Shellular Funicular Structures

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Doctor of Philosophy (PhD)
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Civil and Environmental Engineering
Mechanical Engineering
Graphic Statics
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Akbari, Mostafa

Structures with the geometry of minimal surfaces consist of a continuous surface where the internal forces are distributed on a surface with consistent mean curvature rather than the cross-section of the members. Recent studies show that the high surface-to-volume ratio in minimal surface geometries enhances cell proliferation and cell-to-cell interactions, maximizing both the porosity and mechanical performance of the system. This research introduces a novel approach for designing a discrete approximation of these geometries and fabricating them in the context of graphic statics, named shellular (shell cellular) funicular structures. \ In the first thrust, the author provides a method to design and manipulate anticlastic polyhedral geometries using 3D graphic statics (3DGS) thanks to 3d graphs in form and force diagrams, named labyrinths. This is an intuitive method for designing shellular funicular structures as lightweight, efficient structures in the context of 3DGS. Furthermore, the method translates strut-based cellular funicular structures to shell-based (shellular) funicular structures (SFS). This technique reduces the edge lengths in the form diagram, distributing the internal forces in the structure. This will improve the mechanical performance of the structure as well as the fabrication process. Moreover, translating strut-based funicular structures to shellular funicular structures enables the structures to resist normal and shear forces in their planes, qualifying them for different loading scenarios. Although one can design these efficient structures using this technique, the fabrication process of these structures might be time-consuming and labor-intensive. In order to fabricate these structures out of a flat sheet of material and automate the fabrication process, in the next thrust, the research proposes a self-folding origami technique to fabricate shellular funicular structures out of a flat sheet of material. After designing the folding pattern of the geometry using a tuck-folding technique, the required forces for folding the pattern to the shellular structure are computed and the folding process is computationally simulated using a physically-based simulation technique. The method uses active materials to replicate the simulated behavior in the real world, saving material, cost, and reducing the need for labor. This research has impacts on different fields in different scales from micro-scale cellular materials and tissue engineering to design and fabrication of buildings’ components in macro-scales.

Akbarzadeh, Masoud
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