in cable theory      316
Elliptic integrals in Kirchhoff's problem      169
Elliptic integrals in the optimization of membranes      437
Elliptic integrals in the solution of Foeppl — Karman's equations      508
Elliptic integrals in the solutions of the elastica      169
Elliptic integrals of the second kind      183
Elongation of a string      304
Emde, F.      170 172 173 660
Environment in continua      9
Equilibrium, process close to      25
Ericksen, J.L.      5 9 10 44 64 75 141 267 287 555 626 658
Error in science      5 6
Euclidean transformations      21
Euler $\Gamma$ function      442
Euler angles in rods      142 164 218
Euler differential equation      236
Euler load under improper constraints      226
Euler load, definition of      170
Euler variational equations for hyperelastic shells      642
Euler variational equations for reinforced membranes      449
Euler variational equations for thick plates      476
Euler variational equations in beams with nonconvex strain energy      286
Euler variational equations in rods theories      119 153 236
Euler variational equations in shallow membranes      417
Euler, L.      5 13 20 61 167 168 320 442 555 598 647 658
Eversion of a cylindrical shell      646
Expansion, coefficient of      31
Faber — Krahn inequality for membranes      443
Faber, G.      443 658
Faedo — Galerkin method in buckling theory      247
Faedo — Galerkin method in elastodynamics      39
Faedo, A.      39
Farshad, M.      329 658
Feng, W.W.      399 659 665
Fibers, envelope of      387
Fibers, inextensible in a net      385
Fibers, tension in      388
Field, definition of      11
Fillunger, P.      113 659
First fundamental form in shells      550 555
First fundamental form in the three-dimensional theory of shells      555
First fundamental form of a developable surface      597 604
First fundamental form of a surface      386 503
First integral for a curved rod      204
First integral for the equations of a cylindrical shell      604
First integral in Kirchhoff's problem of snapping      301
First integral of Foeppl — Karman equations      508
First integral of the equations of elastica      175
Fischer, D.H.      4 659
Fit region, notion of      8
Flamant, M.      101
Flexural rigidity of a beam      71
Flexural rigidity of a plate      456
Flexural rigidity of a shell      552
Fluid, definition of      23
Flux, surface flux      12
Foeppl — Karman's theory, derivation of      501—506
Foeppl — Karman's theory, existence theory for a noncircular plate      514—517
Foeppl — Karman's theory, first integral for the equations      508
Foeppl — Karman's theory, objections to      4
Foeppl — Karman's theory, solution for the circular plate      509—514
Foeppl, A.      4 100 371 659
Folding, folding back of a net      387
Follower load in dynamical buckling      259
Follower load in the elastica      181
Follower load, Beck's paradox      183
Follower load, definition of      181
Four Vertex Theorem      241
Fourier series in beams theories      104 105
Fourier series in the dynamics of membranes      425
Fourier, J.B.      20
Frame indifference, application to rods      162
Frame indifference, axiom of      21
Fraser, W.B.      246 659
Frechet, M.      600
Frenet — Serret formulae      151 163 244
Frenet, J.F.      151
Friction in cables      316—322
Friction in the motion of a mass point      340
Friction in the peeling of a string      359 363
Friedman, M.D.      301 656
Friedmann, P.      141 144 663
Friedrichs, K.O.      532 659
Frobenius method in ordinary differential equations      440
Frobenius, G.F.      440
Funicular curve of a string      329
Galerkin method in buckling theory      247 260
Galerkin method in elastodynamics      39
Galerkin, B.      39
Galilei, G.      303 659
Galileian invariance in shells      626
Gauss curvature      558
Gauss equations for a surface      389
