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Oden J.T. Ч Finite Elements: An Introduction (Vol. 1)
Oden J.T. Ч Finite Elements: An Introduction (Vol. 1)

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Ќазвание: Finite Elements: An Introduction (Vol. 1)

јвтор: Oden J.T.

јннотаци€:

Our purpose in writing this book is to provide the undergraduate student of engineering and science with a concise introduction to finite element methods Ч one that will give a reader, equipped with little more than calculus, some matrix algebra, and ordinary differential equations, a clear idea of what the finite element method is, how it works, why it makes sense, and how to use it to solve problems of interest to him. We imposed on ourselves three constraints that we felt were of fundamental importance in designing a text of this type.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1981

 оличество страниц: 258

ƒобавлена в каталог: 16.04.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$H(^{h}_{0})$      11 16
${C}^{1}$ basis functions      233Ч237
${H}^{1}$      55Ч56 43 147 223Ч224 244
${H}^{1}$ norm      57
${H}^{1}_{0}$      7Ч11 16 20 23 56Ч58 60 241
${H}^{2}$      231
${H}^{2}_{0}$      235Ч236
${H}^{h}$      58 224 232 235
${H}^{h}_{0}$      16 23 39
A-posteriori estimates      36
A-priori estimates      36
Accuracy, of finite element approximation      36Ч39 189 197 see УErrorsФ
Admissible functions      see УTest functionФ
Admissible functions, for one-dimensional problems      7
Admissible functions, for three-dimensional problems      223
Admissible functions, for two-dimensional problems      57 147
Admissible functions, fourth-order problRems      231Ч232
Approximation, best Galerkin      14Ч15
Approximation, interpretation of      31Ч36
Approximation, of systems      241
Approximation, of three-dimensional problems      224
Approximation, of time-dependent problems      249
Approximation, of two-dimensional problems      162 165
Approximation, of two-point problems by finite elements      73Ч76
Area coordinates      201Ч205
Area coordinates, and nonlinear maps      202
Area coordinates, definition      201
Backward difference scheme      251
Banded matrix      26
Banded matrix, elimination of      118Ч121
Banded matrix, storage of      118Ч121 209
Bandwidth, definition of      119
Basis functions, ${C}^{1}$-type      232 234 236Ч237
Basis functions, for Galerkin's method      11Ч15 59
Basis functions, for model two-point problem      15Ч23
Basis functions, global      33 67 69 157 234
Basis functions, Hermite      233Ч237
Basis functions, Lagrange polynomial      67 195 204
Basis functions, on rectangles      159 236Ч237
Basis functions, on triangles      154 157 237
Basis functions, piecewise-constant      22
Basis functions, piecewise-linear      17 20 25 30 38 67Ч68 85 154 157
Basis functions, piecewise-polynomial      16
Basis functions, piecewise-quadratic      23
Beam bending      238Ч239
Bicubic rectangle      237
Biharmonic equation      235Ч236 239
Body forces      44
Boundaries, parametric definition of      141Ч142 193
Boundaries, smoothness of      132
Boundary condition data, input of      104 212Ч223
Boundary conditions, calculation and flowchart of      216
Boundary conditions, clamped plate      235
Boundary conditions, compatability of      229Ч230
Boundary conditions, convective      216
Boundary conditions, essential      43 49 55Ч56 60 81 138 140 223 231Ч232
Boundary conditions, for biharmonic equation      235
Boundary conditions, for fourth-order problems      229Ч230
Boundary conditions, for general two-point problems      42 79Ч84
Boundary conditions, in CODE2      218Ч229
Boundary conditions, inCODEl      107Ч109
Boundary conditions, natural (definition)      49 138 146 231Ч232
Boundary integrals, computation of      191Ч192
Boundary, restriction of shape functions      191
Brick element      226
Capacitance matrix      see УMass matrixФ
Chain rule, in area coordinates      205
Chain rule, in shape function transformation      189
Charge      4
Classical boundary-value problem      3 8 40Ч52 62 224 228Ч229 235 240
Compatability condition for, data in two-point problems      83 141 228Ч230
Complete polynomials, integration error for      160Ч161 205Ч208
Completeness, and rate of convergence      197Ч198
Conservation principle      43 47 49Ч51 83 136 138 141 246Ч247
Conservation principle, of electric flux      44
Conservation principle, of energy      44
