Homogenization in Elasticity Problems on Combined Structures

Abstract

We study elasticity problems in the plane (space) which is reinforced with a periodic thin network (box structure). This highly contrasting medium depends on two small related parameters e and h which control the size of a periodicity cell and thickness of the reinforcement. For combined structures, we prove the classical homogenization principle, which is the same for any relations between parameters e and h; this is in a contrast with the case of thin structures. We use the method of two-scale convergence with respect to a variable measure, which is natural for combined structures. Bibliography: 17 titles.