Hidden Symmetry of Global Solutions in Twisted Elastic Rings

Summary.

We investigate global equilibria of twisted, isotropic elastic rings. The high degree of symmetry in the problem leads to nonisolated solutions. We prove that all solutions are flip-symmetric, and from this we can globally isolate all solution branches. We derive possible other choices for boundary conditions systematically and show that other conditions necessarily lead to spurious solutions. We show global computations performed by the Parallel Simplex Algorithm.