Generalized abeille tiles: Topologically interlocked space-filling shapes generated based on fabric symmetries

•We have introduced the concept of Generalized Abeille Tiles (GATs) that are generalizations of Abeille vaults, introduced by architect Joseph Abeille.•We have developed to develop a theoretical framework for GATs that leverages the theory of bi-axial 2-fold woven fabrics.•We provide algorithms for...

Full description

Saved in:
Bibliographic Details
Published in:Computers & graphics 2020-06, Vol.89, p.156-166
Main Authors: Akleman, Ergun, Krishnamurthy, Vinayak R., Fu, Chia-An, Subramanian, Sai Ganesh, Ebert, Matthew, Eng, Matthew, Starrett, Courtney, Panchal, Haard
Format: Article
Language:English
Subjects:
3D Tile design
Abeille vault
Assemblies
First principles
Space-Filling shapes
Stress concentration
Structural analysis
Tessellation of space
Tiles
Topologically interlocking shapes
Vaults
Woven fabrics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•We have introduced the concept of Generalized Abeille Tiles (GATs) that are generalizations of Abeille vaults, introduced by architect Joseph Abeille.•We have developed to develop a theoretical framework for GATs that leverages the theory of bi-axial 2-fold woven fabrics.•We provide algorithms for constructing GATs by using 2D and 3D Voronoi decomposition with higher dimensional Voronoi sites (curves and surfaces) based on bi-axial woven fabrics.•We present a comparative structural analysis of GATs as individual shapes as well as tiled assemblies for three different fabric patterns using plain and twill weave patterns. [Display omitted] In this paper, we present a simple and intuitive approach for designing a new class of space-filling shapes that we call Generalized Abeille Tiles (GATs). GATs are generalizations of Abeille vaults, introduced by the French engineer and architect Joseph Abeille in late 1600s. Our approach is based on two principles. The first principle is the correspondence between structures proposed by Abeille and the symmetries exhibited by woven fabrics. We leverage this correspondence to develop a theoretical framework for GATs beginning with the theory of bi-axial 2-fold woven fabrics. The second principle is the use of Voronoi decomposition with higher dimensional Voronoi sites (curves and surfaces). By configuring these new Voronoi sites based on weave symmetries, we provide a method for constructing GATs. Subsequently, we conduct a comparative structural analysis of GATs as individual shapes as well as tiled assemblies for three different fabric patterns using plain and twill weave patterns. Our analysis reveals interesting relationship between the choice of fabric symmetries and the corresponding distribution of stresses under loads normal to the tiled assemblies.
ISSN:0097-8493
1873-7684
DOI:10.1016/j.cag.2020.05.016