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Smirnov A.L. — Asymptotic Methods in the Buckling Theory of Elastic Shells
Smirnov A.L. — Asymptotic Methods in the Buckling Theory of Elastic Shells

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Название: Asymptotic Methods in the Buckling Theory of Elastic Shells

Автор: Smirnov A.L.

Аннотация:

This book contains solutions to the most typical problems of thin elastic shells buckling under conservative loads. The linear problems of bifurcation of shell equilibrium are considered using a two-dimensional theory of the Kirchhoff–Love type. The explicit approximate formulas obtained by means of the asymptotic method permit one to estimate the critical loads and find the buckling modes.

The solutions to some of the buckling problems are obtained for the first time in the form of explicit formulas. Special attention is devoted to the study of the shells of negative Gaussian curvature, the buckling of which has some specific features. The buckling modes localized near the weakest lines or points on the neutral surface are constructed, including the buckling modes localized near the weakly supported shell edge. The relations between the buckling modes and bending of the neutral surface are analyzed. Some of the applied asymptotic methods are standard; the others are new and are used for the first time in this book to study thin shell buckling. The solutions obtained in the form of simple approximate formulas complement the numerical results, and permit one to clarify the physics of buckling.


Язык: en

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 347

Добавлена в каталог: 27.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Bending, infinitesimal surface      63
Boundary condition, additional      161
Boundary condition, clamped edge      14 17 18
Boundary condition, clamped group      165 168
Boundary condition, free edge group      165 168
Boundary condition, geometric      63 64
Boundary condition, homogeneous      42
Boundary condition, main      161 163 207 217
Boundary condition, Navier      18 53
Boundary condition, non-tangential      168 226 251 252 261 265 301
Boundary condition, self-adjoint      71
Boundary condition, separation      151 163 168
Boundary condition, simple support      17 18 48 53 122 154 212
Boundary condition, simple support group      165 168
Boundary condition, special group      168 171
Boundary condition, tangential      166
Boundary condition, weak edge      54
Boundary condition, weak support      23
Boundary condition, weak support group      165
Boundary value problem, "on spectrum"      138 153
Coefficient, Lame      5
Effect, Dubjaga — Karman — Brazier      91
Eigensize      227 230 233 239 245 261 264—266
Energy, potential      34 35 38
Energy, potential, additional      45
Energy, potential, extension      34
Energy, potential, of tangential deformation      52
Energy, potential, under bending      52
Equation, Volterra      228
Equation, Weber      107
Equilibrium state      37 39—41
Equilibrium state, adjacent      39 42 45
Equilibrium state, axisymmetric      40
Equilibrium state, basic      39
Equilibrium state, bifurcation      39
Equilibrium state, branching      39
Equilibrium state, buckling      39
Equilibrium state, non-axisymmetric      40
Equilibrium state, seconary bifurcation      40
Equilibrium state, stability analysis      37
Equilibrium state, stable      37 39 40
Equilibrium state, unstable      39 40
Force, Archimedean      267
Force, generalized      15—17
Force, principal vector      26
Formula, Euler      58 108
Formula, Grashof — Bress      61 246 247
Formula, Lorenz — Timoshenko      57 123 272 314 316
Formula, Southwell — Papkovich      60 144 145
Formula, Southwell — Timoshenko      59
Function, Airy      235 236 289 294
Function, fast varying      303
Function, slowly varying      63 303
Function, weakly increasing with differentiation      13
Function, weakly varying      42
Gaussian curvature      103 104
Gaussian curvature, alternating      66 216 234
Gaussian curvature, close to zero      24
Gaussian curvature, negative      23 54 64 65 69 209 211 215 216 218 231 237 245 261 269 305 307 309 310
Gaussian curvature, not small      215
Gaussian curvature, positive      215 245
Gaussian curvature, zero      23 54 70 133 187 215 269 305 306 310
Generatrix, weakest      70 91 93 95 98 102 104 105 119 122 135 136 139 140 144—147 152 175 177 181—183 185 194—198 202
Hypotheses, Kirchhoff — Love      12 19 29 45
Index of variation      19 22
Index of variation, partial      23 24
Kronecker delta      115
Line, weakest      70 131 133 210
Load, axial compression      20 21 23 34 86 101 108 109 122
Load, axial compression, non-homogeneous      103 111 122
Load, axial force      40 70 79 84—86 98 109
Load, axisymmetric      70
Load, bending moment      98
Load, body      38
Load, boundary      20 47
Load, combined      61 70 84 85 88 99 102 119
Load, conservative      37
Load, critical      20 37 39—42
Load, critical, asymptotically double      86
Load, critical, close      70
Load, critical, double      80
Load, critical, lower      41
