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| Villaggio P. — Mathematical models for elastic structures |
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| Предметный указатель |
Abduction, process of 4
Acceleration in continua 9
Acceleration in peeling 357
Acceleration in rods 249
Acceleration in slipping 363
Acceleration in strings 340
Adiabatic invariant, notion of 353
Adler, C.L. 283 285 654
Adrianov, I.V. 525 654
Airy stress function in plane elasticity 102 112—117 497
Airy, G.B. 102
Alembert, solution 55 338 353
Alternative, theorem of 613 615
Amerio, L. 337 654
Antman, S. 62 64 66 68 72 108 147 163 164 165 166 241 267 272 276 277 282 283 285 304 326 340 343 539 543 546 633 635 638 642 643 654 662 664
Area, change of 10
Area, element of 10
Area, element of area in rod theory 66
Aris, R. vii 654
Aristotle 100
Aron, H. 555 654
Arzela, C. 295 391
Ascoli — Arzela, theorem of 295 391
Ascoli, G. 295 391
Asymptotic expansions at the comers of a plate 499
Asymptotic expansions in deriving the shell equations 620—625
Asymptotic expansions in justifying the Foeppl — Karman equations 517—522
Asymptotic expansions in rod theory 158—161
Asymptotic expansions in solving the shell equations 635—637
Asymptotic expansions in the heavy ring 209
Averaging of displacements in rods 83 91
Averaging of loads 50 66
Averaging of the elastic moduli of a rod 132
Averaging procedure in rods 63 66—69
Averaging, method in plates with variable thickness 478
Axial vector 454
Babuska, I. 498 500 501 655
Bagemihl, F. 662
Baiocchi, C. 337 655
Balance equations for constitutively non-linear plates 541
Balance equations for membranes 368 372
Balance equations for networks 388
Balance equations for plates 454
Balance equations for plates in large strains 505
Balance equations for rods 165 166
Balance equations for shells 553 634
Balance equations for shells in the three-dimensional theory 558
Balance equations in continua 11—14
Balance equations of angular momentum 18
Balance equations of kinetic energy 18 19
Balance equations of mass 16
Balance equations of momentum 17
Balance equations on a surface of discontinuity 13 14
Balance equations, dynamical b.e. for rods 250
Balance equations, local form of 15
Ball, J. 36 655
Baluch, M.H. 581 582 659
Barnes, D.C. 237 239 655
Base vectors in a strained rod 111
Base vectors in continua 62
Base vectors in membranes 404
Base vectors in rod theory 62 108
Base vectors in shells 549
Batra, R. 44 50 655
Bauchau, O.A. 144 145 655
Bauer, L. 415 608 609 655
Beck, M. 183 245 655
Beeckman, I. 61 303
Beltrami — Michell's compatibility equations 506
Beltrami, E. 77
Bending invariance, property of the stress resultants 389
Bendsoe, M.P. 401 655
Benson, R.C. 185 655
Berdichevskii, T.L. 132 135 285 582 655
Berger's equation for the circular plate 523—525
Berger's equation in plate theory 522 523
Berger's equation, asymptotic justification of Berger's equation 525 526
Berger's equation, derivation of B.e. from Foeppl — Karman's equations 526 527 531
Berger, H.M. 246 522 655
Berger, M.S. 517 655
Berger, N. 588 655
Bernadou, M. 564 566 655
Bernoulli, D. 303 655
Bernoulli, James 5 20 61 303 306 655 656
Bernoulli, James II 459 647 656
Bessel functions as solutions of Foeppl — Karman's equations 511
Bessel functions in Berger's theory 523—525
Bessel functions in cap forming 602
Bessel functions, modified Bessel functions 414
Bessel's differential equation 222 375 523
Bessel, F.W. 375
Betti 40 656
Betti's theorem 41 42 137
Bickley, W.G. 177 656
Bieberbach, L. 386 656