Gauss, C.F.      389 562
Geckeler, J.W.      5 103 564 578 659
Germain — Lagrange equation for the plate plane      457
Germain, Sophie      457 459 659
Geymonat, G.      161 657
Goldberg, J.E.      581 582 659
Golubitsky, M      281 659
Gordienko, B.A.      150 659
Green's function for an axisymmetric membrane      419
Green's function for rotations      43
Green's function for the circular Foeppl — Karman plate      511
Green's function for the dilation      43
Green's function for the Laplace operator      370
Green's theorem for plates with variable thickness      482
Green, A.E.      167 267 582 659
Green, G.      5 20 37
Greenhill, A.G.      5 256 259 659
Gurtin, M.      454 581 659
Hadamard stability, counterexample in membranes      368
Hadamard, J.      368
Hall, H.M.      210 659
Hamilton principle in beams in large strains      153
Hamilton principle in membrane dynamics      423
Hamilton principle in rods      290
Hamilton principle in shock models      58
Hamilton, W.R.      58 153
Hamiltonian function for shells      643
Hamiltonian system in rod theory      283
Hammersley, J.M.      vii 659
Hartshorne, C.      663
Healey, T.J.      348 659
Heat equation, similarity of heat equation with the taping equation      365
Heat supply, notion of      19
Heat, flux      19 22
Heat, internal production of      8
Heijden, A. v.      90 665
Helical deformation in the bending of elastica      176
Helical deformation of a prism      141
Helical strips, exact solution for      593—596
Helicoidal filaments in a pretwisted rod      122 123
Hellinger — Toepliz — Reissner, variational principle      581
Hellinger, E.      581
Helmholtz, H.L.F.      472
Hencky, H.      372 524 659
Herrmann, G.      59 672
Hertz, H.      2 3 5
Hessian matrix for hyperelastic rods      272
Hilbert space, $H^{1}$, in membranes      403
Hilbert space, $H^{1}, H^{2}$, in plates      492
Hilbert space, $H^{1}, H^{2}$, in shells      565 574
Hilbert space, $H^{1}_{0}, H^{1}$      38 337
Hilbert space, $H^{2, p}$      404
Hilbert space, $L^{2}$ and $H^{2}_{0}$ in shell theory      515
Hilbert space, Hilbert subspace of inextensional displacements      624
Hilbert, D.      38 225 495 657
Hoelder inequality in the reinforcement of a membrane      449
Hoelder, L.O.      449
Hong, C.H.      144 145 655
Hooke, R.      303 659
Hooks, theory of      113
Horgan, C.O.      600 659
Hruska, F.H.      210 659
Hsu, S.B.      177 392 659
Huang, N.C.      216 399 659
Huddleston, J.V.      204 206 660
Hugoniot, P.H.      345
Hunt, G.W.      617 660
Huygens, C.      303
Hydrodynamics forces on a cable      312 313
Hyperelastic material in plates      478 479
Hyperelastic material in rods      272
Hyperelastic material in shells      642 644
Hyperelastic material, definition of      27
Hysteresis, loop in nonlinear beams      288
Impact of a string against an obstacle      337—339
Impact, longitudinal on a bar      51—60
Imperfections in shells      610
Implicit function theorem in rod stability      242
Inertia tensor      249
Initial conditions in elastodynamics      33
Irvine, H.M.      307 309 311 315 660
Isaacson, E.      635 660
Isocoric motion      11
Isocoric, isocoric deformation of a hollow sphere      649
Isotropic function      24
Isotropic material      23 268
Iteration procedure in buckling of shells      613
Iteration procedure in net theory      387
Iteration procedure in semilinear membranes      372
Iteration procedure in shell theory      606
Jacobi polynomials      146
Jacobi, K.G.J.      146
Jacobian determinant      10
Jacobian determinant, condition for positive definiteness in shells      633
Jacobian determinant, time derivative of      13
Jacobian elliptic functions in Kirchhoff's problem      172
Jacobian matrix for nonlinear membranes      381
Jahnke, E.      170 172 173 660
John, F.      559 586 587 660
