Boundary homogenization and reduction of dimension in a Kirchhoff-Love plate

We investigate the asymptotic behavior, as e tends to 0(+), of the transverse displacement of a Kirchhoff-Love plate composed of two domains Omega(+)(epsilon) boolean OR Omega(-)(epsilon) subset of R-2 depending on e in the following way. The set Omega(+)(epsilon) is a union of fine teeth, having small cross section of size epsilon and constant height, epsilon-periodically distributed on the upper side of a horizontal thin strip with vanishing height he, as e tends to 0(+). The structure is clamped on the top of the teeth, with a free boundary elsewhere, and subjected to a transverse load. As e tends to 0(+), we obtain a "continuum" bending model of rods in the limit domain of the comb, while the limit displacement is independent of the vertical variable in the rescaled (with respect to h(epsilon)) strip. We show that the displacement in the strip is equal to the displacement on the base of the teeth if h(epsilon) >> epsilon(4). However, if the strip is thin enough (i.e., h(epsilon) similar or equal to epsilon(4)), we show that microscopic oscillations of the displacement in the strip, between the basis of the teeth, may produce a limit average field different from that on the base of the teeth; i.e., a discontinuity in the transmission condition may appear in the limit model.