NEW MODEL FOR THIN PLATES WITH RAPIDLY VARYING THICKNESS. III: COMPARISON OF DIFFERENT SCALINGS.

This work continues a series of papers on the bending of thin, symmetric plates with rapidly varying thickness. Motivated by recent developments in structural optimization the authors have studied plates with thickness of order epsilon varying on a length scale of order epsilon **a. There are three different regimes, depending on whether a less than 1 (the case of relatively slow thickness variation), a equals 1 (when the variation is on the same scale as the mean thickness), or a greater than 1 (the case of relatively fast thickness variation). The question of which scaling produces the most rigid structure for a given thickness profile is asked.