  Thick origami structures are considered here as assemblies of polygonal
panels hinged to each other along their edges according to a corresponding
origami crease pattern. The determination of the internal actions caused by
external loads in such structures is not an easy task, owing to their high
degree of static indeterminacy, and the likelihood of unwanted self-balanced
internal actions induced by manufacturing imperfections. Here we present a
method for reducing the degree of static indeterminacy which can be applied to
several thick origami structures to make them isostatic. The method utilizes
sliding hinges, which permit also the relative translation along the hinge
axis, to replace conventional hinges. After giving the analytical description
of both types of hinges and describing a rigid folding simulation procedure
based on the integration of the exponential map, we present the static analysis
of a series of noteworthy examples based on the Miura-ori pattern, the
Yoshimura pattern, and the Kresling pattern. The method can be applied for the
design and realization of thick origami structures with adequate strength to
resist external actions.
