Geodesic
About homogenization of elasticity problems on combined structures
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 114-144

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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. 
@article{ZNSL_2004_310_a6,
     author = {S. E. Pastukhova},
     title = {About homogenization of elasticity problems on combined structures},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {114--144},
     publisher = {mathdoc},
     volume = {310},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a6/}
}
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S. E. Pastukhova. About homogenization of elasticity problems on combined structures. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 114-144. http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a6/