Conservation principle, of linear momentum      44 242Ч243 247
Conservation principle, of mass      44
Constitutive equation      43 44 46 49 136 140 243 247
Constitutive equation, Stokes' law      44
Convergence in an ${H}_{0}^{1}$ sense      11
Convergence rates      36Ч37 189 197 see УErrorsФ
Coordinate function, derivatives      189 201
Coulomb's law      44
Cube element      225Ч227
Cubic triangle      240
Curvilinear coordinates, from master element map      176Ч177
Darcy's law      44
Data, management of      90
Data, of a boundary-value problem      1 140 229Ч230
Deformations, calculation of      127Ч130
Deformations, of an elastic bar      44
Degrees-of-freedom      12 15 59 235Ч237
Degrees-of-freedom, definition of      12
Degrees-of-freedom, for beam element      238
Degrees-of-freedom, for fourth-order problems      235Ч237
Degrees-of-freedom, symbolism      236Ч237
Derivatives, directional      133
Derivatives, of element transformation      183
Diffusion      247
Dirac delta      2 4 46 48 84 144 167 232
Divergence theorem      136 137 143 145
Divergence, definition of      134
Elastic modulus      246
Elasticity      242 244 246Ч247
Electrostatics      44
Element calculations, flow chart of      30
Element calculations, for ODE system      242
Element calculations, general      187Ч194
Element calculations, transformation to master element      177
Element calculations, two-dimensional      175Ч121
Element flux vector      166
Element matrices, assembly of      91
Element matrices, calculation of      26 74Ч76 91 187 190
Element matrices, for time dependent problems      251
Element transformations, in three dimensions      225Ч226
Element transformations, in two dimensions      175Ч187
Energy, conservation of      247
Energy, first variation of      61Ч64
Energy, functional      60Ч64
Energy, norm      36 38 57 114
Energy, second variation of      61Ч64
Energy, strain      32Ч33 36
entropy      247
Equilibrium equations      243
Errors, analysis of      37Ч38 57
Errors, asymptotic estimates of      35
Errors, estimates      35Ч38 70
Errors, estimates for two-point problems      84Ч85
Errors, estimates, a-posteriori      36
Errors, estimates, a-priori      36
Errors, in Galerkin approximation      14
Errors, interpolation      67
Errors, log-log-plots of      37
Errors, measures      38
Errors, pointwise      38 124
Errors, quadrature      190
Errors, residual      53
Essential boundary condition      see УBoundary conditionsФ
Evolution problems      see УTime dependent problemsФ
Extrapolation      33Ч34
Finite element mesh, definition      16
Finite element method, definition      1
Finite element, definition      1 16
Flow through pourous media      44 247
Fluid flow      44 242
Flux      43 45Ч46 48Ч49 73 74 76Ч77 80 247
Flux, electric      44
Flux, flow rate      44
Flux, heat flux      44
Flux, jump in      46
Flux, shear stress      44
Forward difference scheme      250
Fourier series      10
Fourier's law      44 247
Fourth-order problems      222 228Ч240
Fourth-order problems, essential boundary conditions      231Ч232
Fourth-order problems, natural boundary conditions      231Ч232
Fourth-order problems, two-dimensional      235Ч239
Fourth-order problems, two-point problem      228Ч235
Fully discrete method      250
Functional, definition      60
Galerkin approximation, finite element subspace for      23 58
Galerkin approximation, for the general one-dimensional boundary value problem      58Ч60 73
Galerkin approximation, for the model problem      10Ч15
Galerkin's method, definition      12
Gauss' theorem      see УDivergence theoremФ
Gaussian elimination      109Ч111
Gaussian quadrature      23 95 190 206
Global matrices      105Ч107 228
Gradient, definition of      133
Green Ч Gauss Theorem      148
Green's formula      143 148
Heat conduction      44 247
Heat sources      44
Hermite interpolation      233Ч237
Hooke's law      see УConstitutive equationФ
Hyperbolic equation      248
Ill-posed problem      48 55 230Ч238
Implicit time integration      251Ч252
Initial-value problems      41 248Ч252
Integrals, coordinate transformation of      190
Integrals, on boundaries      191Ч192
Integration, exact for tetrahedra      228
Integration, exact for triangles      207Ч208
Integration, points, definition of      93
Integration, rules for one dimension      75 91Ч95
Integration, rules for quadrilaterals      199
Integration, rules for triangles      205
Interpolant, finite element      22 72
