The way from shell buckling to Miura-ori

The notorious problem of buckling of thin cylindrical shell was finally solved with the assumption of “in-extensional deformation”, proposed by Y. Yoshimura. The resulting polyhedral surface is now called Yoshimura-pattern. It is to be noted that the in-extensional deformation is certainly the basic property of origami that is our present subject.
Inspired with the Yoshimura pattern, I have challenged the problem of buckling of a thin infinite plate under external contraction. I imagined that, under less constraint boundary conditions, a pseudo problem of packaging a thin sheet of film into a point can be solved. Without doubt, the possible solution should have the property of in-extensional deformation. Or, it should be realized with origami models. Soon after the start of this study, I had arrived at a simple origami model that fulfils all of relevant conditions and is mathematically elegant. Then, I was confident of the result and started the verification phase of the study.
However, I faced to a tough barrier of bureaucracy instead of technical difficulty. In the 1970’s, using a super computer for studying origami was not easily justified even if at the prominent space institute, ISAS. Finally, with the elaborate effort of K. Tanizawa, we had completed the computational verification. Ironically, the first application of the concept was the 2-Dimensional Solar Array Experiment on the Japanese satellite by ISAS, 1995~6.

*To support this presentation, some old origami models used for this study will be shown.

About Koryo Miura

Koryo Miura is a Professor Emeritus at the University of Tokyo and Inst. Space & Astronautical Science. He was also a Resident Research Associate at NASA Langley Research Center (1966~67) and an honorary member of the International Association for Shell & Spatial Structures.

He is also the president of the upcoming 6th International Meeting of Origami in Science, Mathematics and Education to be held in Tokyo, August 10~13, 2014.