About homogenization of elasticity problems on combined structures

We study elasticity problems in the plane (space) reinforced with periodic thin network (box structure). This highly contrasting medium depends on two small related parameters $\varepsilon$ and $h$ connected with each other which controlling size of periodicity cell and thickness of reinforcement. For combined structures we prove classical homogenization principle the same for any interrelation between parameters $\varepsilon$ and $h$ that is quite contrary to the case of thin structures. We use method of 2-scale convergence with respect to variable measure natural to combined structures.