Bifurcation points for nonlinearly elastic plates 546
Bifurcation points for the equilibrium of shells 608
Bifurcation points in the solutions of the elastica 172
Bifurcation points in the stability of a circular rod 245
Bifurcation points, bifurcation points according to Poincare 174
Bifurcation points, localization of 245 246
Bifurcation points, singularity theory in 281
Bifurcation points, subcritical 281
Bifurcation points, theorems on 546 639 640
Bifurcation points, transcritical 282
Billington, D.P. 530 656
Binet, J.P.M. 165
Bird-cage condition in wires 212
Bisshop, K.E. 183 656
Bliss, G. 422 656
Body as primitive notion 7
Body forces in continua 8
Boundary conditions for a thick plate 452
Boundary conditions for a thin plate 5
Boundary conditions for hyperelastic shells 642
Boundary conditions for shells 553 554
Boundary conditions of place 32
Boundary conditions of pressure 33
Boundary conditions of traction 33
Boundary conditions, hard and soft in a plate 500
Boussinesq — Cerruti solution in elasticity 5
Boussinesq — Papkovic — Neuber solution in elasticity 5
Boussinesq, J. 5 47 48 73 466 656
Brazier's effect in cylindrical shells 596
Brazier, L.G. 596
Breaking condition in the peeling of a membrane 427
Breaking condition in the peeling of a string 358
Bridge, equations of suspension bridge 328
Bromberg, E. 404 656
Bromwich, T.J. 54
Bryan, G.H. 532 656
Bucco, D. 522 656
Buckling of membranes 419
Buckling of nonlinearly elastic plates 538—546
Buckling of plates 532—535
Buckling of shells 607—620
Buckling of the elastica 169 218 219
Buckling, dynamical 259
Buckling, load 5 170
Buckling, snap bridge in rods 300
Buckling, subcritical 277 620
Budiansky, B. 246
Burridge, R. 187 190 357 360 426 427 656
Buttazzo, G. 447 449 656
Byrd, P.F. 301 656
Cables with an elastic core 216
Cables, capstan condition for 320
Cables, classical solutions for 326—328
Cables, dragging logs by 315
Cables, kinking of 195
| Cables, loops in 195
Cables, planar solutions for 305
Cables, solutions for linearly elastic cables 310
Cables, stiffening of 309—311
Calculus of variations in plates with variable thickness 491—494
Calculus of variations in the reinforcement of membranes 447 448
Calculus of variations in the weak optimization of plates 492—493
Calculus of variations in variational inequalities 403
Calculus of variations, Fundamental Lemma of 58
Calderer, Carme 635 649 654 656
Callegari, A.J. 372 395 415 655 656
Capelo, A. 337 655
Caps, Cauchy's theorem 17
Caps, forming of 561
Caps, shallow caps 404 412—414
Caps, spherical caps under hydrostatic pressure 409 414
Caps, theory of spherical caps 404—412 425 426
Carrier, G.F. 199 322 656
Carrol, M.M. 419 656
Carus, Wilson 100
Cauchy sequence in a variational problem 403
Cauchy — Kowalewsky theorem in axisymmetric membranes 423
Cauchy — Kowalewsky theorem in nonlinear rods 280
Cauchy — Riemann equations in membrane theory 369
Cauchy, A.L. 5 20 27 280 656
Cayley — Hamilton theorem 588
Cayley, A. 588
Celigoj, C. 222 656
Central inversion in plane elasticity 115
Cerruti, V. 47
Cheng, K.T. 485 486 489 656
Cheo, L.S. 532 656
Chree, C. 57 58 656
Christensen, R.M. 90 656
Christoffel symbols in shell theory 550 560 621
Christoffel, E.B. 550
Chu, C. 117 656
Chwalla, E. 224 656 657
Ciarlet, P.G. 33 34 36 37 158 517 521 564 566 621 623 625 657
Cimetiere, A. 161 657
Clapeyron theorem in optimizing plates 486
Clapeyron theorem in the reinforcement of membranes 448
Clapeyron, B.P.E. 5
Cleavage of a beam 190
Clebsch's theory of rods 202
