Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Wolf J.P. — The Scaled Boundary Finite Element Method
Wolf J.P. — The Scaled Boundary Finite Element Method



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: The Scaled Boundary Finite Element Method

Автор: Wolf J.P.

Аннотация:

A novel computational procedure called the scaled boundary
finite-element method is described which combines the advantages of
the finite-element and boundary-element methods: Of the
finite-element method that no fundamental solution is required and
thus expanding the scope of application, for instance to anisotropic
material without an increase in complexity and that singular
integrals are avoided and that symmetry of the results is
automatically satisfied. Of the boundary-element method that the
spatial dimension is reduced by one as only the boundary is
discretized with surface finite elements, reducing the data
preparation and computational efforts, that the boundary conditions
at infinity are satisfied exactly and that no approximation other
than that of the surface finite elements on the boundary is
introduced. In addition, the scaled boundary finite-element method
presents appealing features of its own: an analytical solution inside
the domain is achieved, permitting for instance accurate stress
intensity factors to be determined directly and no spatial
discretization of certain free and fixed boundaries and interfaces
between different materials is required. In addition, the scaled
boundary finite-element method combines the advantages of the
analytical and numerical approaches. In the directions parallel to
the boundary, where the behaviour is, in general, smooth, the
weighted-residual approximation of finite elements applies, leading
to convergence in the finite-element sense. In the third (radial)
direction, the procedure is analytical, permitting e.g.
stress-intensity factors to be determined directly based on their
definition or the boundary conditions at infinity to be satisfied
exactly. In a nutshell, the scaled boundary finite-element method is
a semi-analytical fundamental-solution-less boundary-element method
based on finite elements. The best of both worlds is achieved in two
ways: with respect to the analytical and numerical methods and with
respect to the finite-element and boundary-element methods within the
numerical procedures. The book serves two goals: Part I is an
elementary text, without any prerequisites, a primer, but which using
a simple model problem still covers all aspects of the method and
Part II presents a detailed derivation of the general case of
statics, elastodynamics and diffusion.


Язык: en

Рубрика: Математика/Численные методы/Конечные элементы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 363

