On modelling of medium thickness plates with a uniperiodic structure

The aim of this contribution is to propose a new averaged 2D-model of non-homogeneous Reissner-Mindlin elastic plates with one-directional periodic structure. So far, the averaged 2D-models of periodic plates were formulated on the basis of the known asymptotic homogenization theory in the framework of which the effect of repetive cell size on the overall plate behaviour is neglected. To remove this drawback the tolerance averaging of the plate equations was applied, cf. Woźniak and Wierzbicki (2000). It is shown that the aforementioned cell size effect plays an important role not only in dynamie problems (like for plates with two-directional periodic structure) but also in the quasi-stationary and stability problems. The obtained results are compared with those derived for the plates having a periodic structure in two directions as well as for the plates described in the framework of homogenization.