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Panasenko G.P. — Multiscale Modelling for Structures and Composites
Panasenko G.P. — Multiscale Modelling for Structures and Composites

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Название: Multiscale Modelling for Structures and Composites

Автор: Panasenko G.P.


Rod structures are widely used in modern engineering. These are bars, beams, frames and trusses of structures, gridwork, network, framework and other constructions. Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these hypotheses do not allow to consider some important effects, for instance the boundary layer effects near the points of junction of rods. So the question concerning the limits of applicability of structural mechanics hypotheses and the possibilities of their refinement arise. In this connection the asymptotic analysis of equations of mathematical physics, the equations of elasticity in rod structures (without these hypotheses and simplifying assumptions being imposed) is undertaken in the present book. Moreover, a lot of modern structures are made of composite materials and therefore the material of the rods is not homogeneous. This inhomogeneity of the material can generate some unexpected effects. These effects are analysed in the present book. The methods of multi-scale modelling are presented in the book by the homogenization, multi-level asymptotic analysis and the domain decomposition. These methods give an access to a new class of hybrid models combining macroscopic description with "microscopic zooms".

Major features are:
- Rigorous mathematical analysis of structures without hypotheses of the Kirchhoff-Love, Kirchhoff-Clebsch type
- Taking into consideration the inhomogeneity of the rods and plates
- New numerical algorithms decomposing a structure in 3D and 1D parts with someinterface conditions between them.

Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 398

Добавлена в каталог: 12.05.2008

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Предметный указатель
Asymptotic partial domain decomposition      337
Asymptotic partial domain decomposition, solution (formal)      23
Boundary layer corrector      26
Boundary layer corrector in homogenization      32
Boundary layer corrector in homogenization, techniques      26
Cell problem      5 39 120
Cell problem, code EFMODUL      6 120
Conductivity equation      2 37
Contrasting coefficients      110
Effective coefficients      5 6
Elasticity equation      2 57
Equivalent homogeneous plate      154
Finite element method      346
Finite rod structures      12 162
FL-convergence      168 251
Formal asymptotic solution (f.a.s.)      23
Heterogeneous plate      130
Heterogeneous plate, rod      21
High order homogenization method      22
Homogenization method      9 22
Homogenized boundary conditions      26 33
Homogenized boundary conditions, equation      25
Homogenized boundary conditions, equation of high order      25 31
Korn inequality      18 243 321
L-convergence      15 167 250
Lattice (skeletal) structure      13 248
Macroscopic (slow) variable      9
Method of asymptotic partial decomposition of domain      337
Microscopic (fast) va riab l e      9
Multi-component homogenization      110
Multi-scale models      ix 337
Navier — Stokes equation      217
Net      270
Non-stationary (time dependent, non-steady state) model      98
Non-stationary (time dependent, non-steady state) model, elasticity equation      103
Partial homogenization      373
Plate      130
Poincar’e inequality      17 233 318
Poincar’e — Friedrichs inequality      17 233 251 318
Random coefficients      307
Rectangular lattice      13 249
Rod (bar)      21
Section      161 248
Shape optimization      173
Steady-state (stationary) model      36 57
Stress analysis      9
Tube (pipe) structure      215
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