Intrinsic non-flat-foldability of two-tile DDC surfaces composed of glide-reflected irregular quadrilaterals

Sareh, Pooya ORCID: 0000-0003-1836-2598 and Chen, Yao (2020) Intrinsic non-flat-foldability of two-tile DDC surfaces composed of glide-reflected irregular quadrilaterals. INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 185. p. 105881.

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Official URL: http://dx.doi.org/10.1016/j.ijmecsci.2020.105881

Abstract

Functional origami tessellations have certain geometric or physical properties - such as flat-foldability and rigid-foldability - which make them of particular interest for a broad range of applications in science, engineering, and architecture. While some simple variations of certain functional origami tessellations can be designed trivially, a systematic symmetry-reduction scheme is proved to be productive for the computational generation of more complex, non-trivial variations. Such a scheme has been previously applied to the developable double corrugation (DDC) surface, widely known as the Miura-ori, resulting in the development of novel crystalline derivatives, the symmetry groups of which are subgroups of the parent pattern. Computational algorithms can search for and find flat-foldable solutions for a large number of derivatives of the DDC surface, but fail to find solutions for all of them. In this paper, we exploit the symmetry reduction scheme along with classical plane geometry to analytically demonstrate why some crystallographic derivatives of this pattern do not exist. To this end, by applying the local flat-foldability condition at the vertices of different orbits associated with each tessellation, we show that such patterns are never flat-foldable, regardless of the geometric specifications of their constituting quadrilateral facets. In particular, we prove that two-tile DDC surfaces composed of glide-reflected irregular quadrilaterals are intrinsically non-flat-foldable, resulted from geometric incompatibilities between the properties of certain unit cells and the local flat-foldability condition.

Item Type:	Article
Depositing User:	Symplectic Admin
Date Deposited:	30 Jul 2020 15:44
Last Modified:	18 Jan 2023 23:48
DOI:	10.1016/j.ijmecsci.2020.105881
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3091277