Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers

Aya Abe; Ichiro Hagiwara; Yang Yang; Chie Nara

doi:doi:10.11648/j.ijmea.20221006.13

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Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers

Aya Abe, Ichiro Hagiwara, Yang Yang, Chie Nara

Published in International Journal of Mechanical Engineering and Applications (Volume 10, Issue 6)

Received: 2 November 2022 Accepted: 21 November 2022 Published: 29 November 2022

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Abstract

Producing industrial goods with origami structure, such as cans or bottles which can be folded neatly after drinking up, is an idea anyone could easily think of. However, this idea has not been put in practical use yet. Recently, Tachi-Miura polyhedron (TMP) is gaining attention as a 3-dimensional version of Miura-Ori. Meanwhile, Nojima Polyhedron (NP) has been found to be similar as TMP and it is considered that both are able to be analyzed from the point of pairing origami structures proposed by Nojima. The pairing origami is generated by sticking the symmetry 2-dimensional parts to each other to create 3-dimensional shapes. In this study, NP and TMP are focused on and the possibility of the idea is examined. NP which is a mirror symmetry structure and TMP which is a glide symmetry structure, both can be folded not only in the axial but also in the radial direction, and so it would be convenient if they can be applied to beverage containers. In this study, whether both structures are rigid folding or not is investigated geometrically, and then how this gives influence on the energy absorbing characteristics is considered quantically. In the generation of the model, since NP is not rigid folding, a model with accurate coordinates cannot be established because deformation occurs on the surface at the folding stage, so the coordinates are determined by approximation. On the other hand, in the case of TMP, the coordinates of each point can be accurately indicated by parameters, so a model with accurate coordinates is established. Moreover, an engineering possibility to apply both structures in beverage containers is explored by studying their crushing characteristics on simulation. As a result, whether a rigid folding or not has some influence on its deformation mode, however it is shown that it has no influence on the purpose to investigate its possibility for industrialization. This is the first step to make sure the effective usages of the foldable pairing origami structure.

Published in	International Journal of Mechanical Engineering and Applications (Volume 10, Issue 6)
DOI	10.11648/j.ijmea.20221006.13
Page(s)	144-159
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Origami Engineering, Energy Absorption Property, Rigid Folding, 4 Folding Lines Type, 6 Folding Lines Type, Reversed Spiral Origami Structure, Nojima Polyhedron, Tachi-Miura Polyhedron

References

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APA Style

Aya Abe, Ichiro Hagiwara, Yang Yang, Chie Nara. (2022). Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers. International Journal of Mechanical Engineering and Applications, 10(6), 144-159. https://doi.org/10.11648/j.ijmea.20221006.13

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ACS Style

Aya Abe; Ichiro Hagiwara; Yang Yang; Chie Nara. Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers. Int. J. Mech. Eng. Appl. 2022, 10(6), 144-159. doi: 10.11648/j.ijmea.20221006.13

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AMA Style

Aya Abe, Ichiro Hagiwara, Yang Yang, Chie Nara. Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers. Int J Mech Eng Appl. 2022;10(6):144-159. doi: 10.11648/j.ijmea.20221006.13

