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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.
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Рубрика: Математика /
Серия: Сделано в холле
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 1981
Количество страниц: 342
Добавлена в каталог: 18.02.2014
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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 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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