Multi-scale Modelling for Structures and Composites - Panasenko, G.; SpringerLink (Online service) (Dordrecht : Springer Netherlands, 2005)
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".
Introduction: Basic Notions and Methods -- Heterogeneous Rod -- Heterogeneous Plate -- Finite Rod Structures -- Lattice Structures -- The Multi-Scale Domain Decomposition.
Keywords: MATHEMATICS; DIFFERENTIAL EQUATIONS, PARTIAL; MECHANICAL ENGINEERING; MATHEMATICS; MATHEMATICS, GENERAL; PARTIAL DIFFERENTIAL EQUATIONS; STRUCTURAL MECHANICS