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@article{10.11648/j.ijmea.20221006.13,
  author = {Aya Abe and Ichiro Hagiwara and Yang Yang and Chie Nara},
  title = {Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {10},
  number = {6},
  pages = {144-159},
  doi = {10.11648/j.ijmea.20221006.13},
  url = {https://doi.org/10.11648/j.ijmea.20221006.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20221006.13},
  abstract = {Producing industrial goods with origami structure, such as cans or bottles which can be folded neatly after drinking up, is an idea anyone could easily think of. However, this idea has not been put in practical use yet. Recently, Tachi-Miura polyhedron (TMP) is gaining attention as a 3-dimensional version of Miura-Ori. Meanwhile, Nojima Polyhedron (NP) has been found to be similar as TMP and it is considered that both are able to be analyzed from the point of pairing origami structures proposed by Nojima. The pairing origami is generated by sticking the symmetry 2-dimensional parts to each other to create 3-dimensional shapes. In this study, NP and TMP are focused on and the possibility of the idea is examined. NP which is a mirror symmetry structure and TMP which is a glide symmetry structure, both can be folded not only in the axial but also in the radial direction, and so it would be convenient if they can be applied to beverage containers. In this study, whether both structures are rigid folding or not is investigated geometrically, and then how this gives influence on the energy absorbing characteristics is considered quantically. In the generation of the model, since NP is not rigid folding, a model with accurate coordinates cannot be established because deformation occurs on the surface at the folding stage, so the coordinates are determined by approximation. On the other hand, in the case of TMP, the coordinates of each point can be accurately indicated by parameters, so a model with accurate coordinates is established. Moreover, an engineering possibility to apply both structures in beverage containers is explored by studying their crushing characteristics on simulation. As a result, whether a rigid folding or not has some influence on its deformation mode, however it is shown that it has no influence on the purpose to investigate its possibility for industrialization. This is the first step to make sure the effective usages of the foldable pairing origami structure.},
 year = {2022}
}

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TY  - JOUR
T1  - Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers
AU  - Aya Abe
AU  - Ichiro Hagiwara
AU  - Yang Yang
AU  - Chie Nara
Y1  - 2022/11/29
PY  - 2022
N1  - https://doi.org/10.11648/j.ijmea.20221006.13
DO  - 10.11648/j.ijmea.20221006.13
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 144
EP  - 159
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20221006.13
AB  - Producing industrial goods with origami structure, such as cans or bottles which can be folded neatly after drinking up, is an idea anyone could easily think of. However, this idea has not been put in practical use yet. Recently, Tachi-Miura polyhedron (TMP) is gaining attention as a 3-dimensional version of Miura-Ori. Meanwhile, Nojima Polyhedron (NP) has been found to be similar as TMP and it is considered that both are able to be analyzed from the point of pairing origami structures proposed by Nojima. The pairing origami is generated by sticking the symmetry 2-dimensional parts to each other to create 3-dimensional shapes. In this study, NP and TMP are focused on and the possibility of the idea is examined. NP which is a mirror symmetry structure and TMP which is a glide symmetry structure, both can be folded not only in the axial but also in the radial direction, and so it would be convenient if they can be applied to beverage containers. In this study, whether both structures are rigid folding or not is investigated geometrically, and then how this gives influence on the energy absorbing characteristics is considered quantically. In the generation of the model, since NP is not rigid folding, a model with accurate coordinates cannot be established because deformation occurs on the surface at the folding stage, so the coordinates are determined by approximation. On the other hand, in the case of TMP, the coordinates of each point can be accurately indicated by parameters, so a model with accurate coordinates is established. Moreover, an engineering possibility to apply both structures in beverage containers is explored by studying their crushing characteristics on simulation. As a result, whether a rigid folding or not has some influence on its deformation mode, however it is shown that it has no influence on the purpose to investigate its possibility for industrialization. This is the first step to make sure the effective usages of the foldable pairing origami structure.
VL  - 10
IS  - 6
ER  -

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Author Information

Aya Abe

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan
Ichiro Hagiwara

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan
Yang Yang

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan
Chie Nara

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan

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APA Style

Aya Abe, Ichiro Hagiwara, Yang Yang, Chie Nara. (2022). Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers. International Journal of Mechanical Engineering and Applications, 10(6), 144-159. https://doi.org/10.11648/j.ijmea.20221006.13

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ACS Style

Aya Abe; Ichiro Hagiwara; Yang Yang; Chie Nara. Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers. Int. J. Mech. Eng. Appl. 2022, 10(6), 144-159. doi: 10.11648/j.ijmea.20221006.13

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AMA Style

Aya Abe, Ichiro Hagiwara, Yang Yang, Chie Nara. Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers. Int J Mech Eng Appl. 2022;10(6):144-159. doi: 10.11648/j.ijmea.20221006.13

