Rigorous presentation of Mathematical Homogenization Theory is the subject of numerous publications. This book, however, is intended to fill the gap in the analytical and numerical performance of the corresponding asymptotic analysis of the static and dynamic behaviors of heterogenous systems. Numerous concrete applications to composite media, heterogeneous plates and shells are considered. A lot of details, numerical results for cell problem solutions, calculations of high-order terms of asymptotic expansions, boundary layer analysis etc., are included. 0 Introduction.- 1 Definitions, assumptions and theorems in homogenization problems.- 2 Application of cell functions for the calculation of binary composite elastic moduli.- 3 Asymptotic study of linear vibrations of a stretched beam with concentrated masses and discrete elastic supports.- 4 Reinforced plates.- 5 Problems of elasticity theory for reinforced orthotropic plates.- 6 Reinforced shells.- 7 Corrugated plates.- 8 Other periodic structures.- 9 Perforated plates and shells.- Concluding remarks. Perspectives and open problems.- References.
