Analysis of multiple bifurcation behaviour for periodic structures
Archives of Mechanics Volume 72 Issue 4
Page 283-306
published_at 2020-08-10
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| File | |
| Title ( eng ) |
Analysis of multiple bifurcation behaviour for periodic structures
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| Creator |
NAKAZAWA M.
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| Source Title |
Archives of Mechanics
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| Volume | 72 |
| Issue | 4 |
| Start Page | 283 |
| End Page | 306 |
| Abstract |
The classification of simple singularities in the post-buckling analysis of truss structures is well-known for elastic stability. To focus on multiple singularities including a hilltop bifurcation point (h-BP) and its bifurcation paths, we reviewed the multiple bifurcation analysis of multi-folding microstructure (MFM) models with periodic symmetry. Because the Jacobian at the h-BP of the MFM involves multiple 0-eigenvalues, it is challenging to analyse the bifurcation paths from the h-BP accurately. In this study, we investigated the multiple folding mechanism by analysing the neighbourhood of the h-BP and the symmetric subgroups of the geometric system in the two-dimensional plane and three-dimensional core of the MFM. We demonstrated that through the classification of multiple h-BP and bifurcation paths, it is possible to determine the unknown bifurcation equilibrium paths following h-BP, based on the Jacobian stability and the mechanism of symmetric subgroups in group theory containing the relationships between the primary path and the known bifurcation path(s) in the MFM system with periodic symmetry.
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| Keywords |
periodic symmetry
post-buckling analysis
multiple bifurcation
hill-top bifurcation
multi-folding microstructure
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| Descriptions |
This research is indirectly supported by the Grant-in-Aid for Challenging Exploratory Research of the Japan Society for the Promotion of Science; KAKENHI Grant Number JP18K18888.
A part of this manuscript was presented at the conference of CMM 2019. |
| Language |
eng
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| Resource Type | journal article |
| Publisher |
Institute of Fundamental Technological Research
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| Date of Issued | 2020-08-10 |
| Rights |
Copyright © 2020 by IPPT PAN, Warszawa
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| Publish Type | Version of Record |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0373-2029
[DOI] 10.24423/aom.3433
[DOI] https://doi.org/10.24423/aom.3433
[URI] https://am.ippt.pan.pl/am/index
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