Copy | Download

@article{10.11648/j.ijmea.20221006.13,
  author = {Aya Abe and Ichiro Hagiwara and Yang Yang and Chie Nara},
  title = {Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {10},
  number = {6},
  pages = {144-159},
  doi = {10.11648/j.ijmea.20221006.13},
  url = {https://doi.org/10.11648/j.ijmea.20221006.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20221006.13},
  abstract = {Producing industrial goods with origami structure, such as cans or bottles which can be folded neatly after drinking up, is an idea anyone could easily think of. However, this idea has not been put in practical use yet. Recently, Tachi-Miura polyhedron (TMP) is gaining attention as a 3-dimensional version of Miura-Ori. Meanwhile, Nojima Polyhedron (NP) has been found to be similar as TMP and it is considered that both are able to be analyzed from the point of pairing origami structures proposed by Nojima. The pairing origami is generated by sticking the symmetry 2-dimensional parts to each other to create 3-dimensional shapes. In this study, NP and TMP are focused on and the possibility of the idea is examined. NP which is a mirror symmetry structure and TMP which is a glide symmetry structure, both can be folded not only in the axial but also in the radial direction, and so it would be convenient if they can be applied to beverage containers. In this study, whether both structures are rigid folding or not is investigated geometrically, and then how this gives influence on the energy absorbing characteristics is considered quantically. In the generation of the model, since NP is not rigid folding, a model with accurate coordinates cannot be established because deformation occurs on the surface at the folding stage, so the coordinates are determined by approximation. On the other hand, in the case of TMP, the coordinates of each point can be accurately indicated by parameters, so a model with accurate coordinates is established. Moreover, an engineering possibility to apply both structures in beverage containers is explored by studying their crushing characteristics on simulation. As a result, whether a rigid folding or not has some influence on its deformation mode, however it is shown that it has no influence on the purpose to investigate its possibility for industrialization. This is the first step to make sure the effective usages of the foldable pairing origami structure.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Characteristic Analysis of Two Pairing Origami Polyhedrons and Their Application to Beverage Containers
AU  - Aya Abe
AU  - Ichiro Hagiwara
AU  - Yang Yang
AU  - Chie Nara
Y1  - 2022/11/29
PY  - 2022
N1  - https://doi.org/10.11648/j.ijmea.20221006.13
DO  - 10.11648/j.ijmea.20221006.13
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 144
EP  - 159
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20221006.13
AB  - Producing industrial goods with origami structure, such as cans or bottles which can be folded neatly after drinking up, is an idea anyone could easily think of. However, this idea has not been put in practical use yet. Recently, Tachi-Miura polyhedron (TMP) is gaining attention as a 3-dimensional version of Miura-Ori. Meanwhile, Nojima Polyhedron (NP) has been found to be similar as TMP and it is considered that both are able to be analyzed from the point of pairing origami structures proposed by Nojima. The pairing origami is generated by sticking the symmetry 2-dimensional parts to each other to create 3-dimensional shapes. In this study, NP and TMP are focused on and the possibility of the idea is examined. NP which is a mirror symmetry structure and TMP which is a glide symmetry structure, both can be folded not only in the axial but also in the radial direction, and so it would be convenient if they can be applied to beverage containers. In this study, whether both structures are rigid folding or not is investigated geometrically, and then how this gives influence on the energy absorbing characteristics is considered quantically. In the generation of the model, since NP is not rigid folding, a model with accurate coordinates cannot be established because deformation occurs on the surface at the folding stage, so the coordinates are determined by approximation. On the other hand, in the case of TMP, the coordinates of each point can be accurately indicated by parameters, so a model with accurate coordinates is established. Moreover, an engineering possibility to apply both structures in beverage containers is explored by studying their crushing characteristics on simulation. As a result, whether a rigid folding or not has some influence on its deformation mode, however it is shown that it has no influence on the purpose to investigate its possibility for industrialization. This is the first step to make sure the effective usages of the foldable pairing origami structure.
VL  - 10
IS  - 6
ER  -

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