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Control of connectivity and rigidity in prismatic assemblies.
Gary P T Choi1,2, Siheng Chen1, Lakshminarayanan Mahadevan1,3,4
1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
Proceedings. Mathematical, Physical, and Engineering Sciences
|January 7, 2021
Summary
This study presents deterministic and stochastic protocols to control the connectivity and rigidity of 3D prismatic assemblies. These methods offer scale-independent algorithms for manipulating topological structures.
Area of Science:
- Mechanical Engineering
- Materials Science
- Computational Geometry
Background:
- Understanding the topological connectivity of 3D assemblies is crucial for controlling their mechanical properties.
- Existing methods for manipulating rigidity and connectivity can be complex and scale-dependent.
Purpose of the Study:
- To develop deterministic and stochastic protocols for controlling topological connectivity in 3D prismatic assemblies.
- To investigate methods for managing internal degrees of freedom and connected components.
- To establish scale-independent algorithms for assembly manipulation.
Main Methods:
- Utilizing elementary number theory for a hierarchical deterministic protocol.
- Employing a stochastic protocol based on percolation transitions.
- Developing algorithms for cutting or gluing prismatic assemblies.
Main Results:
- A deterministic protocol successfully controls rigidity and connectivity.
- A stochastic protocol achieves similar control via percolation.
- Both approaches provide scale-independent manipulation capabilities.
Conclusions:
- Deterministic and stochastic methods offer effective control over the topological connectivity of 3D prismatic assemblies.
- These protocols enable precise manipulation of internal degrees of freedom and connected components.
- The developed algorithms are scale-independent, offering versatile applications in assembly design and modification.
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