Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     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: 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 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 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2021 | | О проекте