  Previous work introduced a lower-dimensional numerical model for the
geometric nonlinear simulation and optimization of compliant pressure actuated
cellular structures. This model takes into account hinge eccentricities as well
as rotational and axial cell side springs. The aim of this article is twofold.
First, previous work is extended by introducing an associated continuum model.
This model is an exact geometric representation of a cellular structure and the
basis for the spring stiffnesses and eccentricities of the numerical model.
Second, the state variables of the continuum and numerical model are linked via
discontinuous stress constraints on the one hand and spring stiffness, hinge
eccentricities on the other hand. An efficient optimization algorithm that
fully couples both sets of variables is presented. The performance of the
proposed approach is demonstrated with the help of an examples.