Jones, R.      522 656
Jordan, C.      146
Jorgensen, L.      434 440 660
Jump conditions in string theory      339 345
Jump conditions, across a surface of discontinuity      14
Karman, Th. v.      4 100 414 418 419 660
Kauderer, H.      291 660
Keller, H.B.      608 609 610 655 660
Keller, J.B.      187 190 227 230 316 331 357 360 426 427 656 660 661 664 665
Kerr, A.D.      535 660
Kinematically admissible displacement field in the rod theory      125 126
Kirchhoff's approximation in the existence theory of Kirchhoff's problem      293—298
Kirchhoff's approximation in the treatment of nonlinear rods      289
Kirchhoff's boundary conditions for plates      5 458
Kirchhoff's hypothesis for constitutively nonlinear rods      267 268
Kirchhoff's hypothesis for Cosserat rods      166 167
Kirchhoff's hypothesis for hyperelastic rods      267
Kirchhoff's hypothesis for shells      551 628
Kirchhoff's hypothesis in curved rods      135
Kirchhoff's hypothesis in rods under large strains      138
Kirchhoff's hypothesis in the rod theory      106
Kirchhoff's hypothesis, generalized      640
Kirchhoff's hypothesis, removing Kirchhoff's hypothesis      267 628
Kirchhoff, G.      x 5 61 167 176 289 660
Kneser, A.      336 662
Knops, R.J.      649 660
Knots      212
Knots, sheepshank      318
Knots, square      317
Knowles, J.K.      73 75 664
Kohn, R.V.      472 482 662
Koirnn, H.      662
Koiter, W.T.      625 660 665
Kojma, N.      195 198 666
Kolosov, G.V.      5 660
Korman, T.      581 659
Korn inequality in shell theory      574
Korn, A.      40 660
Kotchine, K.N.E.      15 660
Kowalewsky, Sonia      280
Krahn, E.      443 661
Krein, M.G.      239 661
Kronecker, L.      247 549
Kunoh, T.      215 661
Ladezeve, P.      589 661
Lagrange multipliers in beam optimization      234—237
Lagrange multipliers in optimizing reinforced plates      487 490
Lagrange multipliers in shell theory      642
Lagrange multipliers in strings      348
Lagrange, G.L.      303 304 457 459 661
Lagrangean function for shells      643
Lamb, H.      103 207 661
Lame, G.      5
Landau, L.D.      3 661
Laplace operator in membrane theory      368
Laplace operator in the equations of linear elasticity      38 39
Laplace, P.S. de      368
Lateral motion of the particles of a beam      252
Lateral motion of the particles of a beam in large strains      255
Lauricella, G.      40 661
Laws, N.      167 267 659
Lax, P.D.      566
le d'Alembert, J.R.,      55 303 353 651 657
Le Dret, H.      161 657
Lebedev, L.P.      573 665
Leech, C.M.      215 661
Legendre integral      436
Legendre polynomials in buckling of shells      611
Legendre polynomials in rod theory      146
Legendre polynomials in shell theory      569 639
Legendre transformation      283
Legendre — Hadamard condition      33
Legendre, A.M.      283
Leibniz, G.W.      303
Leko, T.      90 656
Levine, H.A.      649 660 665
Levinski, T.      484 661
Levinson, M.      90 474 475 657 661
Lewy      403 404 661
Libai, A.      600 602 629 661
Lifschitz, E.M.      3 661
Linder, F.      578 661
Linearization of Foeppl — Karman's equations      606
Linearization, equivalent      247
Lions, J.L.      39 402 661
Lipschitz condition to define inextensibility      391
Lipschitz, R.O.S.      391
Littlewood, J.E.      353 661
Load, branching in buckling of shells      614
Load, configuration dependent      44 181
Load, dead      36
Load, follower      44 481
Load, hydrostatic on rods      240 273
Load, hydrostatic on strings      313
Load, imperfect in shells      610
Load, motion dependent      44
Loading device, soft and hard in beams      287
Loading device, theory of      5 44—51
Local action, axiom of      21
Lods, V.      625 657
Loesch, F.      170 172 173 660
Logic in mechanics      10
Lord Kelvin, (W. Thompson)      2 3 5 28 660
1 2 3 4
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