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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
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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