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| Villaggio P. — Mathematical models for elastic structures |
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| Предметный указатель |
Lord Rayleigh 3 224 367 443 564 647 648 663
Lorenz, H. 353
Lottati, L 259 661
Love, A.E.H. 2 47 48 54 58 71 73 80 85 86 87 89 100 102 103 106 110 114 142 145 150 165 171 176 202 204 207 219 221 248 252 254 451 455 461 466 502 547 551 552 553 555 563 583 661
Lower semicontinuous functional in membrane theory 449
Maddocks, J.H. 316 661
Magenes, E. 39 661
Maisonneuve, O. 75 661
Mansfield, E.H. 440 593 661
Mansfield, L. 199 661
Marlow, R.S. 277 654
Material description in continuum theory 8
Matkowsky, B.J. 261 663
Maximum principle for elliptic second-order equations 369
Maximum principle of Pontryagin 239
Maxwell's line for beams with nonconvex strain energy 288
Maxwell's theorem of reciprocity 99
Maxwell, J.C. 99 288
Maz'ya, V.G. 499 661
Mazumdar, J. 522 656
Mean curvature 558
Megareus, G. 437 661
Membranes under unilateral constraints 392—404
Membranes, conformal mapping in 370
Membranes, exact equations of 379—382
Membranes, existence theory for 372—379
Membranes, Foeppl's semilinear theory of 371
Membranes, Hadamard stability of 368
Membranes, Hencky's solution for 372
Membranes, maximum principle in 369
Membranes, plane 367—385
Membranes, stress resultants in 366
Membranes, theories of 366—367
Mersenne, M. 61
Metric tensor in membranes 400
Metric tensor in rod theory 62
Metric tensor in shells 550 559
Miara, B. 564 566 625 657
Michell — Prandtl instability in beams 220 221
Michell's theory for rods 76—81
Michell's theory for thick plates bent by transverse forces 462—465
Michell's theory for thick plates loaded at the boundary 460—462
Michell's transformation in plane elasticity 130
Michell, A.G.M. 5 662
Michell, J.H. 61 76 114 115 117 130 221 222 460 466 662
Milgram, A.N. 566
Mill, J.S. 4
Mindlin's theory for thick plates under shear 473
Mindlin, R.D. 59 473 662
Misyura, V. 582 655
Model, different descriptions of a 1
Model, fallacies in a x
Model, formulation of a viii ix
Model, properties of a viii
Model, qualities of a ix
Moduli of Lame 26 29
Moduli of Young and Poisson 31
Moduli, elastic of Cauchy 29
Monochromatic solutions 265
Monotonicity conditions in plates 533
Monotonicity conditions in rod theory 267
Monotonicity conditions in shells 635
Mooney's material in membranes 394 400
Mooney's material in shells 605 629 631
Mooney's material in the stability of membranes 421
Mooney's material, moduli of a Mooney's material 394
Mooney, M. 394
Mostowski, A. 664
Motion of small amplitude of a rod 263
Motion, isochoric 11
Motion, notion of 7
Motion-dependent loads 44
Mueller, I. 12 16 25 662
Mullin, M. 514 662
Nageswara, B.R. 181 662
Naghdi, P.M. 566 662
Nanson, E.J. 10 662
Narashima, R. 291 662
Navier, C.L.M.H. 5 662
Nazarov, S.A. 499 661
Necas, J. 34 657
Needleman, A. 635 662
Negron-Marrero, P.V. 543 546 654 662
Nemat-Nasser, S. 44 662
Neo — Hookean material in the stability of membranes 422
Nested sequence of functions 374
Networks, balance equations for 388
Networks, folding in itself of a 387
Networks, Servant's equations for 386
Networks, solution by iteration for 387
Networks, theory of 385—391
Neuber's theory for thick plates 468—470
Neuber's theory for thick plates under shear 466—468
Neuber, H. 5 466 467 469 496 497 662
Neumann problem in membrane theory 370
Neumann problem in rod theory 73 79
Neumann, F. 23 370 662
Neutral axis in a pretwisted rod 124
Nicholson, J.W. 90 91 656 662
Nicolai, E.L. 183 662
