Prestress Stability of Triangulated Convex Polytopes and Universal Second Order Rigidity

TL;DR

This paper establishes a connection between universal second-order rigidity and prestress stability, proving that certain triangulated convex polytopes in three-space are prestress stable, which advances understanding of their structural stability.

Contribution

It demonstrates that universal second-order rigidity implies prestress stability and proves the prestress stability of triangulated convex polytopes in three-space.

Findings

Universal second-order rigidity implies prestress stability.

Triangulated convex polytopes in three-space are prestress stable.

Holes in polytopes are positioned to ensure stability.

Abstract

We prove that universal second-order rigidity implies universal prestress stability and that triangulated convex polytopes in three-space (with holes appropriately positioned) are prestress stable.