2 research outputs found
Boundary Homogenization and Reduction of Dimension in a Kirchhoff-Love Plate
We investigate the asymptotic behavior, as tends to zero, of the transverse displacement of a Kirchhoff-Love plate composed by the union of two domains contained in the plane: and and depending on in the following way. The set is a union of fine teeth, having small cross section of size and constant height, periodically distributed on the upper side of a horizontal thin strip with vanishing height , as tends to zero. The structure is clamped on the top of the teeth, with a free boundary elsewhere, and subjected to a transverse load. As tends to zero, 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 ) strip. We show that the displacement in the strip is equal to the displacement on the basis of the teeth if . However, if the strip is thin enough (i.e., ), we show that microscopic oscillations of the displacement in the strip, between the basis of then 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