Nietzsche, F. 2
Niordson, F.I. 485 662
Noll, W. 8 11 20 662 665
Novozhilov, V.V. 75 662
Obstacle, problems for membranes 392—404
Obstacle, problems for strings 336
Olhoff, N. 334 485 486 489 656 662
Ono, K. 361 662
Optimization of a column 227
Optimization of a reinforced plate 486—494
Optimization of a spheroidal reservoir 441 442
Optimization of a string 331—333
Optimization of heavy membranes 437
Optimization of membranes filled by air and water 434—443
Optimization of the opening of a membrane 440
Optimization of the shape of a plate 494—498
Optimization, anomalous 237
Optimization, unconstrained 237
Optimization, weak optimization of a plate 491
Papkovic, P.F. 5 466 662
Parallelogram law in proving the existence of a minimum 403
Parker, D.F. 138 662
Particle, Notion of 7
Pastrone, F. 640 642 657
Payne, L.E. 445 600 649 659 660 662
Pearson, K. 27 665
Peeling of a membrane 427
Peeling of a tape 187 357—361
Peirce, C.S. 4 663
Permanence of matter, axiom of 9
Perturbation, regular 242
Perturbation, singular 292
Phase portrait in shell theory 644
Phase portrait in the dynamics of a spring 341
Phase portrait, center in 265 652
Phase portrait, saddle point in 266 652
Phillips, J.W. 210 212 213 215 216 657 663
Physical admissibility, conditions of physical admissibility in rods 268
Pierce, J.F. 282 654
Piola, G. 28
Pipkin, A.C. 385 388 390 663
Pitkaeranta, J. 500 654
Planar solutions for rods 203
Planar solutions for strings 329
Plane stress in rods 81
Plane stress, generalized 81
Plates under hydrostatic load 535—538
Plates with variable thickness 477—484
Plates, Berger's equation for 522—523
Plates, boundary conditions for thick 470 476
| Plates, buckled states of plates in nonlinear elasticity 538—546
Plates, equilibrium equations of 454
Plates, Foeppl — Karman theory for 501—522
Plates, Germain — Lagrange equation 457
Plates, influence of shear in thick 473
Plates, influence of shear in thin 470
Plates, Kirchhoff's boundary conditions 458
Plates, Michell's theory for thick 460—465
Plates, optimization of 485—498
Plates, paradoxes for 498—501 535—538
Plates, reinforced by ribs 482
Plates, Reissner's theory of nonlinear circular 470 527—529
Plates, stress resultants in 452
Plates, theories of 451—546
Plates, total potential energy for thick 476
Plates, wrinkling of 531—535
Plaut, R.H. 259 663
Pochhammer, L. 57 58 663
Poincare inequality in Foeppl — Karman's theory 515
Poincare inequality in the treatment of strings 350
Poincare, J.H. 174 280
Poisson's ratio 31
Poisson, S.D. 31 458
Polar decomposition, theorem of 10
Polar media 64
Polyconvexity condition in elasticity 36
Pontryagin's maximum principle 239
Pontryagin, L.S. 239
Prager, W. 129 663
Prandtl function in torsion 121
Prandtl, L. 221 222 224 663
Primitive concepts in mechanics 7
Production of a field at distance or intrinsic 7
Production of a field of internal energy 19
Protter, M.H. 369 663
Prouse, G. 337
Quadratic functionals in minimum problems 403
Quasistatic motion of a tape 366
Rabinowitz, P.H. 546 639 657 663
Radial stress distribution 114
Rankine, W.J.H. 309 345
Raoult, A. 161 657
Rasmussen, S.H. 334 662
Rayleigh conjecture on membranes 443
Rayleigh quotient 224
Rayleigh quotient in membrane theory 444
Rayleigh quotient with Lagrangean multipliers 235
Reference configuration, definition of 7
Regularity of the solutions of Foeppl — Karman's equations 517
Regularity of the solutions of variational inequalities 404
Reinforcement 51
Reinforcement, optimization of the 446—450
Reiss, E.L. 261 298 372 395 415 514 532 608 609 655 656 663
