| Summary: | A special family of origami, rigid origami is when each paper facet surrounded with crease lines neither stretches nor bends during folding. In recent years, deployable structures and patterned sheets inspired by rigid origami have gained popularity among researchers in the fields of both mathematics and engineering. The focus of this thesis is on the kinematic modeling of the deployable structures, the mechanical behaviour and the mechanics of the Miura-ori patterned sheets.
The first part of this thesis is devoted to kinematic modeling of deployable surfaces. A kinematic model of mobile assemblies has been proposed based on the closed adjacent assembly of four spherical 4R linkages. To ensure the assemblies have a mobility of one, the kinematic compatibility conditions of the model have been obtained. The solutions to the compatibility conditions cover the existing one degree of freedom mobile assemblies, as well as twelve novel ones. In total, eighteen types of mobile assemblies have been devised. Based on the solutions, relationships between kinematic variables, hybrid assemblies, networks and rigid origami patterns for flat surfaces have been studied.
The second part of the thesis focuses on the kinematic modeling of the deployable prismatic structures. A kinematic model has been introduced based on closed opposite assembly of spherical 4R linkages. The kinematic compatibility conditions of these mobile assemblies have then been derived. Two groups of even-sided deployable prismatic structures have been obtained. For the 4-sided case, one structure incorporates a kite-shaped intersection, whereas the other incorporates a parallelogram. Unit variations have been discussed. Straight and curvy multi-layer prisms have been obtained by changing the dihedral angles between the intersecting planes. A general method to design even-sided multi-layer deployable prismatic structures has been proposed using the geometric conditions of the origami patterns. All the deployable structures constructed using this method can be deployed and folded along the central axis with a single degree of freedom; this makes them usable for a wide range of engineering applications.
An investigation of deformations in patterned sheets forms the final part of this thesis. A Miura-ori patterned sheet was made from copolymer Elvaloy by compression molding and its deformation behavior was investigated experimentally and using finite element analysis. Mechanical tests have been performed on the material and patterned sheet. FE simulations using ABAQUS/Explicit have been carried out to analyse deformations on the patterned sheet. Based on the simulation results, the deformation patterns on the patterned sheet under different loading conditions were examined, as well as their energy absorption capacities. Theoretical analyses based on the deformation patterns predicted the mechanical behaviour of the patterned sheet. Therefore, the geometry and material of the patterned sheet can be designed to meet the requirements of a certain application.
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