Load, critical, sensitivity      57 127
Load, critical, tetra-multiple      129 148
Load, critical, upper      41 42 51 52 70
Load, dead      43
Load, designed      41
Load, edge      16 26 37 131
Load, edge, external      26
Load, external      38
Load, external homogeneous      180
Load, follower      14 43 44
Load, follower, normal      44
Load, follower, surface      43 44
Load, moment, bending      109
Load, moment, torsional      79 86
Load, non-conservative      38 44
Load, normal      40
Load, one-parametric      50
Load, parameter      50
Load, pressure, external      131
Load, pressure, external homogeneous      40 119 145 146 185
Load, pressure, external normal      213
Load, pressure, homogeneous      84 86
Load, pressure, hydrostatic      11 38
Load, pressure, internal      61 81 82 101 103 187 191 192
Load, pressure, normal      44 85
Load, pressure, normal homogeneous      81
Load, static      37
Load, static, conservative edge      38
Load, static, conservative surface      38
Load, surface      14 26 45
Load, surface, dead      44 45
Load, surface, external      11 20 35 79
Load, surface, tangential      29
Load, torsion      213
Load, wind      26
Method, Bubnov — Galerkin      91 146 147 198
Method, energy      49 62
Method, Goldenveizer      2
Method, Lagrange      37
Method, Maslov      3 70
Mitred joint pipe      147
Moment, bending      23
Moment, principal      26
Parallel, weakest      69 79 81—84 87—89 161 295
Pit      121 128 130
Pit, amplitude      127
Pit, center of      127
Pit, depth      114 121 127
Pit, domain      129
Pit, inclination      127
Pit, inclination angle      114
Pit, phase      127
Pit, size      114
Point, bifurcation      39 40
Point, turning      71 72
Point, weak      111 122
Point, weakest      70—72 103 112 115 119—123 128 129 131 163
Polynomial, Hermite      74 125 140
Problem, Sturm — Liouville      223 228
Relations, Codazzi — Gauss      8 65 88
Relations, constitutive      7 12 17 19 20 22 25 27 33
Relations, Novozhilov — Balabukh      13
Shell in a liquid      253
Shell of revolution      20 21 23 25 30
Shell with imperfections      32 41 42 47 48
Shell with slanted edges      70
Shell with variable thickness      133
Shell, closed      133
Shell, conic      26 70 133 135 143 158 176 180 183 200 203
Shell, conic, circular      183 185
Shell, conic, straight circular      199
Shell, conic, truncated      185
Shell, convex      111 115 133 209
Shell, convex, shallow      49
Shell, cupola      245 250
Shell, cylindrical      21 26 32 33 111 122 128—130 133 135 143 144
Shell, cylindrical, cantilever      146
Shell, cylindrical, circular      33 122 129 143—146
Shell, cylindrical, elliptic      104 148 196
Shell, cylindrical, long      33 34
Shell, cylindrical, moderate length      20 147
Shell, cylindrical, non-circular      32 33 70 122 133 145 147
Shell, elliptic      82—86 88 89 119 122 148
Shell, elliptic, oblate      82 90
Shell, elliptic, prolate      82 119
Shell, elliptical      291 296
Shell, elliptical, oblate      291
Shell, nearly conic      203 204 207 213
Shell, nearly cylindrical      203 213
Shell, non-closed      140
Shell, reinforced      187
Shell, shallow      31
Shell, spherical      56 57 80
Shell, toroidal      234
Stability criterion, bifurcation      37
Stability criterion, dynamic      37
Stability criterion, Euler      37 48
Stability criterion, limit point      37
Stress-couple      11 35
Stress-couple, vector      11 35
Stress-resultant      11 15 16 35
Stress-resultant, hoop      80 85
Stress-resultant, membrane      29
Stress-resultant, projection      16
Stress-resultant, shear      22
Stress-resultant, vector      11 35
Stress-strain state      20 46
Stress-strain state, additional      133
Stress-strain state, chacteristic      20
Stress-strain state, character      22
Stress-strain state, classification      19 22
Stress-strain state, combined      23
Stress-strain state, edge effect      23 29 134
Stress-strain state, edge effect, non-linear      24 30
Stress-strain state, edge effect, simple      20 24 30 31
Stress-strain state, fast varying      34 47
Stress-strain state, general      17 19 20 47 299
Stress-strain state, infinitesimal pure bendings      23
Stress-strain state, initial      42 48 122 133
Stress-strain state, main      134 135
Stress-strain state, membrane      22 27 42 45 47 48 111 133
Stress-strain state, moment      24 47
Stress-strain state, momentless      22
Stress-strain state, partial      19
Stress-strain state, post-buckling      41
Stress-strain state, pre-buckling      41
Stress-strain state, pseudo-bendings      23 66
Stress-strain state, pure bending      23
Stress-strain state, pure moment      23
Stress-strain state, semi-momentless      23 33 133 134
Theorem, Kirchhoff      38
Theory, elasticity      17
Theory, Liapunov      37
Theory, shell      7 17
Theory, shell, errors      19
Theory, shell, Kirchhoff — Love      17
Theory, shell, linear      19 20
Theory, shell, technical      29 43 47
Theory, shell, two-dimensional      12
Theory, surface      7
Transform, Fourier      96 106 123
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