Graph-Theoretical Description and Continuity Problems for Stress Propagation Through Complex Strut Lattices

TL;DR

This paper explores how graph theory can be used to predict stress distribution in complex strut lattices, emphasizing the importance of geometric features and boundary conditions for accurate modeling.

Contribution

It introduces modified centrality parameters that incorporate topology and geometry, improving stress prediction accuracy and computational efficiency in lattice structures.

Findings

Modified centrality parameters better predict local stress.

Inclusion of boundary conditions enhances model accuracy.

Validation through birefringence imaging and finite element analysis.

Abstract

Interconnected networks of rigid struts are critical for application in lightweight, load-bearing structures. However, accurately modeling stress distribution in these strut lattices poses significant computational challenges due to its strong dependence on organizational patterns, boundary conditions, and collective effects. Leveraging two-dimensional strut lattices that enable visualization of local elastic deformation, we investigate how graph theory (GT) provides a framework for stress prediction. We investigate how the geometric features often neglected by GT play a crucial role in the behavior of anisotropic networks. We also address the challenge of topological continuity that arises when applying discrete mathematics to physical structures. We show that modified centrality parameters combining lattice topology with geometry more accurately predict local stress, as validated through birefringence imaging and finite element modeling. Finally, we show how further improvements are made by incorporating strut lattice boundary conditions into the centrality definition, in a manner that simultaneously simplifies the computational cost.