  On the example of linearized elasticity we provide a framework for
simultaneous homogenization and dimension reduction in the setting of
linearized elasticity as well as non-linear elasticity for the derivation of
homogenized von K\'arm\'an plate and bending rod models. The framework
encompasses even perforated domains and domains with oscillatory boundary,
provided that the corresponding extension operator can be constructed. Locality
property of $\Gamma$-closure is established, i.e. every energy density obtained
by the homogenization process can be in almost every point be obtained as the
limit of periodic energy densities.
