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Necas J., Hlavacek I. — Mathematical Theory of Elastic and Elastico-Plastic Bodies: An Introduction
Necas J., Hlavacek I. — Mathematical Theory  of Elastic and  Elastico-Plastic Bodies: An Introduction



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Название: Mathematical Theory of Elastic and Elastico-Plastic Bodies: An Introduction

Авторы: Necas J., Hlavacek I.

Аннотация:

The theory of elasticity represents a branch of applied mathematics which, although now classical in one sense, in another still continues to develop rapidly in various directions. Many famous mathematicians in the past were often inspired by problems from this field of mechanics. However, the theory of plasticity is much younger and less mature.
We have written a book on elasticity and plasticity with the aim of acquainting the reader not only with the basic concepts and relations, but also with the contemporary state of the theory, at least in those areas familiar to us. These are, for example, the nonlinear models of elasto-plastic bodies and of large deflections of plates, unilateral boundary value problems, variational principles, the finite element method and so on.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 342

Добавлена в каталог: 18.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A posteriori error bounds      259 322
Admissible stress field      61
Admissible stress field, geometrically      61
Admissible stress field, statically      61 106
Airy stress function      161
Airy stress function for generalized plane stress      164
Airy stress function for plane stress      162
Airy stress function, Dirichlet problem for      165 167
Airy stress function, semi-inverse method for      176
Airy stress function, variational problem for      168
Angle of shear      33
Axisymmetric problem      178
Banach's principle of contraction      136
Basic boundary value problems of elasticity      58 91
Basis      110 113
Basis, function      236 246
Basis, local unit      113
Beltrami — Michell equations      58
Bending moment of beam      188 198
Bending moment of plate      200 204
Bending moment, rigidity of plate      207
Bernoulli hypothesis      195
body      20
Body, force      20
bulk modulus      46
Cauchy quadric of stress      25
Christoffel symbols      116
Coerciveness of functional      88
Coerciveness of strain      79
Coerciveness of system of operators      242
Compatibility      36
Compatibility, conditions of      68 104
Compatibility, Saint-Venant equations of      37
Conforming finite elements      245
Contact conditions      100
Convergence, rate of      240
Convergence, weak      88
Coordinate curve      110
Covariant derivative      116
Curvilinear coordinates      109
Curvilinear coordinates, orthogonal      110
Deformation operators      220
Deformation, elastic      42
Deformation, plastic      42
Deformation, theory of elasto-plastic body      125
Deviator of small strain tensor      36
Diffeomorphism      29
Differential, Gateaux      89
Differential, strictly monotone      263
Dilatation, cubical      36
Displacement vector      29
Domain      17
Domain with Lipschitz boundary      17
Elasticity, linear theory of      43
Element for equilibrium model      253
Element of Clough and Tocher      247
Element, cubic      246
Element, linear      236
Element, quintic      246
Embedding      75
Energy bounds for plane strain      157
Energy bounds, complementary      65 119
Energy bounds, potential      63 118 178
Energy bounds, strain      71
Energy bounds, two-sided      261
Equations of equilibrium      23
Equations of Sophie Germain      207
Equations of von Karman      208 281
Equations, Saint-Venant of compatibility      37
Equilibrium, astatic      147
Equilibrium, conditions of total      95 180
Equilibrium, finite element models      240 248
Flow theory of plasticity      54 131 322
Flow theory of plasticity with strain hardening      329
Fourier transform      80
Friedrichs' method      64
Function of asymptotically optimal hypothesis      192
Function with finite energy      72
Function, absolutely continuous      18
Function, equicontinuous in the mean      75
Function, Hopf      285
Function, uniformly bounded      75
Gateaux differential      89
Gradient      111
Hardening, strain      55
Hencky material      54
Hencky relation      51
Hooke's law      43
Hooke's law in curvilinear coordinates      117
Hooke's law, generalized for isotropic material      43
Indicatrix      296
Integral, surface      19
Intensity of shear strain      36
Intensity of shear stress      28
Internal state variable      52 132
Invariant      24
Invariant of finite strain      34
Invariant, form      115
Isomorphism      121
Kantorovic's method      186
Kirchhoff hypothesis      201
