  This paper investigates the optimal distribution of hard and soft material on
elastic plates. In the class of isometric deformations stationary points of a
Kirchhoff plate functional with incorporated material hardness function are
investigated and a compliance cost functional is taken into account. Under
symmetry assumptions on the material distribution and the load it is shown that
cylindrical solutions are stationary points. Furthermore, it is demonstrated
that the optimal design of cylindrically deforming, clamped rectangular plates
is non trivial, i.e. with a material distribution which is not just depending
on one axial direction on the plate. Analytical results are complemented with
numerical optimization results using a suitable finite element discretization
and a phase field description of the material phases. Finally, using numerical
methods an outlook on the optimal design of non isometrically deforming plates
and shells is given.
