Fig. 1 Two different four-fold unit fragments: ( a ) a trivial unit fragment (TUF) and ( b ) a non-trivial unit fragment (NUF). For each subfigure, the upper part depicts the 2D crease pattern whereas the lower part shows the origami structure with imposed nodal displacements. More

Fig. 2 ( a ) Equivalent planar pin-jointed structure with crossing virtual members for origami facet. ( b ) Flowchart of the form-finding algorithm for four-fold origami based on mountain-valley assignments. More

Fig. 3 Different structural representations of ( a ) TUF- and (b ) NUF-based origami tessellations (adapted from Refs. [ 24 , 50 ]). ( I ) Mountain-valley assignments of origami crease patterns. (II) Directions of imposed initial displacements. (III) Equivalent planar pin-jointed models. More

Fig. 4 ( a ) Defective models obtained from initial displacements based on equivalent planar pin-jointed structures for a ( a ,I) TUF and a ( a ,II) NUF. ( b ) Obtained configurations based on equivalent planar pin-jointed models for the ( b ,I) TUF- and ( b ,II) NUF-based origami tessellations. (... More

Fig. 5 ( a ,i) and ( b ,i) show crease patterns and predictions of initial nodal displacements for TUF and NUF, respectively. ( a ,ii) and ( b ,ii) depict equivalent spatial pin-jointed models with out-of-plane virtual nodes for TUF and NUF, respectively. More

Fig. 6 Top : nonlinear prediction–correction process of a given TUF: ( a ) first correction, ( b ) second correction, ( c ) third correction, ( d ) comparison between the fourth (final) correction and the initial configuration. Bottom : nonlinear prediction–correction process of a given NUF: ( e... More

Fig. 7 Top : crease patterns and imposed initial displacements for four-fold tessellations based on ( a ,I) TUF and ( b ,I) NUF. Bottom : equivalent spatial models with out-of-plane virtual nodes based on ( a ,II) TUF and ( b ,II) NUF. More

Fig. 8 Top : nonlinear prediction–correction process of a 4 × 4 TUF-based origami tessellation: ( a ) first correction, ( b ) second correction, ( c ) third correction, ( d ) comparison between the fourth (final) correction and the initial configuration. Bottom : nonlinear prediction–correction ... More

Fig. 9 Top : sparsity pattern of stiffness matrices for the TUF-based origami tessellation: ( a ) initial stiffness matrix, ( b ) corrected stiffness matrix. Bottom : comparison between initial planar configurations and corrected spatial configurations in terms of the minimum eigenvalue of stiff... More

Fig. 10 ( a ) Equivalent spatial models of TUF-based tessellations with out-of-plane virtual nodes: ( I ) a 6 × 6 module; (II) an 8 × 8 module. ( b ) Nonlinear prediction–correction process of a 6 × 6 TUF-based tessellation: ( I ) first correction; (II) second correction; (III) third correction; (... More