Interpolant, of data      75
Interpolation, error      67
Interpolation, error, rate of convergence      161
Interpolation, Hermite      233Ч235
Interpolation, higher-order      64
Interpolation, Lagrange      65 67
Interpolation, of one-dimensional problems      64Ч73
Interpolation, of problem data      191
Interpolation, piecewise-linear      21
Inverse map ${T}^{-1}_{e}$      179
Invertibility of map      179 182
Isoparametric elements      193
Isotropic      136
Jacobian, for boundary integrals      191Ч192
Jacobian, geometric interpretation of      181Ч182 201Ч202
Jacobian, invertibility condition on      179 182Ч186 194
Jump conditions      46 48 62 73 78 139Ч140 148Ч149
Lagrange, basis functions      67
Lagrange, families      65 67 72Ч73 157 159
Lagrange, interpolation      65 67 72
Lagrange, triangles      203Ч204
Laplaces equation      142
Laplacian operator      143 236
Line source      149 167
Linear momentum, conservation of      242Ч243 2
Linear space      10
Load, vector      23 26 28 62 76 85 164 225
Load, vector for Galerkin's method      12 59
Map ${T}_{e}$, construction of      179Ч187
Map ${T}_{e}$, criteria for      179Ч181
Map ${T}_{e}$, curved elements      207
Map ${T}_{e}$, invertibility conditions      185
Map ${T}_{e}$, using finite element shape functions      180
Mass matrix      250
Master element, calculations on      188Ч193
Master element, in one dimension      65
Master element, in three dimensions      225Ч226
Master element, in two dimensions      175Ч179
Master element, integration      190
Master element, map      176Ч177 235
Master element, shape functions      188
Master element, square      181
Master element, triangle      181 200
Material, modulus      43 45 47 136
Material, modulus-dielectric permittivity, permeability, thermal conductivity, viscosity, Young's modulus of elasticity      44
Material, properties      89Ч99 104
Mesh, construction by master elements      175Ч178
Mesh, finite element      16 23 72Ч73 77 150 223
Mesh, parameter h      36
Mesh, refinement      21 36 125
Midstep time integration      252
Mixed boundary conditions      83
Modulus of elasticity      44 127 242
Natural boundary conditions, definition of      49 138 146 231Ч232
Natural boundary conditions, for beam bending      239
Natural boundary conditions, for fourth order problems      231Ч232
Natural boundary conditions, in one dimension      80
Natural boundary conditions, in three dimensions      223
Natural boundary conditions, in two dimensions      141
Natural boundary conditions, relation to conservation principle      139Ч140
Neumann, boundary conditions      82
Neumann, problem      82 85
Nodal, displacements      168
Nodal, points      16 23 72
Nodal, values      33
Norm, ${H}^{1}-$      57
Norm, definitions of      35
Norm, energy      35 38 57
Norm, maximum      35Ч36
Norm, mean-square      35Ч36 38
Numerical integration      see УIntegrationФ
Orthogonality      14 38
Parabolic equations      247
Parametric map      193
Pascal's triangle      157 204
Penalty method      121Ч123
Plane, strain      127
Plane, stress      127 242Ч246
Plate bending      235
Point loads      see УDirac deltaФ
Point source      see УDirac deltaФ
Poisson's ratio      242 246
Post processing      88 100-11 210Ч225
Principle, conservation      see УConservation principleФ
Principle, of superposition      41
Principle, of virtual work      244 246
Quadratic element      196Ч197
Quadrature      see УIntegrationФ
Quadrature, error      190
Quadrature, Gauss      see УGaussian quadratureФ
Quadrature, points      198Ч199 205Ч206
Quadrature, rules for quadrilaterals      198Ч199
Quadrature, rules for triangles      205Ч206
Quadrature, weights      190 192
Quadrilateral elements      195Ч199 207
Quintic triangle      237
Rate of convergence      36Ч37 84Ч85
Rate of convergence, of interpolation error      161
Refinement of mesh      21 36 125
Residual, for fourth order problems      229
Residual, for the model problem      5
Residual, for time dependent problems      248
Residual, of the differential equation      6 53 144
Self-adjoint, boundary-value problem      26
Self-adjoint, operator      63Ч64
Semi-discrete method      249Ч250
Shape functions, calculation      95Ч96 217 219
Shape functions, definition      26
Shape functions, derivative calculation      95Ч96 189 216Ч227
Shape functions, for one dimension      26Ч27 65Ч68 72Ч74
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