About homogenization of elasticity problems on combined structures

S. E. Pastukhova

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 114-144

Résumé

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.

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