Doubly-Curved Kirigami

 Optimization and Analysis of Doubly-Curved
Kirigami Space Frames

Michael Ramirez
Submitted to the Department of Civil and Environmental Engineering in Partial Fulfillment of the Requirements for the degree of
MASTER OF ENGINEERING IN CIVIL AND ENVIRONMENTAL ENGINEERING
at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 2020

Inspired by the Japanese art of origami and kirigami, the concept of Spin-Valence is used to transform a two-dimensional sheet of metal into a three-dimensional spatial frame. Previous iterations of this design were developed by Emily Baker of the University of Arkansas, mainly by making scaled models.

Recently a frame assembly of Spin-Valence units was analyzed experimentally and computationally to characterize the structural behavior of the system. Transitioning from flat to curved systems and building a full-scale pavilion motivates this study.

This thesis by Michael Ramirez focuses on using optimization to computationally construct doubly-curved configurations of the Spin-Valence pattern logic from input surfaces. To accomplish this, optimization in Rhinoceros v6 and Python v3.7 is used to create a coherent primary and secondary surface.

The final structure is then subjected to finite element analysis using Abaqus 2017. Throughout history, spanning structures have evolved from linear elements such as beams to arches and finally to spatial systems.

Each iteration manipulates form to counterbalance internal element forces with better material efficiency and architectural flexibility. Doubly-curved Spin- Valence surfaces are developed to allow greater versatility of form and frame characteristics.

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