Kirchhoff — Love hypothesis      212
Kolmogorov criterion      75
Korn's inequality      77 79 244
Korn's inequality for $V_{p}$      99
Lagrangian      314
Lame coefficients      44 112
Lame equations      57
Lame, general      56
Limit, elastic      42
Limit, proportional      42
Limit, strength      42
Love's formula      144
Material, anisotropic      43
Material, elasto-inelastic      131
Material, homogeneous      43
Material, isotropic      43
Material, orthotropic      43
Matrix, orthogonal      15
Matrix, stiffness      238
Measure      18
Method of contraction      268
Method of Kacanov      261
Method of Lagrange multipliers      64 67 314
Method of orthogonal projections      104 251
Method of steepest descent      265
Method, compatible models      236
Method, equilibrium models      248
Method, finite element      235
Method, hypercircle      260
Method, mixed models      256
Method, Ritz — Galerkin      234
Minimizing sequence      233
Minty's trick      299
Mollifying of boundary conditions      199 200 206 232
Nodal parameters      246
Normal, unit outer      19
Operator, Lipschitz continuous      269
Operator, strictly monotone      269
Parseval's identity      81
Partition of unity      83
Penalty functional      297 326
Piola — Kirchhoff tensors      274
Plane elasticity      149
Plane strain      149 156
Plane stress      151
Plane, generalized      152
Plastic, perfectly      53 303
Poisson's ratio      49
Prandtl potential function      229
Pressure      25
Principal directions of small strain      35
Principal directions of strain      34
Principal directions of stress      25
Principal directions, extension      35
Principle of Hellinger — Reissner      66 68 258
Principle of Hu Hai Chang and Washizu      67
Principle of minimum complementary energy      66 106 169 171 175 250 253
Principle of virtual displacements      61 87 118
Principle work      61
Principle, Haar — Karman      306
Principle, hybrid      66—70
Principle, potential energy      64 94 100 103 130
Principle, stresses      62 108
Problem of quadratic programming      316
Problem, dual      314
Problem, primal      314
Problem, unilateral boundary value      322
Product, "double dot"      112
Product, inner      13 17 71 112 133
Rectification      19
Relative extension      32
Rigid body translation and rotation      78
Ritz approximation      237
Saddle point      68 258 314
Saint-Venant's principle      141 177
Saint-Venant's principle, Sternberg — Keller version of      146
Set, measurable      18 19
Set, weakly closed      89
Set, weakly compact      88
Shearing force of beam      198
Shearing force, effective of plate      206
Shell      210
Shell, cylindrical      219
Signorini's problem      294
Simple bearing of plate      205
Small rotation      35
Sobolev space      72
Strain tensor, finite      29
Strain tensor, small      34
Stress, maximum shear      27
Stress, normal      21
Stress, notch      155
Stress, principal      25
Stress, shear (tangential)      21
Stress, tensor      23
Stress, vector      20 21
Summation convention      13
Surface, middle      211
Tension      25
Tension, test diagram      42
Tensor      15 16
Tensor in curvilinear coordinates      109
Tensor of order one      16
Tensor, contravariant      110
Tensor, covariant      110
Tensor, finite strain      31
Tensor, physical components of      112
Tensor, skew-symmetric      16 17
Tensor, small strain      34
Tensor, symmetric      17
Tensor, two      16
Theorem, Brouwer fixed point      291
Theorem, Green      20
Theorem, reciprocity      143
Theorem, Rellich      75
Theorem, Somigliana's      144
Torsion of bar      225 255
Torsion of elliptic cross section      230
Torsional rigidity      227
Trace of function      72
Trace of function, theorem      72
Triangulations of domain      236
Triangulations, regular system of      237
Twist angle      227
Twisting moment of plate      204
Uzawa's algorithm      319
Variational inequality      296 297
Variational inequality, approximate solution of      309
Weak (generalized) solution      87
Weak (generalized) solution in curvilinear coordinates      122
Weak (generalized) solution in deformation theory of elasto-plastic body      126
Weak (generalized) solution in terms of stresses      107 123 182
Weak (generalized) solution of generalized plane stress      158
Weak (generalized) solution of plate problem      208
Weak (generalized) solution of problem of plane strain      156
Weak (generalized) solution of shell problem      218 221
Weak (generalized) solution, lower semi-continuity      88
Well-posed problem      91
Yield condition      54
Yield Mises condition      53
Yield point      42
Yield surface      132
Young's modulus of elasticity      43
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