Добавлена в каталог: 20.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Adaptivity, h-hierarchical      335
Adaptivity, h-hierarchical, cylindrical foundation      340
Adaptivity, h-hierarchical, plate with two square holes      338
Advantages      148 349
Assemblage diffusion      198
Assemblage elastodynamics      185
Assemblage finite element      20
Assemblage implementation      144
Assemblage, finite element cell and medium      90
Balloning      167
Base function, reduced set formulation      278
Base function, reduced set, semi-infinite wedge      315
Bessel equation      105 268
Boundary condition at infinity boundary element      39 148
Boundary condition at infinity boundary element, finite element      25 148
Boundary condition at infinity boundary element, radiation condition      243 247
Boundary condition at infinity boundary element, scaled boundary finite element      49 107 119 148 350
Boundary element method      25
Boundary element method, advantages      52 148
Boundary integral equation      29 32
Cavity, spherical      310
Cell width      85
Cell width, analytical limit      92
Characterisation      52
Characteristic length diffusion      199
Characteristic length, elastodynamics      184 188
Characteristic length, model problem      78 79 81 105
Cloning      168
Coefficient matrix implementation      144
Coefficient matrix, base functions, reduced set      279
Coefficient matrix, boundary element method      32
Coefficient matrix, diffusion      197
Coefficient matrix, elastodynamics      184 191 203
Coefficient matrix, illustrative example      47
Coefficient matrix, incompressible material      278
Coefficient matrix, model problem      74 83 87 88
Coefficient matrix, scalar case      100 101
Concept      57 171
Consistent infinitesimal finite element cell method      54 168
Crack      see also Cracked plate
Crack, dam      2
Crack, multiple      286
Cracked plate      290 291 293 294 296 297 338
Cylindrical foundation      340
Dasgupta, G      168
Dashpot diffusion      249
Dashpot elastodynamics      245 246
Dashpot impedance      121 249
Dashpot medium-structure interaction      162 165
Dashpot prism foundation      307
Dashpot scalar case      108
Dashpot, Fourier transformation      158
Dashpot, truncated semi-infinite wedge      119 120 128
Deeks, A.      168
Derivation, mechanically based      79
Derivation, scaled boundary transformation based      65 169 175 195 201
Dimensional analysis      81
Dimensionless frequency diffusion      199
Dimensionless frequency elastodynamics      188 193
Dimensionless frequency, dimensional analysis      82
Dimensionless frequency, material properties varying in radial direction      275
Dimensionless frequency, model problem      77 82 108
Dimensionless frequency, three-dimensional prismatic unbounded medium      281
Dimensionless frequency, two-dimensional layered unbounded medium      280
Dimensionless variable      82
Discontinuity of stress      284 302
Displacement boundary condition, non zero      185
Dynamic condensation equation      92 140 252 269
Dynamic stiffness, analytical solution, bounded medium      266
Dynamic stiffness, analytical solution, truncated semi-infinite wedge      139
Dynamic stiffness, analytical solution, unbounded medium      268
Dynamic stiffness, analytical solution, wedge      139
Dynamic stiffness, finite element cell      90
Dynamic stiffness, Fourier transform pair      157
Dynamic stiffness, high-frequency asymptotic expansion, diffusion      249
Dynamic stiffness, high-frequency asymptotic expansion, elastodynamics unbounded medium      245
Dynamic stiffness, high-frequency asymptotic expansion, truncated semi-infinite wedge      119
Dynamic stiffness, medium-structure interaction      163 165
Dynamic stiffness, model problem, definition      76 91
Dynamic stiffness, model problem, scalar case      106 107
Dynamic stiffness, numerical solution, truncated semi-infinite wedge      123 129
Dynamic stiffness, numerical solution, unbounded medium      252 258
Dynamic stiffness, prism foundation      308
Dynamic stiffness, scaled boundary finite element equation, diffusion      200
Dynamic stiffness, scaled boundary finite element equation, elastodynamics      189 194
Dynamic stiffness, scaled boundary finite element equation, model problem      78 94
Dynamic stiffness, semi-infinite wedge      315
Dynamic stiffness, similar boundaries      81
Dynamic stiffness, spherical cavity,      11
Dynamic stiffness, three-dimensional prismatic unbounded medium      282
Dynamic stiffness, two-dimensional layered unbounded medium      281
Dynamic-stress intensity factor      297
Early-time asymptotic expansion for unit-impulse response, truncated semi-infinite wedge      128
Early-time asymptotic expansion for unit-impulse response, unbounded medium      248
Effective foundation input motion      165
Eigenvalue, base functions, reduced set      279
Eigenvalue, high-frequency asymptotic expansion      245
Eigenvalue, restrictions      348
Eigenvalue, statics, elastostatics      209 261
Eigenvalue, statics, model problem      111 134
Eigenvalue, substructuring with similar boundaries      238
Eigenvalue, three-dimensional prismatic unbounded medium      282
Eigenvalue, two-dimensional layered unbounded medium      281
Electrostatics      5
Energy transmission      119 243
Error estimator, infinite plate with circular hole      328
Error estimator, numerical analysis      318
Error estimator, scaled boundary finite element      325
Far-field displacement, analytical solution      269
Far-field displacement, truncated semi-infinite wedge      131 142
Finite element cell      see Cell
Finite element method      11
Finite element method, advantages      52 148