Reissner's theory for circular plates in large strains 527—529
Reissner's theory for plates under bending and shearing 470
Reissner's theory, exact solutions in 530
Reissner, E. 404 470 472 527 530 567 663 665
Reissner, H. 581
Rellich theorem in plate theory 517
Rellich theorem in shell theory 566
Rellich, F. 517
Riemann problem 347
Riemann, B. 339 347
Ritz, W. 402
Rivlin, R.S. 187 388 390 663
Robinson, R.R. 664
Rods in large strains 65 138—161
Rods under concentrated loads 100—106
Rods under general loads 175—184
Rods with nonconvex strain energy 285—288
Rods, annular, against a wall 185
Rods, bounds on the strain energy of 125—129
Rods, buckling of 169 170
Rods, circular rods under hydrostatic pressure 239 240
Rods, constitutive equations for 68
Rods, director theory of 5 64 162
Rods, dynamical problems in 51—60 248—266
Rods, dynamics in large strains of 246—248 289—302
Rods, effect of damping on 259
Rods, elastica under distributed loads 208
Rods, elastica under follower forces 181 192 193
Rods, generalized twist of 135
Rods, geometrical definition of 62
Rods, hyperelastic 68 272
Rods, influence of constitutive non-linearities on 267 268
Rods, influence of pretwists on strained 118—125 154
Rods, influence of the curvature on 106—117 298—300
Rods, initially twisted 117—125
Rods, Kirchhoff's problem for 167 267—273
Rods, linearly elastic 70—76
Rods, methods of asymptotic expansion in 158—161
Rods, Michell's theory of 76—81
Rods, minimum properties of the solutions of 73—76
Rods, naturally curved 202—216
Rods, Saint-Venant's solutions for 68—73
Rods, stability of 218—248
Rods, strain energy for curved 134
Rods, three-dimensional theory of 64—69
Rods, Timoshenko's correction for 81—93
Rosen, A. 118 120 141 144 154 663
Rotation, infinitesimal 26
Routh, E.J. 306 663
Russel, B. 4 663
Rychter, Z. 125 131 663
Saint-Venant principle 5 73 457
Saint-Venant — Beltrami equations 77 78 102
Sanchez-Palencia, E. 624 663
Sapondzhyan, O.M. 498 664
Sawyers, K.N. 187 664
Scapolla, T. 501 654
Schaeffer, D.G. 281 659
Schmidt, R. 90 183 527 656 664
Schwarz inequality 120 295
Schwarz, H.A. 120
Schwerin, E. 531 664
Second fundamental form in shell theory 561
Sectorial area in Vlasov's theory of beams 95
Sectorial moment of inertia in Vlasov's theory of beams 97
Seidel, W. 662
Semi-inverse method 73
Separation of variables, method of 291
Separatrix in the phase plane 265
Serret, J.A. 51
Servant, M. 385 664
Sewell, M.J. 44 664
Shearer, M. 344 664
Shell theories, balance equations 553
Shell theories, boundary conditions 553 554
Shell theories, buckling in 607—620
Shell theories, dynamical problems in 647—653
Shell theories, estimates for tubes 583—585 600—603
Shell theories, estimates on the stresses 586—589
Shell theories, exact solutions 593—607
Shell theories, existence theory 564—567
Shell theories, Geckeler's approximation 578
Shell theories, hyperelastic shells 605
Shell theories, Kirchhoff — Love's hypothesis 551
Shell theories, linearized extensions and changes of curvatures 551
Shell theories, Reissner's theory 567 568
Shell theories, shallow shell theories 573—577 625
Shell theories, solvability of Reissner's equations 568—573
Shell theories, strains in 550
Shell theories, strains in the three-dimensional theory 557
Shell theories, stress resultants defined according to the three-dimensional theory 558 559
Shell theories, stress resultants in 548
Shih, K.G. 638 664
Shock in strings 340
Shock on a bar 51—60
Shock, absorber 342 448
Shock, approximate theory of 52 53
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