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 this book. The
methods of multi-scale modelling are presented 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".
General
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