Fluid flow      5
Flux singularity      299
Fourier integral      157
Fourier series      155
Fourier transform pair      157 158
Fourier transformation      153
Frequency dimensionless      see Dimensionless frequency
Fundamental solution      25 28 148
Governing equations, diffusion, Cartesian coordinates      194
Governing equations, diffusion, scaled boundary coordinates      195
Governing equations, elastodynamics, Cartesian coordinates      174 190
Governing equations, elastodynamics, scaled boundary coordinates      179
Governing equations, model problem, scaled boundary coordinates      69
Green's theorem      9 202
h-hierarchical adaptivity      335
h-hierarchical adaptivity, cylindrical foundation      340
h-hierarchical adaptivity, plate with two square holes      338
Hamiltonian matrix      209 351
Heat conduction      5
Helmholz equation      55 62 63
High-frequency asymptotic expansion for dynamic stiffness, dashpot      246
High-frequency asymptotic expansion for dynamic stiffness, definition      245
High-frequency asymptotic expansion for dynamic stiffness, diffusion      249
High-frequency asymptotic expansion for dynamic stiffness, eigenvalue      245
High-frequency asymptotic expansion for dynamic stiffness, energy transmission      243
High-frequency asymptotic expansion for dynamic stiffness, hysteretic damping      248
High-frequency asymptotic expansion for dynamic stiffness, scalar case      108
High-frequency asymptotic expansion for dynamic stiffness, spring      247
High-frequency asymptotic expansion for dynamic stiffness, starting boundary condition for analytical solution      268
High-frequency asymptotic expansion for dynamic stiffness, starting boundary condition for numerical solution      252
High-frequency asymptotic expansion for dynamic stiffness, truncated semi-infinite wedge      119 124
Historical note      167
Hysteretic damping, high-frequency expansion for dynamic stiffness      248
Hysteretic damping, model problem      62 107 124
Hysteretic damping, solution nodal force-displacement relationship      258
Hysteretic damping, solution scaled boundary finite element equation in dynamic stiffness      252
Illustrative example, definition      4
Illustrative example, results, boundary element      38
Illustrative example, results, finite element      23
Illustrative example, results, scaled boundary finite element      48
Impedance      120 249 307
Incompressible elastodynamics      277
Infinite element method      167
Infinite grid refinement      167
Infinite plate with circular hole      328
Infinite substructuring      167
Initial stress      232
Instantaneous response      126 160 254
Integration-by-parts formula      9
Integration-by-parts formula, diffusion      196
Integration-by-parts formula, elastodynamics      181 202
Integration-by-parts formula, illustrative example      44
Integration-by-parts formula, model problem      71
Inverse Fourier transformation      125 157 253
Laplace equation      3
Lingering response      126 160 254
Logarithmic mode, analytical solution elastodynamics      265
Logarithmic mode, load varying as power function of radial coodinate in statics      230
Logarithmic mode, rod      216
Logarithmic mode, surface foundation      302
Logarithmic mode, two-dimensional unbounded medium in statics      217 222
Low-frequency expansion of dynamic stiffness, diffusion      240
Low-frequency expansion of dynamic stiffness, elastodynamics      237
Low-frequency expansion of dynamic stiffness, wedge      106 117
Lyapunov equation      237 240 247 256
Magnetostatics      5
Mass, diffusion      240
Mass, elastodynamics      235
Mass, finite element cell      88
Mass, illustrative example      23
Mass, scalar case      106
Mass, substructuring with similar boundaries      239
Mass, wedge      117
Material damping      see Hysteretic damping
Material properties varying in radial direction      271
Material properties varying with depth      277
Mathematical model      2
Mechanically-based derivation      79
Medium structure interaction      161
Medium structure interaction, algebraic equation of motion in frequency domain      163 166
Medium structure interaction, dam embedded in soil      2
Medium structure interaction, differential equation of motion in time domain      162 166
Nodal flux-function relationship      198 200
Nodal force-displacement relationship, elastodynamics      187 192 204
Nodal force-displacement relationship, model problem      76 96
Nodal load differential equation, elastodynamics      188 192
Nodal load differential equation, model problem      77 95
Numerical solution      2
Parent element      15 149.
Physical problem      1
Plate with singularity of flux      299
Plate with two square holes      338
Plate, cracked      see Cracked plate
Plate, infinite with circular hole      328
Poisson's equation      5
Prism foundation      306
Radiation condition      see Boundary condition at infinity
Residual function      6
restrictions      347
Riccati equation      101 113 211 351
Scaled boundary coordinates      see Scaled boundary transformation
Scaled boundary finite element equation in displacement, analytical solution, elastodynamics      260
Scaled boundary finite element equation in displacement, analytical solution, spherical cavity      310
Scaled boundary finite element equation in displacement, analytical solution, truncated semi-infinite wedge      133
Scaled boundary finite element equation in displacement, base functions, reduced set      279
Scaled boundary finite element equation in displacement, elastodynamics, scaled boundary transformation-based derivation      185 192 193
