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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 IntroductionАвторы: 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.
Язык: Рубрика: Математика /Серия: Сделано в холле Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1981Количество страниц: 342Добавлена в каталог: 18.02.2014Операции: Положить на полку |
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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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