Clebsch, A. 3 73 112 165 202 657
Clothing of a surface 385
Codazzi — Gauss equations 562
Codazzi, D. 562
Coerciveness condition in elasticity 37 38
Coerciveness condition in rods 268
Coerciveness condition in shells 621
Coffin, D.W. 535 660
Cohen, H. 640 642 657
Concavity method in the dynamics of shells 649
Configuration, notion of 7
Configuration, undistorted 23
Conformal mapping in membrane theory 370
Conformal mapping in the peeling of two membranes 428
Conformal mapping in the suturing of membranes 432
Conformal mapping, change of the boundary conditions under 371
Constitutive equations 20—31
Constitutive equations for rods 68
Constitutive equations in membrane theory 407
Constitutive equations in plate theory 455 456 479 542
Constitutive equations in shell theory 552 563 586 634
Constitutive equations in string theory 305
Constitutive equations, axioms on 21
Constitutive equations, Clebsch's constitutive equations for curved rods 202
Constitutive equations, definition 20
Constitutive equations, Lame's constitutive equations for rods 68—76
Constraints, proper and improper 225
Constraints, technological 239
Continuity of a bilinear form 38 39
Continuity, absolute, in string theory 350
Continuity, condition for rods 163
Contravariant components of a tensor 549 621
Contravariant components of a vector 62
Convex programming in membranes 399
Convex programming in networks 391
Cooke, D.W. 474 475 657
Cosserat rod, definition of 162
Cosserat surface 626
Cosserat, E. and F. 43 64 162 657
Costello, G.A. 210 212 213 215 216 657 662
Coulomb, C.A. 5 657
Courant, R. 225 495 657
Covariant components of a tensor 549 621
Covariant components of a vector 62
Cowell, R.G. 617 660
Cowper, G.R. 83 88 657
Crandall, M.G. 546 639 657
Curvature tensor 550 552
Da Peppo, D.A. 183 664
Damping in cables 314
Damping, paradoxical effect of 259
Dasek, V. 439 440 657
Day, W.A. 135 657
Day, W.B. 246 657
De Giorgi, E. 277 657
de Saint-Venant, B. 5 54 61 68 71—73 165 663
Dead load, definition of 36
Deformation gradient in continua 9
Degerate solutions 612
Delta function in the peeling of membranes 427
Delta function in the peeling of strings 357
Denman, H.H. 183 658
Density, definition of 7
Density, mathematical 12
Derived quantities 9
Destuynder, P. 158 517 657
Determinism, axiom of 21
Device, concept of loading device 44
Device, hard and soft device in loading rods 287
Diadic, product of vectors 540
Dickey, R.W. 293 298 322 372 379 404 409 411 413 422 425 509 567 572 658
Dirichlet, P.G.L. 368
Displacement, gradient 25
Displacement, vector 25
Divergence theorem in balance equations 13
Divergence theorem in presence of surfaces of discontinuity 14
Doekmeci, M.C. 146 658
Donnell's equation for cylindrical shells 618
Donnell, L.H. 618
Dowd, J.P. 204 206 660
Downs, B. 121 658
Drucker, D. 183 210 658
Duhem, P. 64 658
Duncan's functions 260
Duncan, W.G. 260 658
Dupin — Euler relations in shells 598
Dupin, C. 598
Duva, J.M. 129 658
Eccentricity vector 249
Edge effects in shells 564
Edge of regression 597
Eisenhart, L.P. 196 658
Elastic material, definition of 5
Elastic material, Green's definition of 5
Elastic moduli of Cauchy 29
Elastic moduli of Lame 26 29
Elastic moduli of Young and Poisson 31
Elastica under non-conservative loads 181
Elastica, application of the theory to manipulators 192
Elastica, heavy 208
Elastica, helical bending of 176
Elastica, problem of 168
Elastica, snapping of 177
Elastica, solution for the 5
Elastica, sustained by a couple 176
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