Yoshimura buckling

In mechanical engineering, Yoshimura buckling is a triangular mesh buckling pattern found in thin-walled cylinders under compression along the axis of the cylinder,[1][2][3] producing a corrugated shape resembling the Schwarz lantern. The same pattern can be seen on the sleeves of Mona Lisa.[4]

The Schwarz lantern
The sleeves of Mona Lisa are wrinkled in the Yoshimura buckling pattern

This buckling pattern is named after Yoshimaru Yoshimura (吉村慶丸), the Japanese researcher who provided an explanation for its development in a paper first published in Japan in 1951,[5] and later republished in the United States in 1955.[6] Unknown to Yoshimura,[7] the same phenomenon had previously been studied by Theodore von Kármán and Qian Xuesen in 1941.[8]

The crease pattern for folding the Schwarz lantern from a flat piece of paper, a tessellation of the plane by isosceles triangles, has also been called the Yoshimura pattern based on the same work by Yoshimura.[4][9] The Yoshimura creasing pattern is related to both the Kresling and Hexagonal folds, and can be framed as a special case of the Miura fold.[10] Unlike the Miura fold which is rigidly deformable, both the Yoshimura and Kresling patterns require panel deformation to be folded to a compact state.[11]

References
  1. Foster, C. G. (June 1979). "Some observations on the Yoshimura buckle pattern for thin-walled cylinders". Journal of Applied Mechanics. 46 (2): 377–380. Bibcode:1979JAM....46..377F. doi:10.1115/1.3424558.
  2. de Vries, Jan (2005). "Research on the Yoshimura buckling pattern of small cylindrical thin walled shells". In Karen Fletcher (ed.). Proceedings of the European Conference on Spacecraft Structures, Materials and Mechanical Testing 2005 (ESA SP-581). 10-12 May 2005, Noordwijk, The Netherlands. Bibcode:2005ESASP.581E..21D. {{cite book}}: |journal= ignored (help)
  3. Singer, J.; Arbocz, J.; Weller, T. (2002). Buckling Experiments, Shells, Built-up Structures, Composites and Additional Topics. Vol. 2. John Wiley & Sons Ltd. p. 640. ISBN 9780471974505.
  4. Lang, Robert J. (2018). Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami. CRC Press. Figure 2.23. ISBN 9781482262414.
  5. Nicholas J. Hoff (February 1966). "The Perplexing Behavior of Thin Circular Cylindrical Shells in Axial Compression". Stanford University Department of Aeronautics and Astronautics. Archived from the original on March 4, 2016.
  6. Yoshimura, Yoshimaru (July 1955). On the mechanism of buckling of a circular cylindrical shell under axial compression. Technical Memorandum 1390. National Advisory Committee for Aeronautics.
  7. Dunne, Edward (July 18, 2021). "Yoshimura Crush Patterns". Beyond Reviews: Inside MathSciNet. American Mathematical Society.
  8. von Kármán, Theodore; Tsien, Hsue-Shen (1941). "The buckling of thin cylindrical shells under axial compression". Journal of the Aeronautical Sciences. 8 (8): 303–312. doi:10.2514/8.10722. MR 0006926.
  9. Miura, Koryo; Tachi, Tomohiro (2010). "Synthesis of rigid-foldable cylindrical polyhedra" (PDF). Symmetry: Art and Science, 8th Congress and Exhibition of ISIS. Gmünd.{{cite book}}: CS1 maint: location missing publisher (link)
  10. Reid, Austin (2017). "Geometry and design of origami bellows with tunable response". Physical Review E. 95 (1): 013002. arXiv:1609.01354. Bibcode:2017PhRvE..95a3002R. doi:10.1103/PhysRevE.95.013002. PMID 28208390. S2CID 20057718.
  11. Kidambi, Narayanan (2020). "Dynamics of Kresling Origami Deployment". Physical Review E. 101 (6): 063003. arXiv:2003.10411. Bibcode:2020PhRvE.101f3003K. doi:10.1103/PhysRevE.101.063003. PMID 32688523. S2CID 214611719.


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