Multi-scale Modelling for Structures and Composites

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".

From the reviews of the first edition:

"This book describes the mathematical aspects of the deformation and homogenization of rods. ... The large variety of problems covered makes the book a useful tool for graduate students studying the mathematics and homogenization theory of rods and rod structures." (Sergey K. Serkov, Mathematical Reviews, Issue 2006 g)

"This is a high-quality research monograph on homogenisation theory and applications to modelling of composites and periodic framework structures. The book is based on the results of the recent research, and the author is a well-recognized expert in homogenisation models in mathematical physics and continuum mechanics. ... The book is well-written and includes many good examples." (Alexander Movchan, Zentralblatt MATH, Vol. 1078, 2006)