ABSTRACT
This chapter explores the theoretical studies leading to analytical expressions of the effective properties of the considered materials and structures. Apparently, the concept of effective properties was introduced for the first time in this work. The rigorous link between the conductivity and elastic moduli of fiber-reinforced composite materials can also be referred to the number of useful exact results. When studying the strength of aircraft structures, one has to deal with composite materials and periodically inhomogeneous elements, e.g. ribbed, corrugated, perforated, etc. Filshtinskii, having a good mathematical background, quickly realized that complex analysis, and especially the apparatus of Weierstrass doubly periodic functions, is adequate for these problems. Exact results in the theory of composites are rare and therefore very valuable. In particular, exact results can be used as benchmark examples for approximate methods. Interesting results were obtained for self-dual media, i.e. structures whose components are geometrically the same.
