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| Villaggio P. — Mathematical models for elastic structures |
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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  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,  , in membranes 403
Hilbert space,  , in plates 492
Hilbert space, , in shells 565 574
Hilbert space,  38 337
Hilbert space,  404
| Hilbert space,  and  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
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