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

Akleman, Ergün; Krishnamurthy, Vinayak R.; Fu, Chia-an; Subramanian, Sai Ganesh; Ebert, Matthew; Eng, Matthew R.; Starrett, Courtney; Panchal, Haard

doi:10.1016/j.cag.2020.05.016

Cited by 29 publications

(10 citation statements)

References 24 publications

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“…To overcome this issue, GATs have recently been developed. [ 6 ] The basic premise of GATs is the interpolation of multiple points to form trees. This flexibility allows one to proliferate a single polygon by generating a single polygon in one layer into multiple polygons in another layer, creating tree‐like structures that can interlock better.…”

Section: Prior Workmentioning

confidence: 99%

“…While several prior studies have demonstrated topologically interlocked assemblies using polyhedral blocks ( Figure ), we observe that recent works have introduced topological interlocking with space‐filling blocks. [ 5,6 ] The motivation for our work stems from the observation that these recent works either do not guarantee complete topological interlocking (i.e., only a subset of the shapes interlock in more than one direction/dimension) [ 5 ] or utilize special spatial symmetries (e.g., wallpaper [ 5 ] or weaves [ 6 ] ) to generate such blocks. In this article, the goal is to enable the generation of space‐filling shapes through methods that are 1) guaranteed to produce strong topological interlocking through corrugation and 2) leverage simple geometric principles that are not selective regarding the type of one or the other spatial symmetry ( Figure ).…”

Section: Introductionmentioning

confidence: 99%

“…While several prior studies have demonstrated topologically interlocked assemblies using polyhedral blocks (Figure 1), we observe that recent works have introduced topological interlocking with space-filling blocks. [5,6] The motivation for our work stems from the observation that these…”

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confidence: 99%

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VoroNoodles: Topological Interlocking with Helical Layered 2‐Honeycombs

Ebert,

Akleman,

Krishnamurthy

et al. 2023

Adv Eng Mater

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In this paper, we introduce an approach for modeling topologically interlocked building blocks that can be assembled in a water‐tight manner (space‐filling) to design a variety of spatial structures. Our approach takes inspiration from recent methods utilizing Voronoi tessellation of spatial domains using symmetrically arranged Voronoi sites. We specifically focus our attention on building blocks that result from helical stacking of planar 2‐honeycombs (i.e., tessellations of the plane with a single prototile) generated through a combination of wallpaper symmetries and Voronoi tessellation. This unique combination gives rise to structures that are both space‐filling (owing to Voronoi tessellation) and interlocking (owing to helical trajectories). We develop algorithms to generate two different varieties of helical building blocks, namely, corrugated and smooth. These varieties result naturally from the method of discretization and shape generation and lead to distinct interlocking behavior. In order to study these varieties, we conduct finite element analyses on different families of helical blocks parametrized by: (a) the polygonal unit cell as determined by the wallpaper symmetry and (b) the parameters of the helical line generating the Voronoi tessellation, i.e., the radius and pitch of the helix. Our analyses revealed that the new design of the geometry of the building blocks enables strong variation of the engagement force between the blocks.This article is protected by copyright. All rights reserved.

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Section: Prior Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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VoroNoodles: Topological Interlocking with Helical Layered 2‐Honeycombs

Ebert,

Akleman,

Krishnamurthy

et al. 2023

Adv Eng Mater

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“…Weizmann et al [WAG17] extended this approach and explored different 2D tessellations (regular, semi‐regular and non‐regular tessellations) to discover new TI blocks for building floors. Rather than relying on 2D tessellations, other researchers [KAS ∗ 21,AKF ∗ 20] made a connection between planar assemblies and bi‐axial weaving patterns. They generated tileable blocks (with curved faces) by Voronoi partitioning of space using curve segments whose arrangement follows the weaving patterns; see Figure 21(c).…”

Section: Building Assemblies With Tileable Blocksmentioning

confidence: 99%

State of the Art on Computational Design of Assemblies with Rigid Parts

Wang

Song

Pauly

2021

Computer Graphics Forum

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An assembly refers to a collection of parts joined together to achieve a specific form and/or functionality. Designing assemblies is a non-trivial task as a slight local modification on a part's geometry or its joining method could have a global impact on the structural and/or functional performance of the whole assembly. Assemblies can be classified as structures that transmit force to carry loads and mechanisms that transfer motion and force to perform mechanical work. In this state-of-the-art report, we focus on computational design of structures with rigid parts, which generally can be formulated as a geometric modeling and optimization problem. We broadly classify existing computational design approaches, mainly from the computer graphics community, according to high-level design objectives, including fabricability, structural stability, reconfigurability, and tileability. Computational analysis of various aspects of assemblies is an integral component in these design approaches. We review different classes of computational analysis and design methods, discuss their strengths and limitations, make connections among them, and propose possible directions for future research.

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“…Fabrication II Encoding and Topological Computation on Textile Structures , M. Bright et al [6] Interactive design of castable shapes using two-piece rigid molds, O. Stein et al [7] Generalized Abeille Tiles: Topologically Interlocked Space-Filling Shapes Generated Based on Fabric Symmetries E. Akleman et al [8] …”

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confidence: 99%