Scaled boundary finite element equation in displacement, elastodynamics, virtual work derivation      204
Scaled boundary finite element equation in displacement, illustrative example      45
Scaled boundary finite element equation in displacement, material properties varying in radial direction      275
Scaled boundary finite element equation in displacement, model problem, analytical solution in series expansion      133
Scaled boundary finite element equation in displacement, model problem, mechanically-based derivation      97
Scaled boundary finite element equation in displacement, model problem, scalar case      103 106 107
Scaled boundary finite element equation in displacement, model problem, scaled boundary transformation-based derivation      75
Scaled boundary finite element equation in displacement, statics solution, elastodynamics      209 223
Scaled boundary finite element equation in displacement, statics solution, model problem      111 113
Scaled boundary finite element equation in displacement, three-dimensional prismatic unbounded medium      282
Scaled boundary finite element equation in displacement, two-dimensional layered unbounded medium      280
Scaled boundary finite element equation in dynamic stiffness, analytical solution, elastodynamics      267 269
Scaled boundary finite element equation in dynamic stiffness, analytical solution, model problem      138 141
Scaled boundary finite element equation in dynamic stiffness, analytical solution, spherical cavity      314
Scaled boundary finite element equation in dynamic stiffness, base functions, reduced set      316
Scaled boundary finite element equation in dynamic stiffness, diffusion      200
Scaled boundary finite element equation in dynamic stiffness, elastodynamics      189 193 194
Scaled boundary finite element equation in dynamic stiffness, high-frequency asymptotic expansion, diffusion      249
Scaled boundary finite element equation in dynamic stiffness, high-frequency asymptotic expansion, elastodynamics      249
Scaled boundary finite element equation in dynamic stiffness, high-frequency asymptotic expansion, truncated semi-infinite wedge      119
Scaled boundary finite element equation in dynamic stiffness, material properties varying in radial direction      275
Scaled boundary finite element equation in dynamic stiffness, model problem, analytical solution in series expansion      141
Scaled boundary finite element equation in dynamic stiffness, model problem, mechanically-based derivation      94
Scaled boundary finite element equation in dynamic stiffness, model problem, numerical solution      124
Scaled boundary finite element equation in dynamic stiffness, model problem, scalar case      106 107
Scaled boundary finite element equation in dynamic stiffness, model problem, scaled boundary transformation-based derivation      78
Scaled boundary finite element equation in dynamic stiffness, numerical solution, elastodynamics      252
Scaled boundary finite element equation in dynamic stiffness, numerical solution, embedded prism      307
Scaled boundary finite element equation in dynamic stiffness, numerical solution, model problem      124
Scaled boundary finite element equation in dynamic stiffness, numerical solution, semi-infinite wedge      316
Scaled boundary finite element equation in dynamic stiffness, three-dimensional prismatic unbounded medium      282
Scaled boundary finite element equation in dynamic stiffness, two-dimensional layered unbounded medium      281
Scaled boundary finite element equation in function      198
Scaled boundary finite element equation in time domain, elastodynamics      255
Scaled boundary finite element equation in time domain, truncated semi-infinite wedge      127
Scaled boundary transformation, concept      57 59 173
Scaled boundary transformation, diffusion      195
Scaled boundary transformation, elastodynamics      176 190
Scaled boundary transformation, illustrative example      40
Scaled boundary transformation, material properties varying in radial direction      277
Scaled boundary transformation, model problem      67
Scaled boundary transformation-based derivation, diffusion      194
Scaled boundary transformation-based derivation, elastodynamics      177 189
Scaled boundary transformation-based derivation, model problem      65
Scaling centre, concept      57 172
Scaling centre, illustrative example      40
Scaling centre, infinity      280 281
Scaling centre, model problem      65
Scaling centre, moving on line      351
Scaling centre, substructuring      284
Schur factorisation      211 257
Semi-infinite wedge      315
Separation of variables      173
Shear plate      3 61
Side-face      53 59
Side-face, cylindrical foundation      342
Side-face, elastodynamics      174
Side-face, logarithmic mode      223
Side-face, model problem      73 99
Side-face, prism foundation      306
Side-face, semi-infinite wedge      315
Side-face, substructuring      284
Silvester, P.P.      167
Similar      54 355
Similarity      59 79 347
Similarity centre      see Scaling centre
Singularity of flux      299
Solid modelling      149
Song, Ch.      168
Spherical cavity      310
Spring, diffusion      249
Spring, elastodynamcis      245 247
Spring, Fourier transformation      158
Spring, medium-structure interaction      162 165
Spring, scalar case      108
Spring, truncated semi-infinite wedge      119 120
Static stiffness, analytical solution, elastostatics      210 211
Static stiffness, analytical solution, model problem      112 113
Static stiffness, analytical solution, unbounded two-dimensional medium      212
Static stiffness, finite element cell      87
Static stiffness, illustrative example      16 18
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте