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.
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